WorldWideScience

Sample records for linear least-squares regression

  1. BRGLM, Interactive Linear Regression Analysis by Least Square Fit

    International Nuclear Information System (INIS)

    Ringland, J.T.; Bohrer, R.E.; Sherman, M.E.

    1985-01-01

    1 - Description of program or function: BRGLM is an interactive program written to fit general linear regression models by least squares and to provide a variety of statistical diagnostic information about the fit. Stepwise and all-subsets regression can be carried out also. There are facilities for interactive data management (e.g. setting missing value flags, data transformations) and tools for constructing design matrices for the more commonly-used models such as factorials, cubic Splines, and auto-regressions. 2 - Method of solution: The least squares computations are based on the orthogonal (QR) decomposition of the design matrix obtained using the modified Gram-Schmidt algorithm. 3 - Restrictions on the complexity of the problem: The current release of BRGLM allows maxima of 1000 observations, 99 variables, and 3000 words of main memory workspace. For a problem with N observations and P variables, the number of words of main memory storage required is MAX(N*(P+6), N*P+P*P+3*N, and 3*P*P+6*N). Any linear model may be fit although the in-memory workspace will have to be increased for larger problems

  2. Least median of squares and iteratively re-weighted least squares as robust linear regression methods for fluorimetric determination of α-lipoic acid in capsules in ideal and non-ideal cases of linearity.

    Science.gov (United States)

    Korany, Mohamed A; Gazy, Azza A; Khamis, Essam F; Ragab, Marwa A A; Kamal, Miranda F

    2018-03-26

    This study outlines two robust regression approaches, namely least median of squares (LMS) and iteratively re-weighted least squares (IRLS) to investigate their application in instrument analysis of nutraceuticals (that is, fluorescence quenching of merbromin reagent upon lipoic acid addition). These robust regression methods were used to calculate calibration data from the fluorescence quenching reaction (∆F and F-ratio) under ideal or non-ideal linearity conditions. For each condition, data were treated using three regression fittings: Ordinary Least Squares (OLS), LMS and IRLS. Assessment of linearity, limits of detection (LOD) and quantitation (LOQ), accuracy and precision were carefully studied for each condition. LMS and IRLS regression line fittings showed significant improvement in correlation coefficients and all regression parameters for both methods and both conditions. In the ideal linearity condition, the intercept and slope changed insignificantly, but a dramatic change was observed for the non-ideal condition and linearity intercept. Under both linearity conditions, LOD and LOQ values after the robust regression line fitting of data were lower than those obtained before data treatment. The results obtained after statistical treatment indicated that the linearity ranges for drug determination could be expanded to lower limits of quantitation by enhancing the regression equation parameters after data treatment. Analysis results for lipoic acid in capsules, using both fluorimetric methods, treated by parametric OLS and after treatment by robust LMS and IRLS were compared for both linearity conditions. Copyright © 2018 John Wiley & Sons, Ltd.

  3. Simplified neural networks for solving linear least squares and total least squares problems in real time.

    Science.gov (United States)

    Cichocki, A; Unbehauen, R

    1994-01-01

    In this paper a new class of simplified low-cost analog artificial neural networks with on chip adaptive learning algorithms are proposed for solving linear systems of algebraic equations in real time. The proposed learning algorithms for linear least squares (LS), total least squares (TLS) and data least squares (DLS) problems can be considered as modifications and extensions of well known algorithms: the row-action projection-Kaczmarz algorithm and/or the LMS (Adaline) Widrow-Hoff algorithms. The algorithms can be applied to any problem which can be formulated as a linear regression problem. The correctness and high performance of the proposed neural networks are illustrated by extensive computer simulation results.

  4. Least Squares Adjustment: Linear and Nonlinear Weighted Regression Analysis

    DEFF Research Database (Denmark)

    Nielsen, Allan Aasbjerg

    2007-01-01

    This note primarily describes the mathematics of least squares regression analysis as it is often used in geodesy including land surveying and satellite positioning applications. In these fields regression is often termed adjustment. The note also contains a couple of typical land surveying...... and satellite positioning application examples. In these application areas we are typically interested in the parameters in the model typically 2- or 3-D positions and not in predictive modelling which is often the main concern in other regression analysis applications. Adjustment is often used to obtain...... the clock error) and to obtain estimates of the uncertainty with which the position is determined. Regression analysis is used in many other fields of application both in the natural, the technical and the social sciences. Examples may be curve fitting, calibration, establishing relationships between...

  5. Linear least squares compartmental-model-independent parameter identification in PET

    International Nuclear Information System (INIS)

    Thie, J.A.; Smith, G.T.; Hubner, K.F.

    1997-01-01

    A simplified approach involving linear-regression straight-line parameter fitting of dynamic scan data is developed for both specific and nonspecific models. Where compartmental-model topologies apply, the measured activity may be expressed in terms of: its integrals, plasma activity and plasma integrals -- all in a linear expression with macroparameters as coefficients. Multiple linear regression, as in spreadsheet software, determines parameters for best data fits. Positron emission tomography (PET)-acquired gray-matter images in a dynamic scan are analyzed: both by this method and by traditional iterative nonlinear least squares. Both patient and simulated data were used. Regression and traditional methods are in expected agreement. Monte-Carlo simulations evaluate parameter standard deviations, due to data noise, and much smaller noise-induced biases. Unique straight-line graphical displays permit visualizing data influences on various macroparameters as changes in slopes. Advantages of regression fitting are: simplicity, speed, ease of implementation in spreadsheet software, avoiding risks of convergence failures or false solutions in iterative least squares, and providing various visualizations of the uptake process by straight line graphical displays. Multiparameter model-independent analyses on lesser understood systems is also made possible

  6. Direct integral linear least square regression method for kinetic evaluation of hepatobiliary scintigraphy

    International Nuclear Information System (INIS)

    Shuke, Noriyuki

    1991-01-01

    In hepatobiliary scintigraphy, kinetic model analysis, which provides kinetic parameters like hepatic extraction or excretion rate, have been done for quantitative evaluation of liver function. In this analysis, unknown model parameters are usually determined using nonlinear least square regression method (NLS method) where iterative calculation and initial estimate for unknown parameters are required. As a simple alternative to NLS method, direct integral linear least square regression method (DILS method), which can determine model parameters by a simple calculation without initial estimate, is proposed, and tested the applicability to analysis of hepatobiliary scintigraphy. In order to see whether DILS method could determine model parameters as good as NLS method, or to determine appropriate weight for DILS method, simulated theoretical data based on prefixed parameters were fitted to 1 compartment model using both DILS method with various weightings and NLS method. The parameter values obtained were then compared with prefixed values which were used for data generation. The effect of various weights on the error of parameter estimate was examined, and inverse of time was found to be the best weight to make the error minimum. When using this weight, DILS method could give parameter values close to those obtained by NLS method and both parameter values were very close to prefixed values. With appropriate weighting, the DILS method could provide reliable parameter estimate which is relatively insensitive to the data noise. In conclusion, the DILS method could be used as a simple alternative to NLS method, providing reliable parameter estimate. (author)

  7. COMPARISON OF PARTIAL LEAST SQUARES REGRESSION METHOD ALGORITHMS: NIPALS AND PLS-KERNEL AND AN APPLICATION

    Directory of Open Access Journals (Sweden)

    ELİF BULUT

    2013-06-01

    Full Text Available Partial Least Squares Regression (PLSR is a multivariate statistical method that consists of partial least squares and multiple linear regression analysis. Explanatory variables, X, having multicollinearity are reduced to components which explain the great amount of covariance between explanatory and response variable. These components are few in number and they don’t have multicollinearity problem. Then multiple linear regression analysis is applied to those components to model the response variable Y. There are various PLSR algorithms. In this study NIPALS and PLS-Kernel algorithms will be studied and illustrated on a real data set.

  8. Group-wise partial least square regression

    NARCIS (Netherlands)

    Camacho, José; Saccenti, Edoardo

    2018-01-01

    This paper introduces the group-wise partial least squares (GPLS) regression. GPLS is a new sparse PLS technique where the sparsity structure is defined in terms of groups of correlated variables, similarly to what is done in the related group-wise principal component analysis. These groups are

  9. Penalized linear regression for discrete ill-posed problems: A hybrid least-squares and mean-squared error approach

    KAUST Repository

    Suliman, Mohamed Abdalla Elhag; Ballal, Tarig; Kammoun, Abla; Al-Naffouri, Tareq Y.

    2016-01-01

    This paper proposes a new approach to find the regularization parameter for linear least-squares discrete ill-posed problems. In the proposed approach, an artificial perturbation matrix with a bounded norm is forced into the discrete ill-posed model

  10. Comparison of multiple linear regression, partial least squares and artificial neural networks for prediction of gas chromatographic relative retention times of trimethylsilylated anabolic androgenic steroids.

    Science.gov (United States)

    Fragkaki, A G; Farmaki, E; Thomaidis, N; Tsantili-Kakoulidou, A; Angelis, Y S; Koupparis, M; Georgakopoulos, C

    2012-09-21

    The comparison among different modelling techniques, such as multiple linear regression, partial least squares and artificial neural networks, has been performed in order to construct and evaluate models for prediction of gas chromatographic relative retention times of trimethylsilylated anabolic androgenic steroids. The performance of the quantitative structure-retention relationship study, using the multiple linear regression and partial least squares techniques, has been previously conducted. In the present study, artificial neural networks models were constructed and used for the prediction of relative retention times of anabolic androgenic steroids, while their efficiency is compared with that of the models derived from the multiple linear regression and partial least squares techniques. For overall ranking of the models, a novel procedure [Trends Anal. Chem. 29 (2010) 101-109] based on sum of ranking differences was applied, which permits the best model to be selected. The suggested models are considered useful for the estimation of relative retention times of designer steroids for which no analytical data are available. Copyright © 2012 Elsevier B.V. All rights reserved.

  11. The consistency of ordinary least-squares and generalized least-squares polynomial regression on characterizing the mechanomyographic amplitude versus torque relationship

    International Nuclear Information System (INIS)

    Herda, Trent J; Ryan, Eric D; Costa, Pablo B; DeFreitas, Jason M; Walter, Ashley A; Stout, Jeffrey R; Beck, Travis W; Cramer, Joel T; Housh, Terry J; Weir, Joseph P

    2009-01-01

    The primary purpose of this study was to examine the consistency of ordinary least-squares (OLS) and generalized least-squares (GLS) polynomial regression analyses utilizing linear, quadratic and cubic models on either five or ten data points that characterize the mechanomyographic amplitude (MMG RMS ) versus isometric torque relationship. The secondary purpose was to examine the consistency of OLS and GLS polynomial regression utilizing only linear and quadratic models (excluding cubic responses) on either ten or five data points. Eighteen participants (mean ± SD age = 24 ± 4 yr) completed ten randomly ordered isometric step muscle actions from 5% to 95% of the maximal voluntary contraction (MVC) of the right leg extensors during three separate trials. MMG RMS was recorded from the vastus lateralis during the MVCs and each submaximal muscle action. MMG RMS versus torque relationships were analyzed on a subject-by-subject basis using OLS and GLS polynomial regression. When using ten data points, only 33% and 27% of the subjects were fitted with the same model (utilizing linear, quadratic and cubic models) across all three trials for OLS and GLS, respectively. After eliminating the cubic model, there was an increase to 55% of the subjects being fitted with the same model across all trials for both OLS and GLS regression. Using only five data points (instead of ten data points), 55% of the subjects were fitted with the same model across all trials for OLS and GLS regression. Overall, OLS and GLS polynomial regression models were only able to consistently describe the torque-related patterns of response for MMG RMS in 27–55% of the subjects across three trials. Future studies should examine alternative methods for improving the consistency and reliability of the patterns of response for the MMG RMS versus isometric torque relationship

  12. Boosted regression trees, multivariate adaptive regression splines and their two-step combinations with multiple linear regression or partial least squares to predict blood-brain barrier passage: a case study.

    Science.gov (United States)

    Deconinck, E; Zhang, M H; Petitet, F; Dubus, E; Ijjaali, I; Coomans, D; Vander Heyden, Y

    2008-02-18

    The use of some unconventional non-linear modeling techniques, i.e. classification and regression trees and multivariate adaptive regression splines-based methods, was explored to model the blood-brain barrier (BBB) passage of drugs and drug-like molecules. The data set contains BBB passage values for 299 structural and pharmacological diverse drugs, originating from a structured knowledge-based database. Models were built using boosted regression trees (BRT) and multivariate adaptive regression splines (MARS), as well as their respective combinations with stepwise multiple linear regression (MLR) and partial least squares (PLS) regression in two-step approaches. The best models were obtained using combinations of MARS with either stepwise MLR or PLS. It could be concluded that the use of combinations of a linear with a non-linear modeling technique results in some improved properties compared to the individual linear and non-linear models and that, when the use of such a combination is appropriate, combinations using MARS as non-linear technique should be preferred over those with BRT, due to some serious drawbacks of the BRT approaches.

  13. A Weighted Least Squares Approach To Robustify Least Squares Estimates.

    Science.gov (United States)

    Lin, Chowhong; Davenport, Ernest C., Jr.

    This study developed a robust linear regression technique based on the idea of weighted least squares. In this technique, a subsample of the full data of interest is drawn, based on a measure of distance, and an initial set of regression coefficients is calculated. The rest of the data points are then taken into the subsample, one after another,…

  14. Ordinary least square regression, orthogonal regression, geometric mean regression and their applications in aerosol science

    International Nuclear Information System (INIS)

    Leng Ling; Zhang Tianyi; Kleinman, Lawrence; Zhu Wei

    2007-01-01

    Regression analysis, especially the ordinary least squares method which assumes that errors are confined to the dependent variable, has seen a fair share of its applications in aerosol science. The ordinary least squares approach, however, could be problematic due to the fact that atmospheric data often does not lend itself to calling one variable independent and the other dependent. Errors often exist for both measurements. In this work, we examine two regression approaches available to accommodate this situation. They are orthogonal regression and geometric mean regression. Comparisons are made theoretically as well as numerically through an aerosol study examining whether the ratio of organic aerosol to CO would change with age

  15. Bivariate least squares linear regression: Towards a unified analytic formalism. I. Functional models

    Science.gov (United States)

    Caimmi, R.

    2011-08-01

    Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts ( York, 1966, 1969) is reviewed using a new formalism in terms of deviation (matrix) traces which, for unweighted data, reduce to usual quantities leaving aside an unessential (but dimensional) multiplicative factor. Within the framework of classical error models, the dependent variable relates to the independent variable according to the usual additive model. The classes of linear models considered are regression lines in the general case of correlated errors in X and in Y for weighted data, and in the opposite limiting situations of (i) uncorrelated errors in X and in Y, and (ii) completely correlated errors in X and in Y. The special case of (C) generalized orthogonal regression is considered in detail together with well known subcases, namely: (Y) errors in X negligible (ideally null) with respect to errors in Y; (X) errors in Y negligible (ideally null) with respect to errors in X; (O) genuine orthogonal regression; (R) reduced major-axis regression. In the limit of unweighted data, the results determined for functional models are compared with their counterparts related to extreme structural models i.e. the instrumental scatter is negligible (ideally null) with respect to the intrinsic scatter ( Isobe et al., 1990; Feigelson and Babu, 1992). While regression line slope and intercept estimators for functional and structural models necessarily coincide, the contrary holds for related variance estimators even if the residuals obey a Gaussian distribution, with the exception of Y models. An example of astronomical application is considered, concerning the [O/H]-[Fe/H] empirical relations deduced from five samples related to different stars and/or different methods of oxygen abundance determination. For selected samples and assigned methods, different regression models yield consistent results within the errors (∓ σ) for both

  16. Least square regularized regression in sum space.

    Science.gov (United States)

    Xu, Yong-Li; Chen, Di-Rong; Li, Han-Xiong; Liu, Lu

    2013-04-01

    This paper proposes a least square regularized regression algorithm in sum space of reproducing kernel Hilbert spaces (RKHSs) for nonflat function approximation, and obtains the solution of the algorithm by solving a system of linear equations. This algorithm can approximate the low- and high-frequency component of the target function with large and small scale kernels, respectively. The convergence and learning rate are analyzed. We measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic RKHSs. For sum space of RKHSs with Gaussian kernels, by choosing appropriate parameters, we tradeoff the sample error and regularization error, and obtain a polynomial learning rate, which is better than that in any single RKHS. The utility of this method is illustrated with two simulated data sets and five real-life databases.

  17. The crux of the method: assumptions in ordinary least squares and logistic regression.

    Science.gov (United States)

    Long, Rebecca G

    2008-10-01

    Logistic regression has increasingly become the tool of choice when analyzing data with a binary dependent variable. While resources relating to the technique are widely available, clear discussions of why logistic regression should be used in place of ordinary least squares regression are difficult to find. The current paper compares and contrasts the assumptions of ordinary least squares with those of logistic regression and explains why logistic regression's looser assumptions make it adept at handling violations of the more important assumptions in ordinary least squares.

  18. Power system state estimation using an iteratively reweighted least squares method for sequential L{sub 1}-regression

    Energy Technology Data Exchange (ETDEWEB)

    Jabr, R.A. [Electrical, Computer and Communication Engineering Department, Notre Dame University, P.O. Box 72, Zouk Mikhael, Zouk Mosbeh (Lebanon)

    2006-02-15

    This paper presents an implementation of the least absolute value (LAV) power system state estimator based on obtaining a sequence of solutions to the L{sub 1}-regression problem using an iteratively reweighted least squares (IRLS{sub L1}) method. The proposed implementation avoids reformulating the regression problem into standard linear programming (LP) form and consequently does not require the use of common methods of LP, such as those based on the simplex method or interior-point methods. It is shown that the IRLS{sub L1} method is equivalent to solving a sequence of linear weighted least squares (LS) problems. Thus, its implementation presents little additional effort since the sparse LS solver is common to existing LS state estimators. Studies on the termination criteria of the IRLS{sub L1} method have been carried out to determine a procedure for which the proposed estimator is more computationally efficient than a previously proposed non-linear iteratively reweighted least squares (IRLS) estimator. Indeed, it is revealed that the proposed method is a generalization of the previously reported IRLS estimator, but is based on more rigorous theory. (author)

  19. Solving linear inequalities in a least squares sense

    Energy Technology Data Exchange (ETDEWEB)

    Bramley, R.; Winnicka, B. [Indiana Univ., Bloomington, IN (United States)

    1994-12-31

    Let A {element_of} {Re}{sup mxn} be an arbitrary real matrix, and let b {element_of} {Re}{sup m} a given vector. A familiar problem in computational linear algebra is to solve the system Ax = b in a least squares sense; that is, to find an x* minimizing {parallel}Ax {minus} b{parallel}, where {parallel} {center_dot} {parallel} refers to the vector two-norm. Such an x* solves the normal equations A{sup T}(Ax {minus} b) = 0, and the optimal residual r* = b {minus} Ax* is unique (although x* need not be). The least squares problem is usually interpreted as corresponding to multiple observations, represented by the rows of A and b, on a vector of data x. The observations may be inconsistent, and in this case a solution is sought that minimizes the norm of the residuals. A less familiar problem to numerical linear algebraists is the solution of systems of linear inequalities Ax {le} b in a least squares sense, but the motivation is similar: if a set of observations places upper or lower bounds on linear combinations of variables, the authors want to find x* minimizing {parallel} (Ax {minus} b){sub +} {parallel}, where the i{sup th} component of the vector v{sub +} is the maximum of zero and the i{sup th} component of v.

  20. Penalized linear regression for discrete ill-posed problems: A hybrid least-squares and mean-squared error approach

    KAUST Repository

    Suliman, Mohamed Abdalla Elhag

    2016-12-19

    This paper proposes a new approach to find the regularization parameter for linear least-squares discrete ill-posed problems. In the proposed approach, an artificial perturbation matrix with a bounded norm is forced into the discrete ill-posed model matrix. This perturbation is introduced to enhance the singular-value (SV) structure of the matrix and hence to provide a better solution. The proposed approach is derived to select the regularization parameter in a way that minimizes the mean-squared error (MSE) of the estimator. Numerical results demonstrate that the proposed approach outperforms a set of benchmark methods in most cases when applied to different scenarios of discrete ill-posed problems. Jointly, the proposed approach enjoys the lowest run-time and offers the highest level of robustness amongst all the tested methods.

  1. Estimasi Model Seemingly Unrelated Regression (SUR dengan Metode Generalized Least Square (GLS

    Directory of Open Access Journals (Sweden)

    Ade Widyaningsih

    2015-04-01

    Full Text Available Regression analysis is a statistical tool that is used to determine the relationship between two or more quantitative variables so that one variable can be predicted from the other variables. A method that can used to obtain a good estimation in the regression analysis is ordinary least squares method. The least squares method is used to estimate the parameters of one or more regression but relationships among the errors in the response of other estimators are not allowed. One way to overcome this problem is Seemingly Unrelated Regression model (SUR in which parameters are estimated using Generalized Least Square (GLS. In this study, the author applies SUR model using GLS method on world gasoline demand data. The author obtains that SUR using GLS is better than OLS because SUR produce smaller errors than the OLS.

  2. Estimasi Model Seemingly Unrelated Regression (SUR dengan Metode Generalized Least Square (GLS

    Directory of Open Access Journals (Sweden)

    Ade Widyaningsih

    2014-06-01

    Full Text Available Regression analysis is a statistical tool that is used to determine the relationship between two or more quantitative variables so that one variable can be predicted from the other variables. A method that can used to obtain a good estimation in the regression analysis is ordinary least squares method. The least squares method is used to estimate the parameters of one or more regression but relationships among the errors in the response of other estimators are not allowed. One way to overcome this problem is Seemingly Unrelated Regression model (SUR in which parameters are estimated using Generalized Least Square (GLS. In this study, the author applies SUR model using GLS method on world gasoline demand data. The author obtains that SUR using GLS is better than OLS because SUR produce smaller errors than the OLS.

  3. Geodesic least squares regression for scaling studies in magnetic confinement fusion

    International Nuclear Information System (INIS)

    Verdoolaege, Geert

    2015-01-01

    In regression analyses for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to scaling laws. We here discuss a new regression method that is robust in the presence of significant uncertainty on both the data and the regression model. The method, which we call geodesic least squares regression (GLS), is based on minimization of the Rao geodesic distance on a probabilistic manifold. We demonstrate the superiority of the method using synthetic data and we present an application to the scaling law for the power threshold for the transition to the high confinement regime in magnetic confinement fusion devices

  4. Analysis of quantile regression as alternative to ordinary least squares

    OpenAIRE

    Ibrahim Abdullahi; Abubakar Yahaya

    2015-01-01

    In this article, an alternative to ordinary least squares (OLS) regression based on analytical solution in the Statgraphics software is considered, and this alternative is no other than quantile regression (QR) model. We also present goodness of fit statistic as well as approximate distributions of the associated test statistics for the parameters. Furthermore, we suggest a goodness of fit statistic called the least absolute deviation (LAD) coefficient of determination. The procedure is well ...

  5. Bounded Perturbation Regularization for Linear Least Squares Estimation

    KAUST Repository

    Ballal, Tarig; Suliman, Mohamed Abdalla Elhag; Al-Naffouri, Tareq Y.

    2017-01-01

    This paper addresses the problem of selecting the regularization parameter for linear least-squares estimation. We propose a new technique called bounded perturbation regularization (BPR). In the proposed BPR method, a perturbation with a bounded

  6. Regularization Techniques for Linear Least-Squares Problems

    KAUST Repository

    Suliman, Mohamed

    2016-04-01

    Linear estimation is a fundamental branch of signal processing that deals with estimating the values of parameters from a corrupted measured data. Throughout the years, several optimization criteria have been used to achieve this task. The most astonishing attempt among theses is the linear least-squares. Although this criterion enjoyed a wide popularity in many areas due to its attractive properties, it appeared to suffer from some shortcomings. Alternative optimization criteria, as a result, have been proposed. These new criteria allowed, in one way or another, the incorporation of further prior information to the desired problem. Among theses alternative criteria is the regularized least-squares (RLS). In this thesis, we propose two new algorithms to find the regularization parameter for linear least-squares problems. In the constrained perturbation regularization algorithm (COPRA) for random matrices and COPRA for linear discrete ill-posed problems, an artificial perturbation matrix with a bounded norm is forced into the model matrix. This perturbation is introduced to enhance the singular value structure of the matrix. As a result, the new modified model is expected to provide a better stabilize substantial solution when used to estimate the original signal through minimizing the worst-case residual error function. Unlike many other regularization algorithms that go in search of minimizing the estimated data error, the two new proposed algorithms are developed mainly to select the artifcial perturbation bound and the regularization parameter in a way that approximately minimizes the mean-squared error (MSE) between the original signal and its estimate under various conditions. The first proposed COPRA method is developed mainly to estimate the regularization parameter when the measurement matrix is complex Gaussian, with centered unit variance (standard), and independent and identically distributed (i.i.d.) entries. Furthermore, the second proposed COPRA

  7. Improved linear least squares estimation using bounded data uncertainty

    KAUST Repository

    Ballal, Tarig

    2015-04-01

    This paper addresses the problemof linear least squares (LS) estimation of a vector x from linearly related observations. In spite of being unbiased, the original LS estimator suffers from high mean squared error, especially at low signal-to-noise ratios. The mean squared error (MSE) of the LS estimator can be improved by introducing some form of regularization based on certain constraints. We propose an improved LS (ILS) estimator that approximately minimizes the MSE, without imposing any constraints. To achieve this, we allow for perturbation in the measurement matrix. Then we utilize a bounded data uncertainty (BDU) framework to derive a simple iterative procedure to estimate the regularization parameter. Numerical results demonstrate that the proposed BDU-ILS estimator is superior to the original LS estimator, and it converges to the best linear estimator, the linear-minimum-mean-squared error estimator (LMMSE), when the elements of x are statistically white.

  8. Improved linear least squares estimation using bounded data uncertainty

    KAUST Repository

    Ballal, Tarig; Al-Naffouri, Tareq Y.

    2015-01-01

    This paper addresses the problemof linear least squares (LS) estimation of a vector x from linearly related observations. In spite of being unbiased, the original LS estimator suffers from high mean squared error, especially at low signal-to-noise ratios. The mean squared error (MSE) of the LS estimator can be improved by introducing some form of regularization based on certain constraints. We propose an improved LS (ILS) estimator that approximately minimizes the MSE, without imposing any constraints. To achieve this, we allow for perturbation in the measurement matrix. Then we utilize a bounded data uncertainty (BDU) framework to derive a simple iterative procedure to estimate the regularization parameter. Numerical results demonstrate that the proposed BDU-ILS estimator is superior to the original LS estimator, and it converges to the best linear estimator, the linear-minimum-mean-squared error estimator (LMMSE), when the elements of x are statistically white.

  9. Least Squares Data Fitting with Applications

    DEFF Research Database (Denmark)

    Hansen, Per Christian; Pereyra, Víctor; Scherer, Godela

    As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data....... In a number of applications, the accuracy and efficiency of the least squares fit is central, and Per Christian Hansen, Víctor Pereyra, and Godela Scherer survey modern computational methods and illustrate them in fields ranging from engineering and environmental sciences to geophysics. Anyone working...... with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems. Included are • an overview of computational methods together with their properties and advantages • topics from statistical regression analysis...

  10. Bounded Perturbation Regularization for Linear Least Squares Estimation

    KAUST Repository

    Ballal, Tarig

    2017-10-18

    This paper addresses the problem of selecting the regularization parameter for linear least-squares estimation. We propose a new technique called bounded perturbation regularization (BPR). In the proposed BPR method, a perturbation with a bounded norm is allowed into the linear transformation matrix to improve the singular-value structure. Following this, the problem is formulated as a min-max optimization problem. Next, the min-max problem is converted to an equivalent minimization problem to estimate the unknown vector quantity. The solution of the minimization problem is shown to converge to that of the ℓ2 -regularized least squares problem, with the unknown regularizer related to the norm bound of the introduced perturbation through a nonlinear constraint. A procedure is proposed that combines the constraint equation with the mean squared error (MSE) criterion to develop an approximately optimal regularization parameter selection algorithm. Both direct and indirect applications of the proposed method are considered. Comparisons with different Tikhonov regularization parameter selection methods, as well as with other relevant methods, are carried out. Numerical results demonstrate that the proposed method provides significant improvement over state-of-the-art methods.

  11. Ordinary Least Squares and Quantile Regression: An Inquiry-Based Learning Approach to a Comparison of Regression Methods

    Science.gov (United States)

    Helmreich, James E.; Krog, K. Peter

    2018-01-01

    We present a short, inquiry-based learning course on concepts and methods underlying ordinary least squares (OLS), least absolute deviation (LAD), and quantile regression (QR). Students investigate squared, absolute, and weighted absolute distance functions (metrics) as location measures. Using differential calculus and properties of convex…

  12. Prediction of retention indices for frequently reported compounds of plant essential oils using multiple linear regression, partial least squares, and support vector machine.

    Science.gov (United States)

    Yan, Jun; Huang, Jian-Hua; He, Min; Lu, Hong-Bing; Yang, Rui; Kong, Bo; Xu, Qing-Song; Liang, Yi-Zeng

    2013-08-01

    Retention indices for frequently reported compounds of plant essential oils on three different stationary phases were investigated. Multivariate linear regression, partial least squares, and support vector machine combined with a new variable selection approach called random-frog recently proposed by our group, were employed to model quantitative structure-retention relationships. Internal and external validations were performed to ensure the stability and predictive ability. All the three methods could obtain an acceptable model, and the optimal results by support vector machine based on a small number of informative descriptors with the square of correlation coefficient for cross validation, values of 0.9726, 0.9759, and 0.9331 on the dimethylsilicone stationary phase, the dimethylsilicone phase with 5% phenyl groups, and the PEG stationary phase, respectively. The performances of two variable selection approaches, random-frog and genetic algorithm, are compared. The importance of the variables was found to be consistent when estimated from correlation coefficients in multivariate linear regression equations and selection probability in model spaces. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  13. Regression model of support vector machines for least squares prediction of crystallinity of cracking catalysts by infrared spectroscopy

    International Nuclear Information System (INIS)

    Comesanna Garcia, Yumirka; Dago Morales, Angel; Talavera Bustamante, Isneri

    2010-01-01

    The recently introduction of the least squares support vector machines method for regression purposes in the field of Chemometrics has provided several advantages to linear and nonlinear multivariate calibration methods. The objective of the paper was to propose the use of the least squares support vector machine as an alternative multivariate calibration method for the prediction of the percentage of crystallinity of fluidized catalytic cracking catalysts, by means of Fourier transform mid-infrared spectroscopy. A linear kernel was used in the calculations of the regression model. The optimization of its gamma parameter was carried out using the leave-one-out cross-validation procedure. The root mean square error of prediction was used to measure the performance of the model. The accuracy of the results obtained with the application of the method is in accordance with the uncertainty of the X-ray powder diffraction reference method. To compare the generalization capability of the developed method, a comparison study was carried out, taking into account the results achieved with the new model and those reached through the application of linear calibration methods. The developed method can be easily implemented in refinery laboratories

  14. Time Scale in Least Square Method

    Directory of Open Access Journals (Sweden)

    Özgür Yeniay

    2014-01-01

    Full Text Available Study of dynamic equations in time scale is a new area in mathematics. Time scale tries to build a bridge between real numbers and integers. Two derivatives in time scale have been introduced and called as delta and nabla derivative. Delta derivative concept is defined as forward direction, and nabla derivative concept is defined as backward direction. Within the scope of this study, we consider the method of obtaining parameters of regression equation of integer values through time scale. Therefore, we implemented least squares method according to derivative definition of time scale and obtained coefficients related to the model. Here, there exist two coefficients originating from forward and backward jump operators relevant to the same model, which are different from each other. Occurrence of such a situation is equal to total number of values of vertical deviation between regression equations and observation values of forward and backward jump operators divided by two. We also estimated coefficients for the model using ordinary least squares method. As a result, we made an introduction to least squares method on time scale. We think that time scale theory would be a new vision in least square especially when assumptions of linear regression are violated.

  15. Advanced statistics: linear regression, part I: simple linear regression.

    Science.gov (United States)

    Marill, Keith A

    2004-01-01

    Simple linear regression is a mathematical technique used to model the relationship between a single independent predictor variable and a single dependent outcome variable. In this, the first of a two-part series exploring concepts in linear regression analysis, the four fundamental assumptions and the mechanics of simple linear regression are reviewed. The most common technique used to derive the regression line, the method of least squares, is described. The reader will be acquainted with other important concepts in simple linear regression, including: variable transformations, dummy variables, relationship to inference testing, and leverage. Simplified clinical examples with small datasets and graphic models are used to illustrate the points. This will provide a foundation for the second article in this series: a discussion of multiple linear regression, in which there are multiple predictor variables.

  16. Normalization Ridge Regression in Practice I: Comparisons Between Ordinary Least Squares, Ridge Regression and Normalization Ridge Regression.

    Science.gov (United States)

    Bulcock, J. W.

    The problem of model estimation when the data are collinear was examined. Though the ridge regression (RR) outperforms ordinary least squares (OLS) regression in the presence of acute multicollinearity, it is not a problem free technique for reducing the variance of the estimates. It is a stochastic procedure when it should be nonstochastic and it…

  17. Robust analysis of trends in noisy tokamak confinement data using geodesic least squares regression

    Energy Technology Data Exchange (ETDEWEB)

    Verdoolaege, G., E-mail: geert.verdoolaege@ugent.be [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium); Laboratory for Plasma Physics, Royal Military Academy, B-1000 Brussels (Belgium); Shabbir, A. [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium); Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching (Germany); Hornung, G. [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium)

    2016-11-15

    Regression analysis is a very common activity in fusion science for unveiling trends and parametric dependencies, but it can be a difficult matter. We have recently developed the method of geodesic least squares (GLS) regression that is able to handle errors in all variables, is robust against data outliers and uncertainty in the regression model, and can be used with arbitrary distribution models and regression functions. We here report on first results of application of GLS to estimation of the multi-machine scaling law for the energy confinement time in tokamaks, demonstrating improved consistency of the GLS results compared to standard least squares.

  18. Parameter estimation of Monod model by the Least-Squares method for microalgae Botryococcus Braunii sp

    Science.gov (United States)

    See, J. J.; Jamaian, S. S.; Salleh, R. M.; Nor, M. E.; Aman, F.

    2018-04-01

    This research aims to estimate the parameters of Monod model of microalgae Botryococcus Braunii sp growth by the Least-Squares method. Monod equation is a non-linear equation which can be transformed into a linear equation form and it is solved by implementing the Least-Squares linear regression method. Meanwhile, Gauss-Newton method is an alternative method to solve the non-linear Least-Squares problem with the aim to obtain the parameters value of Monod model by minimizing the sum of square error ( SSE). As the result, the parameters of the Monod model for microalgae Botryococcus Braunii sp can be estimated by the Least-Squares method. However, the estimated parameters value obtained by the non-linear Least-Squares method are more accurate compared to the linear Least-Squares method since the SSE of the non-linear Least-Squares method is less than the linear Least-Squares method.

  19. Multisplitting for linear, least squares and nonlinear problems

    Energy Technology Data Exchange (ETDEWEB)

    Renaut, R.

    1996-12-31

    In earlier work, presented at the 1994 Iterative Methods meeting, a multisplitting (MS) method of block relaxation type was utilized for the solution of the least squares problem, and nonlinear unconstrained problems. This talk will focus on recent developments of the general approach and represents joint work both with Andreas Frommer, University of Wupertal for the linear problems and with Hans Mittelmann, Arizona State University for the nonlinear problems.

  20. Efectivity of Additive Spline for Partial Least Square Method in Regression Model Estimation

    Directory of Open Access Journals (Sweden)

    Ahmad Bilfarsah

    2005-04-01

    Full Text Available Additive Spline of Partial Least Square method (ASPL as one generalization of Partial Least Square (PLS method. ASPLS method can be acommodation to non linear and multicollinearity case of predictor variables. As a principle, The ASPLS method approach is cahracterized by two idea. The first is to used parametric transformations of predictors by spline function; the second is to make ASPLS components mutually uncorrelated, to preserve properties of the linear PLS components. The performance of ASPLS compared with other PLS method is illustrated with the fisher economic application especially the tuna fish production.

  1. Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

    Czech Academy of Sciences Publication Activity Database

    Bru, R.; Marín, J.; Mas, J.; Tůma, Miroslav

    2014-01-01

    Roč. 36, č. 4 (2014), A2002-A2022 ISSN 1064-8275 Institutional support: RVO:67985807 Keywords : preconditioned iterative methods * incomplete decompositions * approximate inverses * linear least squares Subject RIV: BA - General Mathematics Impact factor: 1.854, year: 2014

  2. Linearized least-square imaging of internally scattered data

    KAUST Repository

    Aldawood, Ali; Hoteit, Ibrahim; Turkiyyah, George M.; Zuberi, M. A H; Alkhalifah, Tariq Ali

    2014-01-01

    Internal multiples deteriorate the quality of the migrated image obtained conventionally by imaging single scattering energy. However, imaging internal multiples properly has the potential to enhance the migrated image because they illuminate zones in the subsurface that are poorly illuminated by single-scattering energy such as nearly vertical faults. Standard migration of these multiples provide subsurface reflectivity distributions with low spatial resolution and migration artifacts due to the limited recording aperture, coarse sources and receivers sampling, and the band-limited nature of the source wavelet. Hence, we apply a linearized least-square inversion scheme to mitigate the effect of the migration artifacts, enhance the spatial resolution, and provide more accurate amplitude information when imaging internal multiples. Application to synthetic data demonstrated the effectiveness of the proposed inversion in imaging a reflector that is poorly illuminated by single-scattering energy. The least-square inversion of doublescattered data helped delineate that reflector with minimal acquisition fingerprint.

  3. Positive solution of non-square fully Fuzzy linear system of equation in general form using least square method

    Directory of Open Access Journals (Sweden)

    Reza Ezzati

    2014-08-01

    Full Text Available In this paper, we propose the least square method for computing the positive solution of a non-square fully fuzzy linear system. To this end, we use Kaffman' arithmetic operations on fuzzy numbers \\cite{17}. Here, considered existence of exact solution using pseudoinverse, if they are not satisfy in positive solution condition, we will compute fuzzy vector core and then we will obtain right and left spreads of positive fuzzy vector by introducing constrained least squares problem. Using our proposed method, non-square fully fuzzy linear system of equations always has a solution. Finally, we illustrate the efficiency of proposed method by solving some numerical examples.

  4. Linear regression in astronomy. II

    Science.gov (United States)

    Feigelson, Eric D.; Babu, Gutti J.

    1992-01-01

    A wide variety of least-squares linear regression procedures used in observational astronomy, particularly investigations of the cosmic distance scale, are presented and discussed. The classes of linear models considered are (1) unweighted regression lines, with bootstrap and jackknife resampling; (2) regression solutions when measurement error, in one or both variables, dominates the scatter; (3) methods to apply a calibration line to new data; (4) truncated regression models, which apply to flux-limited data sets; and (5) censored regression models, which apply when nondetections are present. For the calibration problem we develop two new procedures: a formula for the intercept offset between two parallel data sets, which propagates slope errors from one regression to the other; and a generalization of the Working-Hotelling confidence bands to nonstandard least-squares lines. They can provide improved error analysis for Faber-Jackson, Tully-Fisher, and similar cosmic distance scale relations.

  5. ANYOLS, Least Square Fit by Stepwise Regression

    International Nuclear Information System (INIS)

    Atwoods, C.L.; Mathews, S.

    1986-01-01

    Description of program or function: ANYOLS is a stepwise program which fits data using ordinary or weighted least squares. Variables are selected for the model in a stepwise way based on a user- specified input criterion or a user-written subroutine. The order in which variables are entered can be influenced by user-defined forcing priorities. Instead of stepwise selection, ANYOLS can try all possible combinations of any desired subset of the variables. Automatic output for the final model in a stepwise search includes plots of the residuals, 'studentized' residuals, and leverages; if the model is not too large, the output also includes partial regression and partial leverage plots. A data set may be re-used so that several selection criteria can be tried. Flexibility is increased by allowing the substitution of user-written subroutines for several default subroutines

  6. An improved partial least-squares regression method for Raman spectroscopy

    Science.gov (United States)

    Momenpour Tehran Monfared, Ali; Anis, Hanan

    2017-10-01

    It is known that the performance of partial least-squares (PLS) regression analysis can be improved using the backward variable selection method (BVSPLS). In this paper, we further improve the BVSPLS based on a novel selection mechanism. The proposed method is based on sorting the weighted regression coefficients, and then the importance of each variable of the sorted list is evaluated using root mean square errors of prediction (RMSEP) criterion in each iteration step. Our Improved BVSPLS (IBVSPLS) method has been applied to leukemia and heparin data sets and led to an improvement in limit of detection of Raman biosensing ranged from 10% to 43% compared to PLS. Our IBVSPLS was also compared to the jack-knifing (simpler) and Genetic Algorithm (more complex) methods. Our method was consistently better than the jack-knifing method and showed either a similar or a better performance compared to the genetic algorithm.

  7. A comparison of least squares linear regression and measurement error modeling of warm/cold multipole correlation in SSC prototype dipole magnets

    International Nuclear Information System (INIS)

    Pollock, D.; Kim, K.; Gunst, R.; Schucany, W.

    1993-05-01

    Linear estimation of cold magnetic field quality based on warm multipole measurements is being considered as a quality control method for SSC production magnet acceptance. To investigate prediction uncertainties associated with such an approach, axial-scan (Z-scan) magnetic measurements from SSC Prototype Collider Dipole Magnets (CDM's) have been studied. This paper presents a preliminary evaluation of the explanatory ability of warm measurement multipole variation on the prediction of cold magnet multipoles. Two linear estimation methods are presented: least-squares regression, which uses the assumption of fixed independent variable (xi) observations, and the measurement error model, which includes measurement error in the xi's. The influence of warm multipole measurement errors on predicted cold magnet multipole averages is considered. MSD QA is studying warm/cold correlation to answer several magnet quality control questions. How well do warm measurements predict cold (2kA) multipoles? Does sampling error significantly influence estimates of the linear coefficients (slope, intercept and residual standard error)? Is estimation error for the predicted cold magnet average small compared to typical variation along the Z-Axis? What fraction of the multipole RMS tolerance is accounted for by individual magnet prediction uncertainty?

  8. Preprocessing in Matlab Inconsistent Linear System for a Meaningful Least Squares Solution

    Science.gov (United States)

    Sen, Symal K.; Shaykhian, Gholam Ali

    2011-01-01

    Mathematical models of many physical/statistical problems are systems of linear equations Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the . minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.

  9. New approach to breast cancer CAD using partial least squares and kernel-partial least squares

    Science.gov (United States)

    Land, Walker H., Jr.; Heine, John; Embrechts, Mark; Smith, Tom; Choma, Robert; Wong, Lut

    2005-04-01

    Breast cancer is second only to lung cancer as a tumor-related cause of death in women. Currently, the method of choice for the early detection of breast cancer is mammography. While sensitive to the detection of breast cancer, its positive predictive value (PPV) is low, resulting in biopsies that are only 15-34% likely to reveal malignancy. This paper explores the use of two novel approaches called Partial Least Squares (PLS) and Kernel-PLS (K-PLS) to the diagnosis of breast cancer. The approach is based on optimization for the partial least squares (PLS) algorithm for linear regression and the K-PLS algorithm for non-linear regression. Preliminary results show that both the PLS and K-PLS paradigms achieved comparable results with three separate support vector learning machines (SVLMs), where these SVLMs were known to have been trained to a global minimum. That is, the average performance of the three separate SVLMs were Az = 0.9167927, with an average partial Az (Az90) = 0.5684283. These results compare favorably with the K-PLS paradigm, which obtained an Az = 0.907 and partial Az = 0.6123. The PLS paradigm provided comparable results. Secondly, both the K-PLS and PLS paradigms out performed the ANN in that the Az index improved by about 14% (Az ~ 0.907 compared to the ANN Az of ~ 0.8). The "Press R squared" value for the PLS and K-PLS machine learning algorithms were 0.89 and 0.9, respectively, which is in good agreement with the other MOP values.

  10. Comparison of Classical Linear Regression and Orthogonal Regression According to the Sum of Squares Perpendicular Distances

    OpenAIRE

    KELEŞ, Taliha; ALTUN, Murat

    2016-01-01

    Regression analysis is a statistical technique for investigating and modeling the relationship between variables. The purpose of this study was the trivial presentation of the equation for orthogonal regression (OR) and the comparison of classical linear regression (CLR) and OR techniques with respect to the sum of squared perpendicular distances. For that purpose, the analyses were shown by an example. It was found that the sum of squared perpendicular distances of OR is smaller. Thus, it wa...

  11. Kinetic microplate bioassays for relative potency of antibiotics improved by partial Least Square (PLS) regression.

    Science.gov (United States)

    Francisco, Fabiane Lacerda; Saviano, Alessandro Morais; Almeida, Túlia de Souza Botelho; Lourenço, Felipe Rebello

    2016-05-01

    Microbiological assays are widely used to estimate the relative potencies of antibiotics in order to guarantee the efficacy, safety, and quality of drug products. Despite of the advantages of turbidimetric bioassays when compared to other methods, it has limitations concerning the linearity and range of the dose-response curve determination. Here, we proposed to use partial least squares (PLS) regression to solve these limitations and to improve the prediction of relative potencies of antibiotics. Kinetic-reading microplate turbidimetric bioassays for apramacyin and vancomycin were performed using Escherichia coli (ATCC 8739) and Bacillus subtilis (ATCC 6633), respectively. Microbial growths were measured as absorbance up to 180 and 300min for apramycin and vancomycin turbidimetric bioassays, respectively. Conventional dose-response curves (absorbances or area under the microbial growth curve vs. log of antibiotic concentration) showed significant regression, however there were significant deviation of linearity. Thus, they could not be used for relative potency estimations. PLS regression allowed us to construct a predictive model for estimating the relative potencies of apramycin and vancomycin without over-fitting and it improved the linear range of turbidimetric bioassay. In addition, PLS regression provided predictions of relative potencies equivalent to those obtained from agar diffusion official methods. Therefore, we conclude that PLS regression may be used to estimate the relative potencies of antibiotics with significant advantages when compared to conventional dose-response curve determination. Copyright © 2016 Elsevier B.V. All rights reserved.

  12. Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Kookjin [Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science; Carlberg, Kevin [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Elman, Howard C. [Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science and Inst. for Advanced Computer Studies

    2018-03-29

    Here, we consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions are approximated in a chosen finite-dimensional subspace. It has been shown that the stochastic Galerkin projection technique fails to minimize any measure of the solution error. As a remedy for this, we propose a novel stochatic least-squares Petrov--Galerkin (LSPG) method. The proposed method is optimal in the sense that it produces the solution that minimizes a weighted $\\ell^2$-norm of the residual over all solutions in a given finite-dimensional subspace. Moreover, the method can be adapted to minimize the solution error in different weighted $\\ell^2$-norms by simply applying a weighting function within the least-squares formulation. In addition, a goal-oriented seminorm induced by an output quantity of interest can be minimized by defining a weighting function as a linear functional of the solution. We establish optimality and error bounds for the proposed method, and extensive numerical experiments show that the weighted LSPG method outperforms other spectral methods in minimizing corresponding target weighted norms.

  13. Locally Linear Embedding of Local Orthogonal Least Squares Images for Face Recognition

    Science.gov (United States)

    Hafizhelmi Kamaru Zaman, Fadhlan

    2018-03-01

    Dimensionality reduction is very important in face recognition since it ensures that high-dimensionality data can be mapped to lower dimensional space without losing salient and integral facial information. Locally Linear Embedding (LLE) has been previously used to serve this purpose, however, the process of acquiring LLE features requires high computation and resources. To overcome this limitation, we propose a locally-applied Local Orthogonal Least Squares (LOLS) model can be used as initial feature extraction before the application of LLE. By construction of least squares regression under orthogonal constraints we can preserve more discriminant information in the local subspace of facial features while reducing the overall features into a more compact form that we called LOLS images. LLE can then be applied on the LOLS images to maps its representation into a global coordinate system of much lower dimensionality. Several experiments carried out using publicly available face datasets such as AR, ORL, YaleB, and FERET under Single Sample Per Person (SSPP) constraint demonstrates that our proposed method can reduce the time required to compute LLE features while delivering better accuracy when compared to when either LLE or OLS alone is used. Comparison against several other feature extraction methods and more recent feature-learning method such as state-of-the-art Convolutional Neural Networks (CNN) also reveal the superiority of the proposed method under SSPP constraint.

  14. Prediction of octanol-water partition coefficients of organic compounds by multiple linear regression, partial least squares, and artificial neural network.

    Science.gov (United States)

    Golmohammadi, Hassan

    2009-11-30

    A quantitative structure-property relationship (QSPR) study was performed to develop models those relate the structure of 141 organic compounds to their octanol-water partition coefficients (log P(o/w)). A genetic algorithm was applied as a variable selection tool. Modeling of log P(o/w) of these compounds as a function of theoretically derived descriptors was established by multiple linear regression (MLR), partial least squares (PLS), and artificial neural network (ANN). The best selected descriptors that appear in the models are: atomic charge weighted partial positively charged surface area (PPSA-3), fractional atomic charge weighted partial positive surface area (FPSA-3), minimum atomic partial charge (Qmin), molecular volume (MV), total dipole moment of molecule (mu), maximum antibonding contribution of a molecule orbital in the molecule (MAC), and maximum free valency of a C atom in the molecule (MFV). The result obtained showed the ability of developed artificial neural network to prediction of partition coefficients of organic compounds. Also, the results revealed the superiority of ANN over the MLR and PLS models. Copyright 2009 Wiley Periodicals, Inc.

  15. The least weighted squares I. The asymptotic linearity of normal equations

    Czech Academy of Sciences Publication Activity Database

    Víšek, Jan Ámos

    2002-01-01

    Roč. 9, č. 15 (2002), s. 31-58 ISSN 1212-074X R&D Projects: GA AV ČR KSK1019101 Grant - others:GA UK(CZ) 255/2002/A EK /FSV Institutional research plan: CEZ:AV0Z1075907 Keywords : the least weighted squares * robust regression * asymptotic normality and representation Subject RIV: BA - General Mathematics

  16. Weighted conditional least-squares estimation

    International Nuclear Information System (INIS)

    Booth, J.G.

    1987-01-01

    A two-stage estimation procedure is proposed that generalizes the concept of conditional least squares. The method is instead based upon the minimization of a weighted sum of squares, where the weights are inverses of estimated conditional variance terms. Some general conditions are given under which the estimators are consistent and jointly asymptotically normal. More specific details are given for ergodic Markov processes with stationary transition probabilities. A comparison is made with the ordinary conditional least-squares estimators for two simple branching processes with immigration. The relationship between weighted conditional least squares and other, more well-known, estimators is also investigated. In particular, it is shown that in many cases estimated generalized least-squares estimators can be obtained using the weighted conditional least-squares approach. Applications to stochastic compartmental models, and linear models with nested error structures are considered

  17. An iteratively reweighted least-squares approach to adaptive robust adjustment of parameters in linear regression models with autoregressive and t-distributed deviations

    Science.gov (United States)

    Kargoll, Boris; Omidalizarandi, Mohammad; Loth, Ina; Paffenholz, Jens-André; Alkhatib, Hamza

    2018-03-01

    In this paper, we investigate a linear regression time series model of possibly outlier-afflicted observations and autocorrelated random deviations. This colored noise is represented by a covariance-stationary autoregressive (AR) process, in which the independent error components follow a scaled (Student's) t-distribution. This error model allows for the stochastic modeling of multiple outliers and for an adaptive robust maximum likelihood (ML) estimation of the unknown regression and AR coefficients, the scale parameter, and the degree of freedom of the t-distribution. This approach is meant to be an extension of known estimators, which tend to focus only on the regression model, or on the AR error model, or on normally distributed errors. For the purpose of ML estimation, we derive an expectation conditional maximization either algorithm, which leads to an easy-to-implement version of iteratively reweighted least squares. The estimation performance of the algorithm is evaluated via Monte Carlo simulations for a Fourier as well as a spline model in connection with AR colored noise models of different orders and with three different sampling distributions generating the white noise components. We apply the algorithm to a vibration dataset recorded by a high-accuracy, single-axis accelerometer, focusing on the evaluation of the estimated AR colored noise model.

  18. Updating QR factorization procedure for solution of linear least squares problem with equality constraints.

    Science.gov (United States)

    Zeb, Salman; Yousaf, Muhammad

    2017-01-01

    In this article, we present a QR updating procedure as a solution approach for linear least squares problem with equality constraints. We reduce the constrained problem to unconstrained linear least squares and partition it into a small subproblem. The QR factorization of the subproblem is calculated and then we apply updating techniques to its upper triangular factor R to obtain its solution. We carry out the error analysis of the proposed algorithm to show that it is backward stable. We also illustrate the implementation and accuracy of the proposed algorithm by providing some numerical experiments with particular emphasis on dense problems.

  19. Modeling geochemical datasets for source apportionment: Comparison of least square regression and inversion approaches.

    Digital Repository Service at National Institute of Oceanography (India)

    Tripathy, G.R.; Das, Anirban.

    used methods, the Least Square Regression (LSR) and Inverse Modeling (IM), to determine the contributions of (i) solutes from different sources to global river water, and (ii) various rocks to a glacial till. The purpose of this exercise is to compare...

  20. Post-processing through linear regression

    Science.gov (United States)

    van Schaeybroeck, B.; Vannitsem, S.

    2011-03-01

    Various post-processing techniques are compared for both deterministic and ensemble forecasts, all based on linear regression between forecast data and observations. In order to evaluate the quality of the regression methods, three criteria are proposed, related to the effective correction of forecast error, the optimal variability of the corrected forecast and multicollinearity. The regression schemes under consideration include the ordinary least-square (OLS) method, a new time-dependent Tikhonov regularization (TDTR) method, the total least-square method, a new geometric-mean regression (GM), a recently introduced error-in-variables (EVMOS) method and, finally, a "best member" OLS method. The advantages and drawbacks of each method are clarified. These techniques are applied in the context of the 63 Lorenz system, whose model version is affected by both initial condition and model errors. For short forecast lead times, the number and choice of predictors plays an important role. Contrarily to the other techniques, GM degrades when the number of predictors increases. At intermediate lead times, linear regression is unable to provide corrections to the forecast and can sometimes degrade the performance (GM and the best member OLS with noise). At long lead times the regression schemes (EVMOS, TDTR) which yield the correct variability and the largest correlation between ensemble error and spread, should be preferred.

  1. Estimating Frequency by Interpolation Using Least Squares Support Vector Regression

    Directory of Open Access Journals (Sweden)

    Changwei Ma

    2015-01-01

    Full Text Available Discrete Fourier transform- (DFT- based maximum likelihood (ML algorithm is an important part of single sinusoid frequency estimation. As signal to noise ratio (SNR increases and is above the threshold value, it will lie very close to Cramer-Rao lower bound (CRLB, which is dependent on the number of DFT points. However, its mean square error (MSE performance is directly proportional to its calculation cost. As a modified version of support vector regression (SVR, least squares SVR (LS-SVR can not only still keep excellent capabilities for generalizing and fitting but also exhibit lower computational complexity. In this paper, therefore, LS-SVR is employed to interpolate on Fourier coefficients of received signals and attain high frequency estimation accuracy. Our results show that the proposed algorithm can make a good compromise between calculation cost and MSE performance under the assumption that the sample size, number of DFT points, and resampling points are already known.

  2. Hourly cooling load forecasting using time-indexed ARX models with two-stage weighted least squares regression

    International Nuclear Information System (INIS)

    Guo, Yin; Nazarian, Ehsan; Ko, Jeonghan; Rajurkar, Kamlakar

    2014-01-01

    Highlights: • Developed hourly-indexed ARX models for robust cooling-load forecasting. • Proposed a two-stage weighted least-squares regression approach. • Considered the effect of outliers as well as trend of cooling load and weather patterns. • Included higher order terms and day type patterns in the forecasting models. • Demonstrated better accuracy compared with some ARX and ANN models. - Abstract: This paper presents a robust hourly cooling-load forecasting method based on time-indexed autoregressive with exogenous inputs (ARX) models, in which the coefficients are estimated through a two-stage weighted least squares regression. The prediction method includes a combination of two separate time-indexed ARX models to improve prediction accuracy of the cooling load over different forecasting periods. The two-stage weighted least-squares regression approach in this study is robust to outliers and suitable for fast and adaptive coefficient estimation. The proposed method is tested on a large-scale central cooling system in an academic institution. The numerical case studies show the proposed prediction method performs better than some ANN and ARX forecasting models for the given test data set

  3. Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR is an efficient tool for metamodelling of nonlinear dynamic models

    Directory of Open Access Journals (Sweden)

    Omholt Stig W

    2011-06-01

    Full Text Available Abstract Background Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs to variation in features of the trajectories of the state variables (outputs throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR, where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR and ordinary least squares (OLS regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Results Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback

  4. Hierarchical cluster-based partial least squares regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models.

    Science.gov (United States)

    Tøndel, Kristin; Indahl, Ulf G; Gjuvsland, Arne B; Vik, Jon Olav; Hunter, Peter; Omholt, Stig W; Martens, Harald

    2011-06-01

    Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. HC-PLSR is a promising approach for

  5. Prediction of long-residue properties of potential blends from mathematically mixed infrared spectra of pure crude oils by partial least-squares regression models

    NARCIS (Netherlands)

    de Peinder, P.; Visser, T.; Petrauskas, D.D.; Salvatori, F.; Soulimani, F.; Weckhuysen, B.M.

    2009-01-01

    Research has been carried out to determine the feasibility of partial least-squares (PLS) regression models to predict the long-residue (LR) properties of potential blends from infrared (IR) spectra that have been created by linearly co-adding the IR spectra of crude oils. The study is the follow-up

  6. Total least squares for anomalous change detection

    Science.gov (United States)

    Theiler, James; Matsekh, Anna M.

    2010-04-01

    A family of subtraction-based anomalous change detection algorithms is derived from a total least squares (TLSQ) framework. This provides an alternative to the well-known chronochrome algorithm, which is derived from ordinary least squares. In both cases, the most anomalous changes are identified with the pixels that exhibit the largest residuals with respect to the regression of the two images against each other. The family of TLSQbased anomalous change detectors is shown to be equivalent to the subspace RX formulation for straight anomaly detection, but applied to the stacked space. However, this family is not invariant to linear coordinate transforms. On the other hand, whitened TLSQ is coordinate invariant, and special cases of it are equivalent to canonical correlation analysis and optimized covariance equalization. What whitened TLSQ offers is a generalization of these algorithms with the potential for better performance.

  7. Post-processing through linear regression

    Directory of Open Access Journals (Sweden)

    B. Van Schaeybroeck

    2011-03-01

    Full Text Available Various post-processing techniques are compared for both deterministic and ensemble forecasts, all based on linear regression between forecast data and observations. In order to evaluate the quality of the regression methods, three criteria are proposed, related to the effective correction of forecast error, the optimal variability of the corrected forecast and multicollinearity. The regression schemes under consideration include the ordinary least-square (OLS method, a new time-dependent Tikhonov regularization (TDTR method, the total least-square method, a new geometric-mean regression (GM, a recently introduced error-in-variables (EVMOS method and, finally, a "best member" OLS method. The advantages and drawbacks of each method are clarified.

    These techniques are applied in the context of the 63 Lorenz system, whose model version is affected by both initial condition and model errors. For short forecast lead times, the number and choice of predictors plays an important role. Contrarily to the other techniques, GM degrades when the number of predictors increases. At intermediate lead times, linear regression is unable to provide corrections to the forecast and can sometimes degrade the performance (GM and the best member OLS with noise. At long lead times the regression schemes (EVMOS, TDTR which yield the correct variability and the largest correlation between ensemble error and spread, should be preferred.

  8. Extreme Learning Machine and Moving Least Square Regression Based Solar Panel Vision Inspection

    Directory of Open Access Journals (Sweden)

    Heng Liu

    2017-01-01

    Full Text Available In recent years, learning based machine intelligence has aroused a lot of attention across science and engineering. Particularly in the field of automatic industry inspection, the machine learning based vision inspection plays a more and more important role in defect identification and feature extraction. Through learning from image samples, many features of industry objects, such as shapes, positions, and orientations angles, can be obtained and then can be well utilized to determine whether there is defect or not. However, the robustness and the quickness are not easily achieved in such inspection way. In this work, for solar panel vision inspection, we present an extreme learning machine (ELM and moving least square regression based approach to identify solder joint defect and detect the panel position. Firstly, histogram peaks distribution (HPD and fractional calculus are applied for image preprocessing. Then an ELM-based defective solder joints identification is discussed in detail. Finally, moving least square regression (MLSR algorithm is introduced for solar panel position determination. Experimental results and comparisons show that the proposed ELM and MLSR based inspection method is efficient not only in detection accuracy but also in processing speed.

  9. Parameter Estimation of Permanent Magnet Synchronous Motor Using Orthogonal Projection and Recursive Least Squares Combinatorial Algorithm

    Directory of Open Access Journals (Sweden)

    Iman Yousefi

    2015-01-01

    Full Text Available This paper presents parameter estimation of Permanent Magnet Synchronous Motor (PMSM using a combinatorial algorithm. Nonlinear fourth-order space state model of PMSM is selected. This model is rewritten to the linear regression form without linearization. Noise is imposed to the system in order to provide a real condition, and then combinatorial Orthogonal Projection Algorithm and Recursive Least Squares (OPA&RLS method is applied in the linear regression form to the system. Results of this method are compared to the Orthogonal Projection Algorithm (OPA and Recursive Least Squares (RLS methods to validate the feasibility of the proposed method. Simulation results validate the efficacy of the proposed algorithm.

  10. Linear regression methods a ccording to objective functions

    OpenAIRE

    Yasemin Sisman; Sebahattin Bektas

    2012-01-01

    The aim of the study is to explain the parameter estimation methods and the regression analysis. The simple linear regressionmethods grouped according to the objective function are introduced. The numerical solution is achieved for the simple linear regressionmethods according to objective function of Least Squares and theLeast Absolute Value adjustment methods. The success of the appliedmethods is analyzed using their objective function values.

  11. Who Will Win?: Predicting the Presidential Election Using Linear Regression

    Science.gov (United States)

    Lamb, John H.

    2007-01-01

    This article outlines a linear regression activity that engages learners, uses technology, and fosters cooperation. Students generated least-squares linear regression equations using TI-83 Plus[TM] graphing calculators, Microsoft[C] Excel, and paper-and-pencil calculations using derived normal equations to predict the 2004 presidential election.…

  12. Sulfur Speciation of Crude Oils by Partial Least Squares Regression Modeling of Their Infrared Spectra

    NARCIS (Netherlands)

    de Peinder, P.; Visser, T.; Wagemans, R.W.P.; Blomberg, J.; Chaabani, H.; Soulimani, F.; Weckhuysen, B.M.

    2013-01-01

    Research has been carried out to determine the feasibility of partial least-squares regression (PLS) modeling of infrared (IR) spectra of crude oils as a tool for fast sulfur speciation. The study is a continuation of a previously developed method to predict long and short residue properties of

  13. Brightness-normalized Partial Least Squares Regression for hyperspectral data

    International Nuclear Information System (INIS)

    Feilhauer, Hannes; Asner, Gregory P.; Martin, Roberta E.; Schmidtlein, Sebastian

    2010-01-01

    Developed in the field of chemometrics, Partial Least Squares Regression (PLSR) has become an established technique in vegetation remote sensing. PLSR was primarily designed for laboratory analysis of prepared material samples. Under field conditions in vegetation remote sensing, the performance of the technique may be negatively affected by differences in brightness due to amount and orientation of plant tissues in canopies or the observing conditions. To minimize these effects, we introduced brightness normalization to the PLSR approach and tested whether this modification improves the performance under changing canopy and observing conditions. This test was carried out using high-fidelity spectral data (400-2510 nm) to model observed leaf chemistry. The spectral data was combined with a canopy radiative transfer model to simulate effects of varying canopy structure and viewing geometry. Brightness normalization enhanced the performance of PLSR by dampening the effects of canopy shade, thus providing a significant improvement in predictions of leaf chemistry (up to 3.6% additional explained variance in validation) compared to conventional PLSR. Little improvement was made on effects due to variable leaf area index, while minor improvement (mostly not significant) was observed for effects of variable viewing geometry. In general, brightness normalization increased the stability of model fits and regression coefficients for all canopy scenarios. Brightness-normalized PLSR is thus a promising approach for application on airborne and space-based imaging spectrometer data.

  14. Intelligent Quality Prediction Using Weighted Least Square Support Vector Regression

    Science.gov (United States)

    Yu, Yaojun

    A novel quality prediction method with mobile time window is proposed for small-batch producing process based on weighted least squares support vector regression (LS-SVR). The design steps and learning algorithm are also addressed. In the method, weighted LS-SVR is taken as the intelligent kernel, with which the small-batch learning is solved well and the nearer sample is set a larger weight, while the farther is set the smaller weight in the history data. A typical machining process of cutting bearing outer race is carried out and the real measured data are used to contrast experiment. The experimental results demonstrate that the prediction accuracy of the weighted LS-SVR based model is only 20%-30% that of the standard LS-SVR based one in the same condition. It provides a better candidate for quality prediction of small-batch producing process.

  15. Application of principal component regression and partial least squares regression in ultraviolet spectrum water quality detection

    Science.gov (United States)

    Li, Jiangtong; Luo, Yongdao; Dai, Honglin

    2018-01-01

    Water is the source of life and the essential foundation of all life. With the development of industrialization, the phenomenon of water pollution is becoming more and more frequent, which directly affects the survival and development of human. Water quality detection is one of the necessary measures to protect water resources. Ultraviolet (UV) spectral analysis is an important research method in the field of water quality detection, which partial least squares regression (PLSR) analysis method is becoming predominant technology, however, in some special cases, PLSR's analysis produce considerable errors. In order to solve this problem, the traditional principal component regression (PCR) analysis method was improved by using the principle of PLSR in this paper. The experimental results show that for some special experimental data set, improved PCR analysis method performance is better than PLSR. The PCR and PLSR is the focus of this paper. Firstly, the principal component analysis (PCA) is performed by MATLAB to reduce the dimensionality of the spectral data; on the basis of a large number of experiments, the optimized principal component is extracted by using the principle of PLSR, which carries most of the original data information. Secondly, the linear regression analysis of the principal component is carried out with statistic package for social science (SPSS), which the coefficients and relations of principal components can be obtained. Finally, calculating a same water spectral data set by PLSR and improved PCR, analyzing and comparing two results, improved PCR and PLSR is similar for most data, but improved PCR is better than PLSR for data near the detection limit. Both PLSR and improved PCR can be used in Ultraviolet spectral analysis of water, but for data near the detection limit, improved PCR's result better than PLSR.

  16. A method for the selection of a functional form for a thermodynamic equation of state using weighted linear least squares stepwise regression

    Science.gov (United States)

    Jacobsen, R. T.; Stewart, R. B.; Crain, R. W., Jr.; Rose, G. L.; Myers, A. F.

    1976-01-01

    A method was developed for establishing a rational choice of the terms to be included in an equation of state with a large number of adjustable coefficients. The methods presented were developed for use in the determination of an equation of state for oxygen and nitrogen. However, a general application of the methods is possible in studies involving the determination of an optimum polynomial equation for fitting a large number of data points. The data considered in the least squares problem are experimental thermodynamic pressure-density-temperature data. Attention is given to a description of stepwise multiple regression and the use of stepwise regression in the determination of an equation of state for oxygen and nitrogen.

  17. A least-squares computational ''tool kit''

    International Nuclear Information System (INIS)

    Smith, D.L.

    1993-04-01

    The information assembled in this report is intended to offer a useful computational ''tool kit'' to individuals who are interested in a variety of practical applications for the least-squares method of parameter estimation. The fundamental principles of Bayesian analysis are outlined first and these are applied to development of both the simple and the generalized least-squares conditions. Formal solutions that satisfy these conditions are given subsequently. Their application to both linear and non-linear problems is described in detail. Numerical procedures required to implement these formal solutions are discussed and two utility computer algorithms are offered for this purpose (codes LSIOD and GLSIOD written in FORTRAN). Some simple, easily understood examples are included to illustrate the use of these algorithms. Several related topics are then addressed, including the generation of covariance matrices, the role of iteration in applications of least-squares procedures, the effects of numerical precision and an approach that can be pursued in developing data analysis packages that are directed toward special applications

  18. Support-Vector-based Least Squares for learning non-linear dynamics

    NARCIS (Netherlands)

    de Kruif, B.J.; de Vries, Theodorus J.A.

    2002-01-01

    A function approximator is introduced that is based on least squares support vector machines (LSSVM) and on least squares (LS). The potential indicators for the LS method are chosen as the kernel functions of all the training samples similar to LSSVM. By selecting these as indicator functions the

  19. Bayesian model averaging and weighted average least squares : Equivariance, stability, and numerical issues

    NARCIS (Netherlands)

    De Luca, G.; Magnus, J.R.

    2011-01-01

    In this article, we describe the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals, which implement, respectively, the exact Bayesian model-averaging estimator and the weighted-average least-squares

  20. Use of correspondence analysis partial least squares on linear and unimodal data

    DEFF Research Database (Denmark)

    Frisvad, Jens Christian; Norsker, Merete

    1996-01-01

    Correspondence analysis partial least squares (CA-PLS) has been compared with PLS conceming classification and prediction of unimodal growth temperature data and an example using infrared (IR) spectroscopy for predicting amounts of chemicals in mixtures. CA-PLS was very effective for ordinating...... that could only be seen in two-dimensional plots, and also less effective predictions. PLS was the best method in the linear case treated, with fewer components and a better prediction than CA-PLS....

  1. Quantum algorithm for linear regression

    Science.gov (United States)

    Wang, Guoming

    2017-07-01

    We present a quantum algorithm for fitting a linear regression model to a given data set using the least-squares approach. Differently from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs these numbers in the classical form. So by running it once, one completely determines the fitted model and then can use it to make predictions on new data at little cost. Moreover, our algorithm works in the standard oracle model, and can handle data sets with nonsparse design matrices. It runs in time poly( log2(N ) ,d ,κ ,1 /ɛ ) , where N is the size of the data set, d is the number of adjustable parameters, κ is the condition number of the design matrix, and ɛ is the desired precision in the output. We also show that the polynomial dependence on d and κ is necessary. Thus, our algorithm cannot be significantly improved. Furthermore, we also give a quantum algorithm that estimates the quality of the least-squares fit (without computing its parameters explicitly). This algorithm runs faster than the one for finding this fit, and can be used to check whether the given data set qualifies for linear regression in the first place.

  2. Hyperspectral analysis of soil organic matter in coal mining regions using wavelets, correlations, and partial least squares regression.

    Science.gov (United States)

    Lin, Lixin; Wang, Yunjia; Teng, Jiyao; Wang, Xuchen

    2016-02-01

    Hyperspectral estimation of soil organic matter (SOM) in coal mining regions is an important tool for enhancing fertilization in soil restoration programs. The correlation--partial least squares regression (PLSR) method effectively solves the information loss problem of correlation--multiple linear stepwise regression, but results of the correlation analysis must be optimized to improve precision. This study considers the relationship between spectral reflectance and SOM based on spectral reflectance curves of soil samples collected from coal mining regions. Based on the major absorption troughs in the 400-1006 nm spectral range, PLSR analysis was performed using 289 independent bands of the second derivative (SDR) with three levels and measured SOM values. A wavelet-correlation-PLSR (W-C-PLSR) model was then constructed. By amplifying useful information that was previously obscured by noise, the W-C-PLSR model was optimal for estimating SOM content, with smaller prediction errors in both calibration (R(2) = 0.970, root mean square error (RMSEC) = 3.10, and mean relative error (MREC) = 8.75) and validation (RMSEV = 5.85 and MREV = 14.32) analyses, as compared with other models. Results indicate that W-C-PLSR has great potential to estimate SOM in coal mining regions.

  3. FC LSEI WNNLS, Least-Square Fitting Algorithms Using B Splines

    International Nuclear Information System (INIS)

    Hanson, R.J.; Haskell, K.H.

    1989-01-01

    1 - Description of problem or function: FC allows a user to fit dis- crete data, in a weighted least-squares sense, using piece-wise polynomial functions represented by B-Splines on a given set of knots. In addition to the least-squares fitting of the data, equality, inequality, and periodic constraints at a discrete, user-specified set of points can be imposed on the fitted curve or its derivatives. The subprograms LSEI and WNNLS solve the linearly-constrained least-squares problem. LSEI solves the class of problem with general inequality constraints, and, if requested, obtains a covariance matrix of the solution parameters. WNNLS solves the class of problem with non-negativity constraints. It is anticipated that most users will find LSEI suitable for their needs; however, users with inequalities that are single bounds on variables may wish to use WNNLS. 2 - Method of solution: The discrete data are fit by a linear combination of piece-wise polynomial curves which leads to a linear least-squares system of algebraic equations. Additional information is expressed as a discrete set of linear inequality and equality constraints on the fitted curve which leads to a linearly-constrained least-squares system of algebraic equations. The solution of this system is the main computational problem solved

  4. A Generalized Least Squares Regression Approach for Computing Effect Sizes in Single-Case Research: Application Examples

    Science.gov (United States)

    Maggin, Daniel M.; Swaminathan, Hariharan; Rogers, Helen J.; O'Keeffe, Breda V.; Sugai, George; Horner, Robert H.

    2011-01-01

    A new method for deriving effect sizes from single-case designs is proposed. The strategy is applicable to small-sample time-series data with autoregressive errors. The method uses Generalized Least Squares (GLS) to model the autocorrelation of the data and estimate regression parameters to produce an effect size that represents the magnitude of…

  5. Least-squares fit of a linear combination of functions

    Directory of Open Access Journals (Sweden)

    Niraj Upadhyay

    2013-12-01

    Full Text Available We propose that given a data-set $S=\\{(x_i,y_i/i=1,2,{\\dots}n\\}$ and real-valued functions $\\{f_\\alpha(x/\\alpha=1,2,{\\dots}m\\},$ the least-squares fit vector $A=\\{a_\\alpha\\}$ for $y=\\sum_\\alpha a_{\\alpha}f_\\alpha(x$ is $A = (F^TF^{-1}F^TY$ where $[F_{i\\alpha}]=[f_\\alpha(x_i].$ We test this formalism by deriving the algebraic expressions of the regression coefficients in $y = ax + b$ and in $y = ax^2 + bx + c.$ As a practical application, we successfully arrive at the coefficients in the semi-empirical mass formula of nuclear physics. The formalism is {\\it generic} - it has the potential of being applicable to any {\\it type} of $\\{x_i\\}$ as long as there exist appropriate $\\{f_\\alpha\\}.$ The method can be exploited with a CAS or an object-oriented language and is excellently suitable for parallel-processing.

  6. Application of least squares support vector regression and linear multiple regression for modeling removal of methyl orange onto tin oxide nanoparticles loaded on activated carbon and activated carbon prepared from Pistacia atlantica wood.

    Science.gov (United States)

    Ghaedi, M; Rahimi, Mahmoud Reza; Ghaedi, A M; Tyagi, Inderjeet; Agarwal, Shilpi; Gupta, Vinod Kumar

    2016-01-01

    Two novel and eco friendly adsorbents namely tin oxide nanoparticles loaded on activated carbon (SnO2-NP-AC) and activated carbon prepared from wood tree Pistacia atlantica (AC-PAW) were used for the rapid removal and fast adsorption of methyl orange (MO) from the aqueous phase. The dependency of MO removal with various adsorption influential parameters was well modeled and optimized using multiple linear regressions (MLR) and least squares support vector regression (LSSVR). The optimal parameters for the LSSVR model were found based on γ value of 0.76 and σ(2) of 0.15. For testing the data set, the mean square error (MSE) values of 0.0010 and the coefficient of determination (R(2)) values of 0.976 were obtained for LSSVR model, and the MSE value of 0.0037 and the R(2) value of 0.897 were obtained for the MLR model. The adsorption equilibrium and kinetic data was found to be well fitted and in good agreement with Langmuir isotherm model and second-order equation and intra-particle diffusion models respectively. The small amount of the proposed SnO2-NP-AC and AC-PAW (0.015 g and 0.08 g) is applicable for successful rapid removal of methyl orange (>95%). The maximum adsorption capacity for SnO2-NP-AC and AC-PAW was 250 mg g(-1) and 125 mg g(-1) respectively. Copyright © 2015 Elsevier Inc. All rights reserved.

  7. Multigrid for the Galerkin least squares method in linear elasticity: The pure displacement problem

    Energy Technology Data Exchange (ETDEWEB)

    Yoo, Jaechil [Univ. of Wisconsin, Madison, WI (United States)

    1996-12-31

    Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we prove the convergence of a multigrid (W-cycle) method. This multigrid is robust in that the convergence is uniform as the parameter, v, goes to 1/2 Computational experiments are included.

  8. Determination of carbohydrates present in Saccharomyces cerevisiae using mid-infrared spectroscopy and partial least squares regression.

    Science.gov (United States)

    Plata, Maria R; Koch, Cosima; Wechselberger, Patrick; Herwig, Christoph; Lendl, Bernhard

    2013-10-01

    A fast and simple method to control variations in carbohydrate composition of Saccharomyces cerevisiae, baker's yeast, during fermentation was developed using mid-infrared (mid-IR) spectroscopy. The method allows for precise and accurate determinations with minimal or no sample preparation and reagent consumption based on mid-IR spectra and partial least squares (PLS) regression. The PLS models were developed employing the results from reference analysis of the yeast cells. The reference analyses quantify the amount of trehalose, glucose, glycogen, and mannan in S. cerevisiae. The selection and optimization of pretreatment steps of samples such as the disruption of the yeast cells and the hydrolysis of mannan and glycogen to obtain monosaccharides were carried out. Trehalose, glucose, and mannose were determined using high-performance liquid chromatography coupled with a refractive index detector and total carbohydrates were measured using the phenol-sulfuric method. Linear concentration range, accuracy, precision, LOD and LOQ were examined to check the reliability of the chromatographic method for each analyte.

  9. Teaching the Concept of Breakdown Point in Simple Linear Regression.

    Science.gov (United States)

    Chan, Wai-Sum

    2001-01-01

    Most introductory textbooks on simple linear regression analysis mention the fact that extreme data points have a great influence on ordinary least-squares regression estimation; however, not many textbooks provide a rigorous mathematical explanation of this phenomenon. Suggests a way to fill this gap by teaching students the concept of breakdown…

  10. Wavelength detection in FBG sensor networks using least squares support vector regression

    Science.gov (United States)

    Chen, Jing; Jiang, Hao; Liu, Tundong; Fu, Xiaoli

    2014-04-01

    A wavelength detection method for a wavelength division multiplexing (WDM) fiber Bragg grating (FBG) sensor network is proposed based on least squares support vector regression (LS-SVR). As a kind of promising machine learning technique, LS-SVR is employed to approximate the inverse function of the reflection spectrum. The LS-SVR detection model is established from the training samples, and then the Bragg wavelength of each FBG can be directly identified by inputting the measured spectrum into the well-trained model. We also discuss the impact of the sample size and the preprocess of the input spectrum on the performance of the training effectiveness. The results demonstrate that our approach is effective in improving the accuracy for sensor networks with a large number of FBGs.

  11. Non linear-least-squares fitting for pixe spectra

    International Nuclear Information System (INIS)

    Benamar, M.A.; Tchantchane, A.; Benouali, N.; Azbouche, A.; Tobbeche, S.

    1992-10-01

    An interactive computer program for the analysis of Pixe spectra is described. The fitting procedure consists of computing a function which approximates the experimental data. A nonlinear least-squares fitting is used to determine the parameters of the fit. The program takes into account the low energy tail and the escape peaks

  12. A complex linear least-squares method to derive relative and absolute orientations of seismic sensors

    OpenAIRE

    F. Grigoli; Simone Cesca; Torsten Dahm; L. Krieger

    2012-01-01

    Determining the relative orientation of the horizontal components of seismic sensors is a common problem that limits data analysis and interpretation for several acquisition setups, including linear arrays of geophones deployed in borehole installations or ocean bottom seismometers deployed at the seafloor. To solve this problem we propose a new inversion method based on a complex linear algebra approach. Relative orientation angles are retrieved by minimizing, in a least-squares sense, the l...

  13. Partial Least Squares tutorial for analyzing neuroimaging data

    Directory of Open Access Journals (Sweden)

    Patricia Van Roon

    2014-09-01

    Full Text Available Partial least squares (PLS has become a respected and meaningful soft modeling analysis technique that can be applied to very large datasets where the number of factors or variables is greater than the number of observations. Current biometric studies (e.g., eye movements, EKG, body movements, EEG are often of this nature. PLS eliminates the multiple linear regression issues of over-fitting data by finding a few underlying or latent variables (factors that account for most of the variation in the data. In real-world applications, where linear models do not always apply, PLS can model the non-linear relationship well. This tutorial introduces two PLS methods, PLS Correlation (PLSC and PLS Regression (PLSR and their applications in data analysis which are illustrated with neuroimaging examples. Both methods provide straightforward and comprehensible techniques for determining and modeling relationships between two multivariate data blocks by finding latent variables that best describes the relationships. In the examples, the PLSC will analyze the relationship between neuroimaging data such as Event-Related Potential (ERP amplitude averages from different locations on the scalp with their corresponding behavioural data. Using the same data, the PLSR will be used to model the relationship between neuroimaging and behavioural data. This model will be able to predict future behaviour solely from available neuroimaging data. To find latent variables, Singular Value Decomposition (SVD for PLSC and Non-linear Iterative PArtial Least Squares (NIPALS for PLSR are implemented in this tutorial. SVD decomposes the large data block into three manageable matrices containing a diagonal set of singular values, as well as left and right singular vectors. For PLSR, NIPALS algorithms are used because it provides amore precise estimation of the latent variables. Mathematica notebooks are provided for each PLS method with clearly labeled sections and subsections. The

  14. RCS Leak Rate Calculation with High Order Least Squares Method

    International Nuclear Information System (INIS)

    Lee, Jeong Hun; Kang, Young Kyu; Kim, Yang Ki

    2010-01-01

    As a part of action items for Application of Leak before Break(LBB), RCS Leak Rate Calculation Program is upgraded in Kori unit 3 and 4. For real time monitoring of operators, periodic calculation is needed and corresponding noise reduction scheme is used. This kind of study was issued in Korea, so there have upgraded and used real time RCS Leak Rate Calculation Program in UCN unit 3 and 4 and YGN unit 1 and 2. For reduction of the noise in signals, Linear Regression Method was used in those programs. Linear Regression Method is powerful method for noise reduction. But the system is not static with some alternative flow paths and this makes mixed trend patterns of input signal values. In this condition, the trend of signal and average of Linear Regression are not entirely same pattern. In this study, high order Least squares Method is used to follow the trend of signal and the order of calculation is rearranged. The result of calculation makes reasonable trend and the procedure is physically consistence

  15. Predicting blood β-hydroxybutyrate using milk Fourier transform infrared spectrum, milk composition, and producer-reported variables with multiple linear regression, partial least squares regression, and artificial neural network.

    Science.gov (United States)

    Pralle, R S; Weigel, K W; White, H M

    2018-05-01

    Prediction of postpartum hyperketonemia (HYK) using Fourier transform infrared (FTIR) spectrometry analysis could be a practical diagnostic option for farms because these data are now available from routine milk analysis during Dairy Herd Improvement testing. The objectives of this study were to (1) develop and evaluate blood β-hydroxybutyrate (BHB) prediction models using multivariate linear regression (MLR), partial least squares regression (PLS), and artificial neural network (ANN) methods and (2) evaluate whether milk FTIR spectrum (mFTIR)-based models are improved with the inclusion of test-day variables (mTest; milk composition and producer-reported data). Paired blood and milk samples were collected from multiparous cows 5 to 18 d postpartum at 3 Wisconsin farms (3,629 observations from 1,013 cows). Blood BHB concentration was determined by a Precision Xtra meter (Abbot Diabetes Care, Alameda, CA), and milk samples were analyzed by a privately owned laboratory (AgSource, Menomonie, WI) for components and FTIR spectrum absorbance. Producer-recorded variables were extracted from farm management software. A blood BHB ≥1.2 mmol/L was considered HYK. The data set was divided into a training set (n = 3,020) and an external testing set (n = 609). Model fitting was implemented with JMP 12 (SAS Institute, Cary, NC). A 5-fold cross-validation was performed on the training data set for the MLR, PLS, and ANN prediction methods, with square root of blood BHB as the dependent variable. Each method was fitted using 3 combinations of variables: mFTIR, mTest, or mTest + mFTIR variables. Models were evaluated based on coefficient of determination, root mean squared error, and area under the receiver operating characteristic curve. Four models (PLS-mTest + mFTIR, ANN-mFTIR, ANN-mTest, and ANN-mTest + mFTIR) were chosen for further evaluation in the testing set after fitting to the full training set. In the cross-validation analysis, model fit was greatest for ANN, followed

  16. Spectrum unfolding by the least-squares methods

    International Nuclear Information System (INIS)

    Perey, F.G.

    1977-01-01

    The method of least squares is briefly reviewed, and the conditions under which it may be used are stated. From this analysis, a least-squares approach to the solution of the dosimetry neutron spectrum unfolding problem is introduced. The mathematical solution to this least-squares problem is derived from the general solution. The existence of this solution is analyzed in some detail. A chi 2 -test is derived for the consistency of the input data which does not require the solution to be obtained first. The fact that the problem is technically nonlinear, but should be treated in general as a linear one, is argued. Therefore, the solution should not be obtained by iteration. Two interpretations are made for the solution of the code STAY'SL, which solves this least-squares problem. The relationship of the solution to this least-squares problem to those obtained currently by other methods of solving the dosimetry neutron spectrum unfolding problem is extensively discussed. It is shown that the least-squares method does not require more input information than would be needed by current methods in order to estimate the uncertainties in their solutions. From this discussion it is concluded that the proposed least-squares method does provide the best complete solution, with uncertainties, to the problem as it is understood now. Finally, some implications of this method are mentioned regarding future work required in order to exploit its potential fully

  17. Plane-wave Least-squares Reverse Time Migration

    KAUST Repository

    Dai, Wei

    2012-11-04

    Least-squares reverse time migration is formulated with a new parameterization, where the migration image of each shot is updated separately and a prestack image is produced with common image gathers. The advantage is that it can offer stable convergence for least-squares migration even when the migration velocity is not completely accurate. To significantly reduce computation cost, linear phase shift encoding is applied to hundreds of shot gathers to produce dozens of planes waves. A regularization term which penalizes the image difference between nearby angles are used to keep the prestack image consistent through all the angles. Numerical tests on a marine dataset is performed to illustrate the advantages of least-squares reverse time migration in the plane-wave domain. Through iterations of least-squares migration, the migration artifacts are reduced and the image resolution is improved. Empirical results suggest that the LSRTM in plane wave domain is an efficient method to improve the image quality and produce common image gathers.

  18. Pseudoinverse preconditioners and iterative methods for large dense linear least-squares problems

    Directory of Open Access Journals (Sweden)

    Oskar Cahueñas

    2013-05-01

    Full Text Available We address the issue of approximating the pseudoinverse of the coefficient matrix for dynamically building preconditioning strategies for the numerical solution of large dense linear least-squares problems. The new preconditioning strategies are embedded into simple and well-known iterative schemes that avoid the use of the, usually ill-conditioned, normal equations. We analyze a scheme to approximate the pseudoinverse, based on Schulz iterative method, and also different iterative schemes, based on extensions of Richardson's method, and the conjugate gradient method, that are suitable for preconditioning strategies. We present preliminary numerical results to illustrate the advantages of the proposed schemes.

  19. Consistency of the least weighted squares under heteroscedasticity

    Czech Academy of Sciences Publication Activity Database

    Víšek, Jan Ámos

    2011-01-01

    Roč. 2011, č. 47 (2011), s. 179-206 ISSN 0023-5954 Grant - others:GA UK(CZ) GA402/09/055 Institutional research plan: CEZ:AV0Z10750506 Keywords : Regression * Consistency * The least weighted squares * Heteroscedasticity Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.454, year: 2011 http://library.utia.cas.cz/separaty/2011/SI/visek-consistency of the least weighted squares under heteroscedasticity.pdf

  20. Prediction of clinical depression scores and detection of changes in whole-brain using resting-state functional MRI data with partial least squares regression.

    Directory of Open Access Journals (Sweden)

    Kosuke Yoshida

    Full Text Available In diagnostic applications of statistical machine learning methods to brain imaging data, common problems include data high-dimensionality and co-linearity, which often cause over-fitting and instability. To overcome these problems, we applied partial least squares (PLS regression to resting-state functional magnetic resonance imaging (rs-fMRI data, creating a low-dimensional representation that relates symptoms to brain activity and that predicts clinical measures. Our experimental results, based upon data from clinically depressed patients and healthy controls, demonstrated that PLS and its kernel variants provided significantly better prediction of clinical measures than ordinary linear regression. Subsequent classification using predicted clinical scores distinguished depressed patients from healthy controls with 80% accuracy. Moreover, loading vectors for latent variables enabled us to identify brain regions relevant to depression, including the default mode network, the right superior frontal gyrus, and the superior motor area.

  1. Making the most out of least-squares migration

    KAUST Repository

    Huang, Yunsong; Dutta, Gaurav; Dai, Wei; Wang, Xin; Schuster, Gerard T.; Yu, Jianhua

    2014-01-01

    ) weak amplitudes resulting from geometric spreading, attenuation, and defocusing. These problems can be remedied in part by least-squares migration (LSM), also known as linearized seismic inversion or migration deconvolution (MD), which aims to linearly

  2. Linear regression in astronomy. I

    Science.gov (United States)

    Isobe, Takashi; Feigelson, Eric D.; Akritas, Michael G.; Babu, Gutti Jogesh

    1990-01-01

    Five methods for obtaining linear regression fits to bivariate data with unknown or insignificant measurement errors are discussed: ordinary least-squares (OLS) regression of Y on X, OLS regression of X on Y, the bisector of the two OLS lines, orthogonal regression, and 'reduced major-axis' regression. These methods have been used by various researchers in observational astronomy, most importantly in cosmic distance scale applications. Formulas for calculating the slope and intercept coefficients and their uncertainties are given for all the methods, including a new general form of the OLS variance estimates. The accuracy of the formulas was confirmed using numerical simulations. The applicability of the procedures is discussed with respect to their mathematical properties, the nature of the astronomical data under consideration, and the scientific purpose of the regression. It is found that, for problems needing symmetrical treatment of the variables, the OLS bisector performs significantly better than orthogonal or reduced major-axis regression.

  3. Extracting information from two-dimensional electrophoresis gels by partial least squares regression

    DEFF Research Database (Denmark)

    Jessen, Flemming; Lametsch, R.; Bendixen, E.

    2002-01-01

    of all proteins/spots in the gels. In the present study it is demonstrated how information can be extracted by multivariate data analysis. The strategy is based on partial least squares regression followed by variable selection to find proteins that individually or in combination with other proteins vary......Two-dimensional gel electrophoresis (2-DE) produces large amounts of data and extraction of relevant information from these data demands a cautious and time consuming process of spot pattern matching between gels. The classical approach of data analysis is to detect protein markers that appear...... or disappear depending on the experimental conditions. Such biomarkers are found by comparing the relative volumes of individual spots in the individual gels. Multivariate statistical analysis and modelling of 2-DE data for comparison and classification is an alternative approach utilising the combination...

  4. Determination of carbohydrates present in Saccharomyces cerevisiae using mid-infrared spectroscopy and partial least squares regression

    OpenAIRE

    Plata, Maria R.; Koch, Cosima; Wechselberger, Patrick; Herwig, Christoph; Lendl, Bernhard

    2013-01-01

    A fast and simple method to control variations in carbohydrate composition of Saccharomyces cerevisiae, baker's yeast, during fermentation was developed using mid-infrared (mid-IR) spectroscopy. The method allows for precise and accurate determinations with minimal or no sample preparation and reagent consumption based on mid-IR spectra and partial least squares (PLS) regression. The PLS models were developed employing the results from reference analysis of the yeast cells. The reference anal...

  5. EXPALS, Least Square Fit of Linear Combination of Exponential Decay Function

    International Nuclear Information System (INIS)

    Douglas Gardner, C.

    1980-01-01

    1 - Description of problem or function: This program fits by least squares a function which is a linear combination of real exponential decay functions. The function is y(k) = summation over j of a(j) * exp(-lambda(j) * k). Values of the independent variable (k) and the dependent variable y(k) are specified as input data. Weights may be specified as input information or set by the program (w(k) = 1/y(k)). 2 - Method of solution: The Prony-Householder iteration method is used. For unequally-spaced data, a number of interpolation options are provided. This revision includes an option to call a differential correction subroutine REFINE to improve the approximation to unequally-spaced data when equal-interval interpolation is faulty. If convergence is achieved, the probable errors in the computed parameters are calculated also. 3 - Restrictions on the complexity of the problem: Generally, it is desirable to have at least 10n observations where n equals the number of terms and to input k+n significant figures if k significant figures are expected

  6. PERBANDINGAN ANALISIS LEAST ABSOLUTE SHRINKAGE AND SELECTION OPERATOR DAN PARTIAL LEAST SQUARES (Studi Kasus: Data Microarray

    Directory of Open Access Journals (Sweden)

    KADEK DWI FARMANI

    2012-09-01

    Full Text Available Linear regression analysis is one of the parametric statistical methods which utilize the relationship between two or more quantitative variables. In linear regression analysis, there are several assumptions that must be met that is normal distribution of errors, there is no correlation between the error and error variance is constant and homogent. There are some constraints that caused the assumption can not be met, for example, the correlation between independent variables (multicollinearity, constraints on the number of data and independent variables are obtained. When the number of samples obtained less than the number of independent variables, then the data is called the microarray data. Least Absolute shrinkage and Selection Operator (LASSO and Partial Least Squares (PLS is a statistical method that can be used to overcome the microarray, overfitting, and multicollinearity. From the above description, it is necessary to study with the intention of comparing LASSO and PLS method. This study uses coronary heart and stroke patients data which is a microarray data and contain multicollinearity. With these two characteristics of the data that most have a weak correlation between independent variables, LASSO method produces a better model than PLS seen from the large RMSEP.

  7. Plane-wave Least-squares Reverse Time Migration

    KAUST Repository

    Dai, Wei; Schuster, Gerard T.

    2012-01-01

    convergence for least-squares migration even when the migration velocity is not completely accurate. To significantly reduce computation cost, linear phase shift encoding is applied to hundreds of shot gathers to produce dozens of planes waves. A

  8. Prediction of beef marblingusing Hyperspectral Imaging (HSI and Partial Least Squares Regression (PLSR

    Directory of Open Access Journals (Sweden)

    Victor Aredo

    2017-01-01

    Full Text Available The aim of this study was to build a model to predict the beef marbling using HSI and Partial Least Squares Regression (PLSR. Totally 58 samples of longissmus dorsi muscle were scanned by a HSI system (400 - 1000 nm in reflectance mode, using 44 samples to build t he PLSR model and 14 samples to model validation. The Japanese Beef Marbling Standard (BMS was used as reference by 15 middle - trained judges for the samples evaluation. The scores were assigned as continuous values and varied from 1.2 to 5.3 BMS. The PLSR model showed a high correlation coefficient in the prediction (r = 0.95, a low Standard Error of Calibration (SEC of 0.2 BMS score, and a low Standard Error of Prediction (SEP of 0.3 BMS score.

  9. truncSP: An R Package for Estimation of Semi-Parametric Truncated Linear Regression Models

    Directory of Open Access Journals (Sweden)

    Maria Karlsson

    2014-05-01

    Full Text Available Problems with truncated data occur in many areas, complicating estimation and inference. Regarding linear regression models, the ordinary least squares estimator is inconsistent and biased for these types of data and is therefore unsuitable for use. Alternative estimators, designed for the estimation of truncated regression models, have been developed. This paper presents the R package truncSP. The package contains functions for the estimation of semi-parametric truncated linear regression models using three different estimators: the symmetrically trimmed least squares, quadratic mode, and left truncated estimators, all of which have been shown to have good asymptotic and ?nite sample properties. The package also provides functions for the analysis of the estimated models. Data from the environmental sciences are used to illustrate the functions in the package.

  10. The Multivariate Regression Statistics Strategy to Investigate Content-Effect Correlation of Multiple Components in Traditional Chinese Medicine Based on a Partial Least Squares Method.

    Science.gov (United States)

    Peng, Ying; Li, Su-Ning; Pei, Xuexue; Hao, Kun

    2018-03-01

    Amultivariate regression statisticstrategy was developed to clarify multi-components content-effect correlation ofpanaxginseng saponins extract and predict the pharmacological effect by components content. In example 1, firstly, we compared pharmacological effects between panax ginseng saponins extract and individual saponin combinations. Secondly, we examined the anti-platelet aggregation effect in seven different saponin combinations of ginsenoside Rb1, Rg1, Rh, Rd, Ra3 and notoginsenoside R1. Finally, the correlation between anti-platelet aggregation and the content of multiple components was analyzed by a partial least squares algorithm. In example 2, firstly, 18 common peaks were identified in ten different batches of panax ginseng saponins extracts from different origins. Then, we investigated the anti-myocardial ischemia reperfusion injury effects of the ten different panax ginseng saponins extracts. Finally, the correlation between the fingerprints and the cardioprotective effects was analyzed by a partial least squares algorithm. Both in example 1 and 2, the relationship between the components content and pharmacological effect was modeled well by the partial least squares regression equations. Importantly, the predicted effect curve was close to the observed data of dot marked on the partial least squares regression model. This study has given evidences that themulti-component content is a promising information for predicting the pharmacological effects of traditional Chinese medicine.

  11. Making the most out of the least (squares migration)

    KAUST Repository

    Dutta, Gaurav; Huang, Yunsong; Dai, Wei; Wang, Xin; Schuster, Gerard T.

    2014-01-01

    ) ringiness caused by a ringy source wavelet. To partly remedy these problems, least-squares migration (LSM), also known as linearized seismic inversion or migration deconvolution (MD), proposes to linearly invert seismic data for the reflectivity distribution

  12. Least-Squares Linear Regression and Schrodinger's Cat: Perspectives on the Analysis of Regression Residuals.

    Science.gov (United States)

    Hecht, Jeffrey B.

    The analysis of regression residuals and detection of outliers are discussed, with emphasis on determining how deviant an individual data point must be to be considered an outlier and the impact that multiple suspected outlier data points have on the process of outlier determination and treatment. Only bivariate (one dependent and one independent)…

  13. 8th International Conference on Partial Least Squares and Related Methods

    CERN Document Server

    Vinzi, Vincenzo; Russolillo, Giorgio; Saporta, Gilbert; Trinchera, Laura

    2016-01-01

    This volume presents state of the art theories, new developments, and important applications of Partial Least Square (PLS) methods. The text begins with the invited communications of current leaders in the field who cover the history of PLS, an overview of methodological issues, and recent advances in regression and multi-block approaches. The rest of the volume comprises selected, reviewed contributions from the 8th International Conference on Partial Least Squares and Related Methods held in Paris, France, on 26-28 May, 2014. They are organized in four coherent sections: 1) new developments in genomics and brain imaging, 2) new and alternative methods for multi-table and path analysis, 3) advances in partial least square regression (PLSR), and 4) partial least square path modeling (PLS-PM) breakthroughs and applications. PLS methods are very versatile methods that are now used in areas as diverse as engineering, life science, sociology, psychology, brain imaging, genomics, and business among both academics ...

  14. Regularization by truncated total least squares

    DEFF Research Database (Denmark)

    Hansen, Per Christian; Fierro, R.D; Golub, G.H

    1997-01-01

    The total least squares (TLS) method is a successful method for noise reduction in linear least squares problems in a number of applications. The TLS method is suited to problems in which both the coefficient matrix and the right-hand side are not precisely known. This paper focuses on the use...... schemes for relativistic hydrodynamical equations. Such an approximate Riemann solver is presented in this paper which treats all waves emanating from an initial discontinuity as themselves discontinuous. Therefore, jump conditions for shocks are approximately used for rarefaction waves. The solver...... is easy to implement in a Godunov scheme and converges rapidly for relativistic hydrodynamics. The fast convergence of the solver indicates the potential of a higher performance of a Godunov scheme in which the solver is used....

  15. Prediction of toxicity of nitrobenzenes using ab initio and least squares support vector machines

    International Nuclear Information System (INIS)

    Niazi, Ali; Jameh-Bozorghi, Saeed; Nori-Shargh, Davood

    2008-01-01

    A quantitative structure-property relationship (QSPR) study is suggested for the prediction of toxicity (IGC 50 ) of nitrobenzenes. Ab initio theory was used to calculate some quantum chemical descriptors including electrostatic potentials and local charges at each atom, HOMO and LUMO energies, etc. Modeling of the IGC 50 of nitrobenzenes as a function of molecular structures was established by means of the least squares support vector machines (LS-SVM). This model was applied for the prediction of the toxicity (IGC 50 ) of nitrobenzenes, which were not in the modeling procedure. The resulted model showed high prediction ability with root mean square error of prediction of 0.0049 for LS-SVM. Results have shown that the introduction of LS-SVM for quantum chemical descriptors drastically enhances the ability of prediction in QSAR studies superior to multiple linear regression and partial least squares

  16. Solution of a Complex Least Squares Problem with Constrained Phase.

    Science.gov (United States)

    Bydder, Mark

    2010-12-30

    The least squares solution of a complex linear equation is in general a complex vector with independent real and imaginary parts. In certain applications in magnetic resonance imaging, a solution is desired such that each element has the same phase. A direct method for obtaining the least squares solution to the phase constrained problem is described.

  17. Analysis of interactive fixed effects dynamic linear panel regression with measurement error

    OpenAIRE

    Nayoung Lee; Hyungsik Roger Moon; Martin Weidner

    2011-01-01

    This paper studies a simple dynamic panel linear regression model with interactive fixed effects in which the variable of interest is measured with error. To estimate the dynamic coefficient, we consider the least-squares minimum distance (LS-MD) estimation method.

  18. The Multivariate Regression Statistics Strategy to Investigate Content-Effect Correlation of Multiple Components in Traditional Chinese Medicine Based on a Partial Least Squares Method

    Directory of Open Access Journals (Sweden)

    Ying Peng

    2018-03-01

    Full Text Available Amultivariate regression statisticstrategy was developed to clarify multi-components content-effect correlation ofpanaxginseng saponins extract and predict the pharmacological effect by components content. In example 1, firstly, we compared pharmacological effects between panax ginseng saponins extract and individual saponin combinations. Secondly, we examined the anti-platelet aggregation effect in seven different saponin combinations of ginsenoside Rb1, Rg1, Rh, Rd, Ra3 and notoginsenoside R1. Finally, the correlation between anti-platelet aggregation and the content of multiple components was analyzed by a partial least squares algorithm. In example 2, firstly, 18 common peaks were identified in ten different batches of panax ginseng saponins extracts from different origins. Then, we investigated the anti-myocardial ischemia reperfusion injury effects of the ten different panax ginseng saponins extracts. Finally, the correlation between the fingerprints and the cardioprotective effects was analyzed by a partial least squares algorithm. Both in example 1 and 2, the relationship between the components content and pharmacological effect was modeled well by the partial least squares regression equations. Importantly, the predicted effect curve was close to the observed data of dot marked on the partial least squares regression model. This study has given evidences that themulti-component content is a promising information for predicting the pharmacological effects of traditional Chinese medicine.

  19. A primer on linear models

    CERN Document Server

    Monahan, John F

    2008-01-01

    Preface Examples of the General Linear Model Introduction One-Sample Problem Simple Linear Regression Multiple Regression One-Way ANOVA First Discussion The Two-Way Nested Model Two-Way Crossed Model Analysis of Covariance Autoregression Discussion The Linear Least Squares Problem The Normal Equations The Geometry of Least Squares Reparameterization Gram-Schmidt Orthonormalization Estimability and Least Squares Estimators Assumptions for the Linear Mean Model Confounding, Identifiability, and Estimability Estimability and Least Squares Estimators F

  20. Massively-parallel best subset selection for ordinary least-squares regression

    DEFF Research Database (Denmark)

    Gieseke, Fabian; Polsterer, Kai Lars; Mahabal, Ashish

    2017-01-01

    Selecting an optimal subset of k out of d features for linear regression models given n training instances is often considered intractable for feature spaces with hundreds or thousands of dimensions. We propose an efficient massively-parallel implementation for selecting such optimal feature...

  1. Status of the Monte Carlo library least-squares (MCLLS) approach for non-linear radiation analyzer problems

    Science.gov (United States)

    Gardner, Robin P.; Xu, Libai

    2009-10-01

    The Center for Engineering Applications of Radioisotopes (CEAR) has been working for over a decade on the Monte Carlo library least-squares (MCLLS) approach for treating non-linear radiation analyzer problems including: (1) prompt gamma-ray neutron activation analysis (PGNAA) for bulk analysis, (2) energy-dispersive X-ray fluorescence (EDXRF) analyzers, and (3) carbon/oxygen tool analysis in oil well logging. This approach essentially consists of using Monte Carlo simulation to generate the libraries of all the elements to be analyzed plus any other required background libraries. These libraries are then used in the linear library least-squares (LLS) approach with unknown sample spectra to analyze for all elements in the sample. Iterations of this are used until the LLS values agree with the composition used to generate the libraries. The current status of the methods (and topics) necessary to implement the MCLLS approach is reported. This includes: (1) the Monte Carlo codes such as CEARXRF, CEARCPG, and CEARCO for forward generation of the necessary elemental library spectra for the LLS calculation for X-ray fluorescence, neutron capture prompt gamma-ray analyzers, and carbon/oxygen tools; (2) the correction of spectral pulse pile-up (PPU) distortion by Monte Carlo simulation with the code CEARIPPU; (3) generation of detector response functions (DRF) for detectors with linear and non-linear responses for Monte Carlo simulation of pulse-height spectra; and (4) the use of the differential operator (DO) technique to make the necessary iterations for non-linear responses practical. In addition to commonly analyzed single spectra, coincidence spectra or even two-dimensional (2-D) coincidence spectra can also be used in the MCLLS approach and may provide more accurate results.

  2. Performance improvement of shunt active power filter based on non-linear least-square approach

    DEFF Research Database (Denmark)

    Terriche, Yacine

    2018-01-01

    . This paper proposes an improved open loop strategy which is unconditionally stable and flexible. The proposed method which is based on non-linear least square (NLS) approach can extract the fundamental voltage and estimates its phase within only half cycle, even in the presence of odd harmonics and dc offset......). The synchronous reference frame (SRF) approach is widely used for generating the RCC due to its simplicity and computation efficiency. However, the SRF approach needs precise information of the voltage phase which becomes a challenge under adverse grid conditions. A typical solution to answer this need...

  3. Wave-equation Q tomography and least-squares migration

    KAUST Repository

    Dutta, Gaurav

    2016-03-01

    This thesis designs new methods for Q tomography and Q-compensated prestack depth migration when the recorded seismic data suffer from strong attenuation. A motivation of this work is that the presence of gas clouds or mud channels in overburden structures leads to the distortion of amplitudes and phases in seismic waves propagating inside the earth. If the attenuation parameter Q is very strong, i.e., Q<30, ignoring the anelastic effects in imaging can lead to dimming of migration amplitudes and loss of resolution. This, in turn, adversely affects the ability to accurately predict reservoir properties below such layers. To mitigate this problem, I first develop an anelastic least-squares reverse time migration (Q-LSRTM) technique. I reformulate the conventional acoustic least-squares migration problem as a viscoacoustic linearized inversion problem. Using linearized viscoacoustic modeling and adjoint operators during the least-squares iterations, I show with numerical tests that Q-LSRTM can compensate for the amplitude loss and produce images with better balanced amplitudes than conventional migration. To estimate the background Q model that can be used for any Q-compensating migration algorithm, I then develop a wave-equation based optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ε. Here, ε is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early-arrivals. Through numerical tests on synthetic and field data, I show that noticeable improvements in the migration image quality can be obtained from Q models inverted using wave-equation Q tomography. A key feature of skeletonized inversion is that it is much less likely to get stuck in a local minimum than a standard waveform inversion method. Finally, I develop a preconditioning technique for least-squares migration using a directional Gabor-based preconditioning approach for isotropic

  4. The possibilities of least-squares migration of internally scattered seismic energy

    KAUST Repository

    Aldawood, Ali

    2015-05-26

    Approximate images of the earth’s subsurface structures are usually obtained by migrating surface seismic data. Least-squares migration, under the single-scattering assumption, is used as an iterative linearized inversion scheme to suppress migration artifacts, deconvolve the source signature, mitigate the acquisition fingerprint, and enhance the spatial resolution of migrated images. The problem with least-squares migration of primaries, however, is that it may not be able to enhance events that are mainly illuminated by internal multiples, such as vertical and nearly vertical faults or salt flanks. To alleviate this problem, we adopted a linearized inversion framework to migrate internally scattered energy. We apply the least-squares migration of first-order internal multiples to image subsurface vertical fault planes. Tests on synthetic data demonstrated the ability of the proposed method to resolve vertical fault planes, which are poorly illuminated by the least-squares migration of primaries only. The proposed scheme is robust in the presence of white Gaussian observational noise and in the case of imaging the fault planes using inaccurate migration velocities. Our results suggested that the proposed least-squares imaging, under the double-scattering assumption, still retrieved the vertical fault planes when imaging the scattered data despite a slight defocusing of these events due to the presence of noise or velocity errors.

  5. The possibilities of least-squares migration of internally scattered seismic energy

    KAUST Repository

    Aldawood, Ali; Hoteit, Ibrahim; Zuberi, Mohammad; Turkiyyah, George; Alkhalifah, Tariq Ali

    2015-01-01

    Approximate images of the earth’s subsurface structures are usually obtained by migrating surface seismic data. Least-squares migration, under the single-scattering assumption, is used as an iterative linearized inversion scheme to suppress migration artifacts, deconvolve the source signature, mitigate the acquisition fingerprint, and enhance the spatial resolution of migrated images. The problem with least-squares migration of primaries, however, is that it may not be able to enhance events that are mainly illuminated by internal multiples, such as vertical and nearly vertical faults or salt flanks. To alleviate this problem, we adopted a linearized inversion framework to migrate internally scattered energy. We apply the least-squares migration of first-order internal multiples to image subsurface vertical fault planes. Tests on synthetic data demonstrated the ability of the proposed method to resolve vertical fault planes, which are poorly illuminated by the least-squares migration of primaries only. The proposed scheme is robust in the presence of white Gaussian observational noise and in the case of imaging the fault planes using inaccurate migration velocities. Our results suggested that the proposed least-squares imaging, under the double-scattering assumption, still retrieved the vertical fault planes when imaging the scattered data despite a slight defocusing of these events due to the presence of noise or velocity errors.

  6. New method to incorporate Type B uncertainty into least-squares procedures in radionuclide metrology

    International Nuclear Information System (INIS)

    Han, Jubong; Lee, K.B.; Lee, Jong-Man; Park, Tae Soon; Oh, J.S.; Oh, Pil-Jei

    2016-01-01

    We discuss a new method to incorporate Type B uncertainty into least-squares procedures. The new method is based on an extension of the likelihood function from which a conventional least-squares function is derived. The extended likelihood function is the product of the original likelihood function with additional PDFs (Probability Density Functions) that characterize the Type B uncertainties. The PDFs are considered to describe one's incomplete knowledge on correction factors being called nuisance parameters. We use the extended likelihood function to make point and interval estimations of parameters in the basically same way as the least-squares function used in the conventional least-squares method is derived. Since the nuisance parameters are not of interest and should be prevented from appearing in the final result, we eliminate such nuisance parameters by using the profile likelihood. As an example, we present a case study for a linear regression analysis with a common component of Type B uncertainty. In this example we compare the analysis results obtained from using our procedure with those from conventional methods. - Highlights: • A new method proposed to incorporate Type B uncertainty into least-squares method. • The method constructed from the likelihood function and PDFs of Type B uncertainty. • A case study performed to compare results from the new and the conventional method. • Fitted parameters are consistent but with larger uncertainties in the new method.

  7. The Use of Alternative Regression Methods in Social Sciences and the Comparison of Least Squares and M Estimation Methods in Terms of the Determination of Coefficient

    Science.gov (United States)

    Coskuntuncel, Orkun

    2013-01-01

    The purpose of this study is two-fold; the first aim being to show the effect of outliers on the widely used least squares regression estimator in social sciences. The second aim is to compare the classical method of least squares with the robust M-estimator using the "determination of coefficient" (R[superscript 2]). For this purpose,…

  8. Establishment of regression dependences. Linear and nonlinear dependences

    International Nuclear Information System (INIS)

    Onishchenko, A.M.

    1994-01-01

    The main problems of determination of linear and 19 types of nonlinear regression dependences are completely discussed. It is taken into consideration that total dispersions are the sum of measurement dispersions and parameter variation dispersions themselves. Approaches to all dispersions determination are described. It is shown that the least square fit gives inconsistent estimation for industrial objects and processes. The correction methods by taking into account comparable measurement errors for both variable give an opportunity to obtain consistent estimation for the regression equation parameters. The condition of the correction technique application expediency is given. The technique for determination of nonlinear regression dependences taking into account the dependence form and comparable errors of both variables is described. 6 refs., 1 tab

  9. The Relationship between Economic Growth and Money Laundering – a Linear Regression Model

    Directory of Open Access Journals (Sweden)

    Daniel Rece

    2009-09-01

    Full Text Available This study provides an overview of the relationship between economic growth and money laundering modeled by a least squares function. The report analyzes statistically data collected from USA, Russia, Romania and other eleven European countries, rendering a linear regression model. The study illustrates that 23.7% of the total variance in the regressand (level of money laundering is “explained” by the linear regression model. In our opinion, this model will provide critical auxiliary judgment and decision support for anti-money laundering service systems.

  10. Global Search Strategies for Solving Multilinear Least-Squares Problems

    Directory of Open Access Journals (Sweden)

    Mats Andersson

    2012-04-01

    Full Text Available The multilinear least-squares (MLLS problem is an extension of the linear least-squares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows for moving from one local minimizer to a better one. The efficiency of this strategy is illustrated by the results of numerical experiments performed for some problems related to the design of filter networks.

  11. A least-squares computational ``tool kit``. Nuclear data and measurements series

    Energy Technology Data Exchange (ETDEWEB)

    Smith, D.L.

    1993-04-01

    The information assembled in this report is intended to offer a useful computational ``tool kit`` to individuals who are interested in a variety of practical applications for the least-squares method of parameter estimation. The fundamental principles of Bayesian analysis are outlined first and these are applied to development of both the simple and the generalized least-squares conditions. Formal solutions that satisfy these conditions are given subsequently. Their application to both linear and non-linear problems is described in detail. Numerical procedures required to implement these formal solutions are discussed and two utility computer algorithms are offered for this purpose (codes LSIOD and GLSIOD written in FORTRAN). Some simple, easily understood examples are included to illustrate the use of these algorithms. Several related topics are then addressed, including the generation of covariance matrices, the role of iteration in applications of least-squares procedures, the effects of numerical precision and an approach that can be pursued in developing data analysis packages that are directed toward special applications.

  12. A Generalized Autocovariance Least-Squares Method for Kalman Filter Tuning

    DEFF Research Database (Denmark)

    Åkesson, Bernt Magnus; Jørgensen, John Bagterp; Poulsen, Niels Kjølstad

    2008-01-01

    This paper discusses a method for estimating noise covariances from process data. In linear stochastic state-space representations the true noise covariances are generally unknown in practical applications. Using estimated covariances a Kalman filter can be tuned in order to increase the accuracy...... of the state estimates. There is a linear relationship between covariances and autocovariance. Therefore, the covariance estimation problem can be stated as a least-squares problem, which can be solved as a symmetric semidefinite least-squares problem. This problem is convex and can be solved efficiently...... by interior-point methods. A numerical algorithm for solving the symmetric is able to handle systems with mutually correlated process noise and measurement noise. (c) 2007 Elsevier Ltd. All rights reserved....

  13. PENERAPAN METODE LEAST MEDIAN SQUARE-MINIMUM COVARIANCE DETERMINANT (LMS-MCD DALAM REGRESI KOMPONEN UTAMA

    Directory of Open Access Journals (Sweden)

    I PUTU EKA IRAWAN

    2013-11-01

    Full Text Available Principal Component Regression is a method to overcome multicollinearity techniques by combining principal component analysis with regression analysis. The calculation of classical principal component analysis is based on the regular covariance matrix. The covariance matrix is optimal if the data originated from a multivariate normal distribution, but is very sensitive to the presence of outliers. Alternatives are used to overcome this problem the method of Least Median Square-Minimum Covariance Determinant (LMS-MCD. The purpose of this research is to conduct a comparison between Principal Component Regression (RKU and Method of Least Median Square - Minimum Covariance Determinant (LMS-MCD in dealing with outliers. In this study, Method of Least Median Square - Minimum Covariance Determinant (LMS-MCD has a bias and mean square error (MSE is smaller than the parameter RKU. Based on the difference of parameter estimators, still have a test that has a difference of parameter estimators method LMS-MCD greater than RKU method.

  14. Analysis of γ spectra in airborne radioactivity measurements using multiple linear regressions

    International Nuclear Information System (INIS)

    Bao Min; Shi Quanlin; Zhang Jiamei

    2004-01-01

    This paper describes the net peak counts calculating of nuclide 137 Cs at 662 keV of γ spectra in airborne radioactivity measurements using multiple linear regressions. Mathematic model is founded by analyzing every factor that has contribution to Cs peak counts in spectra, and multiple linear regression function is established. Calculating process adopts stepwise regression, and the indistinctive factors are eliminated by F check. The regression results and its uncertainty are calculated using Least Square Estimation, then the Cs peak net counts and its uncertainty can be gotten. The analysis results for experimental spectrum are displayed. The influence of energy shift and energy resolution on the analyzing result is discussed. In comparison with the stripping spectra method, multiple linear regression method needn't stripping radios, and the calculating result has relation with the counts in Cs peak only, and the calculating uncertainty is reduced. (authors)

  15. Making the most out of least-squares migration

    KAUST Repository

    Huang, Yunsong

    2014-09-01

    Standard migration images can suffer from (1) migration artifacts caused by an undersampled acquisition geometry, (2) poor resolution resulting from a limited recording aperture, (3) ringing artifacts caused by ripples in the source wavelet, and (4) weak amplitudes resulting from geometric spreading, attenuation, and defocusing. These problems can be remedied in part by least-squares migration (LSM), also known as linearized seismic inversion or migration deconvolution (MD), which aims to linearly invert seismic data for the reflectivity distribution. Given a sufficiently accurate migration velocity model, LSM can mitigate many of the above problems and can produce more resolved migration images, sometimes with more than twice the spatial resolution of standard migration. However, LSM faces two challenges: The computational cost can be an order of magnitude higher than that of standard migration, and the resulting image quality can fail to improve for migration velocity errors of about 5% or more. It is possible to obtain the most from least-squares migration by reducing the cost and velocity sensitivity of LSM.

  16. Least square regression based integrated multi-parameteric demand modeling for short term load forecasting

    International Nuclear Information System (INIS)

    Halepoto, I.A.; Uqaili, M.A.

    2014-01-01

    Nowadays, due to power crisis, electricity demand forecasting is deemed an important area for socioeconomic development and proper anticipation of the load forecasting is considered essential step towards efficient power system operation, scheduling and planning. In this paper, we present STLF (Short Term Load Forecasting) using multiple regression techniques (i.e. linear, multiple linear, quadratic and exponential) by considering hour by hour load model based on specific targeted day approach with temperature variant parameter. The proposed work forecasts the future load demand correlation with linear and non-linear parameters (i.e. considering temperature in our case) through different regression approaches. The overall load forecasting error is 2.98% which is very much acceptable. From proposed regression techniques, Quadratic Regression technique performs better compared to than other techniques because it can optimally fit broad range of functions and data sets. The work proposed in this paper, will pave a path to effectively forecast the specific day load with multiple variance factors in a way that optimal accuracy can be maintained. (author)

  17. Estimation of active pharmaceutical ingredients content using locally weighted partial least squares and statistical wavelength selection.

    OpenAIRE

    Kim, Sanghong; Kano, Manabu; Nakagawa, Hiroshi; Hasebe, Shinji

    2011-01-01

    Development of quality estimation models using near infrared spectroscopy (NIRS) and multivariate analysis has been accelerated as a process analytical technology (PAT) tool in the pharmaceutical industry. Although linear regression methods such as partial least squares (PLS) are widely used, they cannot always achieve high estimation accuracy because physical and chemical properties of a measuring object have a complex effect on NIR spectra. In this research, locally weighted PLS (LW-PLS) wh...

  18. Least Squares Problems with Absolute Quadratic Constraints

    Directory of Open Access Journals (Sweden)

    R. Schöne

    2012-01-01

    Full Text Available This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented.

  19. A Simple and Convenient Method of Multiple Linear Regression to Calculate Iodine Molecular Constants

    Science.gov (United States)

    Cooper, Paul D.

    2010-01-01

    A new procedure using a student-friendly least-squares multiple linear-regression technique utilizing a function within Microsoft Excel is described that enables students to calculate molecular constants from the vibronic spectrum of iodine. This method is advantageous pedagogically as it calculates molecular constants for ground and excited…

  20. Least-squares model-based halftoning

    Science.gov (United States)

    Pappas, Thrasyvoulos N.; Neuhoff, David L.

    1992-08-01

    A least-squares model-based approach to digital halftoning is proposed. It exploits both a printer model and a model for visual perception. It attempts to produce an 'optimal' halftoned reproduction, by minimizing the squared error between the response of the cascade of the printer and visual models to the binary image and the response of the visual model to the original gray-scale image. Conventional methods, such as clustered ordered dither, use the properties of the eye only implicitly, and resist printer distortions at the expense of spatial and gray-scale resolution. In previous work we showed that our printer model can be used to modify error diffusion to account for printer distortions. The modified error diffusion algorithm has better spatial and gray-scale resolution than conventional techniques, but produces some well known artifacts and asymmetries because it does not make use of an explicit eye model. Least-squares model-based halftoning uses explicit eye models and relies on printer models that predict distortions and exploit them to increase, rather than decrease, both spatial and gray-scale resolution. We have shown that the one-dimensional least-squares problem, in which each row or column of the image is halftoned independently, can be implemented with the Viterbi's algorithm. Unfortunately, no closed form solution can be found in two dimensions. The two-dimensional least squares solution is obtained by iterative techniques. Experiments show that least-squares model-based halftoning produces more gray levels and better spatial resolution than conventional techniques. We also show that the least- squares approach eliminates the problems associated with error diffusion. Model-based halftoning can be especially useful in transmission of high quality documents using high fidelity gray-scale image encoders. As we have shown, in such cases halftoning can be performed at the receiver, just before printing. Apart from coding efficiency, this approach

  1. Making the most out of the least (squares migration)

    KAUST Repository

    Dutta, Gaurav

    2014-08-05

    Standard migration images can suffer from migration artifacts due to 1) poor source-receiver sampling, 2) weak amplitudes caused by geometric spreading, 3) attenuation, 4) defocusing, 5) poor resolution due to limited source-receiver aperture, and 6) ringiness caused by a ringy source wavelet. To partly remedy these problems, least-squares migration (LSM), also known as linearized seismic inversion or migration deconvolution (MD), proposes to linearly invert seismic data for the reflectivity distribution. If the migration velocity model is sufficiently accurate, then LSM can mitigate many of the above problems and lead to a more resolved migration image, sometimes with twice the spatial resolution. However, there are two problems with LSM: the cost can be an order of magnitude more than standard migration and the quality of the LSM image is no better than the standard image for velocity errors of 5% or more. We now show how to get the most from least-squares migration by reducing the cost and velocity sensitivity of LSM.

  2. Least squares orthogonal polynomial approximation in several independent variables

    International Nuclear Information System (INIS)

    Caprari, R.S.

    1992-06-01

    This paper begins with an exposition of a systematic technique for generating orthonormal polynomials in two independent variables by application of the Gram-Schmidt orthogonalization procedure of linear algebra. It is then demonstrated how a linear least squares approximation for experimental data or an arbitrary function can be generated from these polynomials. The least squares coefficients are computed without recourse to matrix arithmetic, which ensures both numerical stability and simplicity of implementation as a self contained numerical algorithm. The Gram-Schmidt procedure is then utilised to generate a complete set of orthogonal polynomials of fourth degree. A theory for the transformation of the polynomial representation from an arbitrary basis into the familiar sum of products form is presented, together with a specific implementation for fourth degree polynomials. Finally, the computational integrity of this algorithm is verified by reconstructing arbitrary fourth degree polynomials from their values at randomly chosen points in their domain. 13 refs., 1 tab

  3. Multiclass Prediction with Partial Least Square Regression for Gene Expression Data: Applications in Breast Cancer Intrinsic Taxonomy

    Directory of Open Access Journals (Sweden)

    Chi-Cheng Huang

    2013-01-01

    Full Text Available Multiclass prediction remains an obstacle for high-throughput data analysis such as microarray gene expression profiles. Despite recent advancements in machine learning and bioinformatics, most classification tools were limited to the applications of binary responses. Our aim was to apply partial least square (PLS regression for breast cancer intrinsic taxonomy, of which five distinct molecular subtypes were identified. The PAM50 signature genes were used as predictive variables in PLS analysis, and the latent gene component scores were used in binary logistic regression for each molecular subtype. The 139 prototypical arrays for PAM50 development were used as training dataset, and three independent microarray studies with Han Chinese origin were used for independent validation (n=535. The agreement between PAM50 centroid-based single sample prediction (SSP and PLS-regression was excellent (weighted Kappa: 0.988 within the training samples, but deteriorated substantially in independent samples, which could attribute to much more unclassified samples by PLS-regression. If these unclassified samples were removed, the agreement between PAM50 SSP and PLS-regression improved enormously (weighted Kappa: 0.829 as opposed to 0.541 when unclassified samples were analyzed. Our study ascertained the feasibility of PLS-regression in multi-class prediction, and distinct clinical presentations and prognostic discrepancies were observed across breast cancer molecular subtypes.

  4. Partial update least-square adaptive filtering

    CERN Document Server

    Xie, Bei

    2014-01-01

    Adaptive filters play an important role in the fields related to digital signal processing and communication, such as system identification, noise cancellation, channel equalization, and beamforming. In practical applications, the computational complexity of an adaptive filter is an important consideration. The Least Mean Square (LMS) algorithm is widely used because of its low computational complexity (O(N)) and simplicity in implementation. The least squares algorithms, such as Recursive Least Squares (RLS), Conjugate Gradient (CG), and Euclidean Direction Search (EDS), can converge faster a

  5. Biostatistics Series Module 6: Correlation and Linear Regression.

    Science.gov (United States)

    Hazra, Avijit; Gogtay, Nithya

    2016-01-01

    Correlation and linear regression are the most commonly used techniques for quantifying the association between two numeric variables. Correlation quantifies the strength of the linear relationship between paired variables, expressing this as a correlation coefficient. If both variables x and y are normally distributed, we calculate Pearson's correlation coefficient ( r ). If normality assumption is not met for one or both variables in a correlation analysis, a rank correlation coefficient, such as Spearman's rho (ρ) may be calculated. A hypothesis test of correlation tests whether the linear relationship between the two variables holds in the underlying population, in which case it returns a P correlation coefficient can also be calculated for an idea of the correlation in the population. The value r 2 denotes the proportion of the variability of the dependent variable y that can be attributed to its linear relation with the independent variable x and is called the coefficient of determination. Linear regression is a technique that attempts to link two correlated variables x and y in the form of a mathematical equation ( y = a + bx ), such that given the value of one variable the other may be predicted. In general, the method of least squares is applied to obtain the equation of the regression line. Correlation and linear regression analysis are based on certain assumptions pertaining to the data sets. If these assumptions are not met, misleading conclusions may be drawn. The first assumption is that of linear relationship between the two variables. A scatter plot is essential before embarking on any correlation-regression analysis to show that this is indeed the case. Outliers or clustering within data sets can distort the correlation coefficient value. Finally, it is vital to remember that though strong correlation can be a pointer toward causation, the two are not synonymous.

  6. Solve: a non linear least-squares code and its application to the optimal placement of torsatron vertical field coils

    International Nuclear Information System (INIS)

    Aspinall, J.

    1982-01-01

    A computational method was developed which alleviates the need for lengthy parametric scans as part of a design process. The method makes use of a least squares algorithm to find the optimal value of a parameter vector. Optimal is defined in terms of a utility function prescribed by the user. The placement of the vertical field coils of a torsatron is such a non linear problem

  7. Parametric output-only identification of time-varying structures using a kernel recursive extended least squares TARMA approach

    Science.gov (United States)

    Ma, Zhi-Sai; Liu, Li; Zhou, Si-Da; Yu, Lei; Naets, Frank; Heylen, Ward; Desmet, Wim

    2018-01-01

    The problem of parametric output-only identification of time-varying structures in a recursive manner is considered. A kernelized time-dependent autoregressive moving average (TARMA) model is proposed by expanding the time-varying model parameters onto the basis set of kernel functions in a reproducing kernel Hilbert space. An exponentially weighted kernel recursive extended least squares TARMA identification scheme is proposed, and a sliding-window technique is subsequently applied to fix the computational complexity for each consecutive update, allowing the method to operate online in time-varying environments. The proposed sliding-window exponentially weighted kernel recursive extended least squares TARMA method is employed for the identification of a laboratory time-varying structure consisting of a simply supported beam and a moving mass sliding on it. The proposed method is comparatively assessed against an existing recursive pseudo-linear regression TARMA method via Monte Carlo experiments and shown to be capable of accurately tracking the time-varying dynamics. Furthermore, the comparisons demonstrate the superior achievable accuracy, lower computational complexity and enhanced online identification capability of the proposed kernel recursive extended least squares TARMA approach.

  8. Bubble-Enriched Least-Squares Finite Element Method for Transient Advective Transport

    Directory of Open Access Journals (Sweden)

    Rajeev Kumar

    2008-01-01

    Full Text Available The least-squares finite element method (LSFEM has received increasing attention in recent years due to advantages over the Galerkin finite element method (GFEM. The method leads to a minimization problem in the L2-norm and thus results in a symmetric and positive definite matrix, even for first-order differential equations. In addition, the method contains an implicit streamline upwinding mechanism that prevents the appearance of oscillations that are characteristic of the Galerkin method. Thus, the least-squares approach does not require explicit stabilization and the associated stabilization parameters required by the Galerkin method. A new approach, the bubble enriched least-squares finite element method (BELSFEM, is presented and compared with the classical LSFEM. The BELSFEM requires a space-time element formulation and employs bubble functions in space and time to increase the accuracy of the finite element solution without degrading computational performance. We apply the BELSFEM and classical least-squares finite element methods to benchmark problems for 1D and 2D linear transport. The accuracy and performance are compared.

  9. Generalized least squares and empirical Bayes estimation in regional partial duration series index-flood modeling

    DEFF Research Database (Denmark)

    Madsen, Henrik; Rosbjerg, Dan

    1997-01-01

    parameters is inferred from regional data using generalized least squares (GLS) regression. Two different Bayesian T-year event estimators are introduced: a linear estimator that requires only some moments of the prior distributions to be specified and a parametric estimator that is based on specified......A regional estimation procedure that combines the index-flood concept with an empirical Bayes method for inferring regional information is introduced. The model is based on the partial duration series approach with generalized Pareto (GP) distributed exceedances. The prior information of the model...

  10. Non-linear HVAC computations using least square support vector machines

    International Nuclear Information System (INIS)

    Kumar, Mahendra; Kar, I.N.

    2009-01-01

    This paper aims to demonstrate application of least square support vector machines (LS-SVM) to model two complex heating, ventilating and air-conditioning (HVAC) relationships. The two applications considered are the estimation of the predicted mean vote (PMV) for thermal comfort and the generation of psychrometric chart. LS-SVM has the potential for quick, exact representations and also possesses a structure that facilitates hardware implementation. The results show very good agreement between function values computed from conventional model and LS-SVM model in real time. The robustness of LS-SVM models against input noises has also been analyzed.

  11. Selecting the correct weighting factors for linear and quadratic calibration curves with least-squares regression algorithm in bioanalytical LC-MS/MS assays and impacts of using incorrect weighting factors on curve stability, data quality, and assay performance.

    Science.gov (United States)

    Gu, Huidong; Liu, Guowen; Wang, Jian; Aubry, Anne-Françoise; Arnold, Mark E

    2014-09-16

    A simple procedure for selecting the correct weighting factors for linear and quadratic calibration curves with least-squares regression algorithm in bioanalytical LC-MS/MS assays is reported. The correct weighting factor is determined by the relationship between the standard deviation of instrument responses (σ) and the concentrations (x). The weighting factor of 1, 1/x, or 1/x(2) should be selected if, over the entire concentration range, σ is a constant, σ(2) is proportional to x, or σ is proportional to x, respectively. For the first time, we demonstrated with detailed scientific reasoning, solid historical data, and convincing justification that 1/x(2) should always be used as the weighting factor for all bioanalytical LC-MS/MS assays. The impacts of using incorrect weighting factors on curve stability, data quality, and assay performance were thoroughly investigated. It was found that the most stable curve could be obtained when the correct weighting factor was used, whereas other curves using incorrect weighting factors were unstable. It was also found that there was a very insignificant impact on the concentrations reported with calibration curves using incorrect weighting factors as the concentrations were always reported with the passing curves which actually overlapped with or were very close to the curves using the correct weighting factor. However, the use of incorrect weighting factors did impact the assay performance significantly. Finally, the difference between the weighting factors of 1/x(2) and 1/y(2) was discussed. All of the findings can be generalized and applied into other quantitative analysis techniques using calibration curves with weighted least-squares regression algorithm.

  12. A Novel Covert Agent for Stealthy Attacks on Industrial Control Systems Using Least Squares Support Vector Regression

    Directory of Open Access Journals (Sweden)

    Weize Li

    2018-01-01

    Full Text Available Research on stealthiness has become an important topic in the field of data integrity (DI attacks. To construct stealthy DI attacks, a common assumption in most related studies is that attackers have prior model knowledge of physical systems. In this paper, such assumption is relaxed and a covert agent is proposed based on the least squares support vector regression (LSSVR. By estimating a plant model from control and sensory data, the LSSVR-based covert agent can closely imitate the behavior of the physical plant. Then, the covert agent is used to construct a covert loop, which can keep the controller’s input and output both stealthy over a finite time window. Experiments have been carried out to show the effectiveness of the proposed method.

  13. Small-kernel constrained-least-squares restoration of sampled image data

    Science.gov (United States)

    Hazra, Rajeeb; Park, Stephen K.

    1992-10-01

    Constrained least-squares image restoration, first proposed by Hunt twenty years ago, is a linear image restoration technique in which the restoration filter is derived by maximizing the smoothness of the restored image while satisfying a fidelity constraint related to how well the restored image matches the actual data. The traditional derivation and implementation of the constrained least-squares restoration filter is based on an incomplete discrete/discrete system model which does not account for the effects of spatial sampling and image reconstruction. For many imaging systems, these effects are significant and should not be ignored. In a recent paper Park demonstrated that a derivation of the Wiener filter based on the incomplete discrete/discrete model can be extended to a more comprehensive end-to-end, continuous/discrete/continuous model. In a similar way, in this paper, we show that a derivation of the constrained least-squares filter based on the discrete/discrete model can also be extended to this more comprehensive continuous/discrete/continuous model and, by so doing, an improved restoration filter is derived. Building on previous work by Reichenbach and Park for the Wiener filter, we also show that this improved constrained least-squares restoration filter can be efficiently implemented as a small-kernel convolution in the spatial domain.

  14. Linear least-squares method for global luminescent oil film skin friction field analysis

    Science.gov (United States)

    Lee, Taekjin; Nonomura, Taku; Asai, Keisuke; Liu, Tianshu

    2018-06-01

    A data analysis method based on the linear least-squares (LLS) method was developed for the extraction of high-resolution skin friction fields from global luminescent oil film (GLOF) visualization images of a surface in an aerodynamic flow. In this method, the oil film thickness distribution and its spatiotemporal development are measured by detecting the luminescence intensity of the thin oil film. From the resulting set of GLOF images, the thin oil film equation is solved to obtain an ensemble-averaged (steady) skin friction field as an inverse problem. In this paper, the formulation of a discrete linear system of equations for the LLS method is described, and an error analysis is given to identify the main error sources and the relevant parameters. Simulations were conducted to evaluate the accuracy of the LLS method and the effects of the image patterns, image noise, and sample numbers on the results in comparison with the previous snapshot-solution-averaging (SSA) method. An experimental case is shown to enable the comparison of the results obtained using conventional oil flow visualization and those obtained using both the LLS and SSA methods. The overall results show that the LLS method is more reliable than the SSA method and the LLS method can yield a more detailed skin friction topology in an objective way.

  15. First-order system least squares for the pure traction problem in planar linear elasticity

    Energy Technology Data Exchange (ETDEWEB)

    Cai, Z.; Manteuffel, T.; McCormick, S.; Parter, S.

    1996-12-31

    This talk will develop two first-order system least squares (FOSLS) approaches for the solution of the pure traction problem in planar linear elasticity. Both are two-stage algorithms that first solve for the gradients of displacement, then for the displacement itself. One approach, which uses L{sup 2} norms to define the FOSLS functional, is shown under certain H{sup 2} regularity assumptions to admit optimal H{sup 1}-like performance for standard finite element discretization and standard multigrid solution methods that is uniform in the Poisson ratio for all variables. The second approach, which is based on H{sup -1} norms, is shown under general assumptions to admit optimal uniform performance for displacement flux in an L{sup 2} norm and for displacement in an H{sup 1} norm. These methods do not degrade as other methods generally do when the material properties approach the incompressible limit.

  16. Emulating facial biomechanics using multivariate partial least squares surrogate models.

    Science.gov (United States)

    Wu, Tim; Martens, Harald; Hunter, Peter; Mithraratne, Kumar

    2014-11-01

    A detailed biomechanical model of the human face driven by a network of muscles is a useful tool in relating the muscle activities to facial deformations. However, lengthy computational times often hinder its applications in practical settings. The objective of this study is to replace precise but computationally demanding biomechanical model by a much faster multivariate meta-model (surrogate model), such that a significant speedup (to real-time interactive speed) can be achieved. Using a multilevel fractional factorial design, the parameter space of the biomechanical system was probed from a set of sample points chosen to satisfy maximal rank optimality and volume filling. The input-output relationship at these sampled points was then statistically emulated using linear and nonlinear, cross-validated, partial least squares regression models. It was demonstrated that these surrogate models can mimic facial biomechanics efficiently and reliably in real-time. Copyright © 2014 John Wiley & Sons, Ltd.

  17. Least Square Support Vector Machine Classifier vs a Logistic Regression Classifier on the Recognition of Numeric Digits

    Directory of Open Access Journals (Sweden)

    Danilo A. López-Sarmiento

    2013-11-01

    Full Text Available In this paper is compared the performance of a multi-class least squares support vector machine (LSSVM mc versus a multi-class logistic regression classifier to problem of recognizing the numeric digits (0-9 handwritten. To develop the comparison was used a data set consisting of 5000 images of handwritten numeric digits (500 images for each number from 0-9, each image of 20 x 20 pixels. The inputs to each of the systems were vectors of 400 dimensions corresponding to each image (not done feature extraction. Both classifiers used OneVsAll strategy to enable multi-classification and a random cross-validation function for the process of minimizing the cost function. The metrics of comparison were precision and training time under the same computational conditions. Both techniques evaluated showed a precision above 95 %, with LS-SVM slightly more accurate. However the computational cost if we found a marked difference: LS-SVM training requires time 16.42 % less than that required by the logistic regression model based on the same low computational conditions.

  18. Aspects of robust linear regression

    NARCIS (Netherlands)

    Davies, P.L.

    1993-01-01

    Section 1 of the paper contains a general discussion of robustness. In Section 2 the influence function of the Hampel-Rousseeuw least median of squares estimator is derived. Linearly invariant weak metrics are constructed in Section 3. It is shown in Section 4 that $S$-estimators satisfy an exact

  19. Efficient Model Selection for Sparse Least-Square SVMs

    Directory of Open Access Journals (Sweden)

    Xiao-Lei Xia

    2013-01-01

    Full Text Available The Forward Least-Squares Approximation (FLSA SVM is a newly-emerged Least-Square SVM (LS-SVM whose solution is extremely sparse. The algorithm uses the number of support vectors as the regularization parameter and ensures the linear independency of the support vectors which span the solution. This paper proposed a variant of the FLSA-SVM, namely, Reduced FLSA-SVM which is of reduced computational complexity and memory requirements. The strategy of “contexts inheritance” is introduced to improve the efficiency of tuning the regularization parameter for both the FLSA-SVM and the RFLSA-SVM algorithms. Experimental results on benchmark datasets showed that, compared to the SVM and a number of its variants, the RFLSA-SVM solutions contain a reduced number of support vectors, while maintaining competitive generalization abilities. With respect to the time cost for tuning of the regularize parameter, the RFLSA-SVM algorithm was empirically demonstrated fastest compared to FLSA-SVM, the LS-SVM, and the SVM algorithms.

  20. Spectral/hp least-squares finite element formulation for the Navier-Stokes equations

    International Nuclear Information System (INIS)

    Pontaza, J.P.; Reddy, J.N.

    2003-01-01

    We consider the application of least-squares finite element models combined with spectral/hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/hp algorithm to the numerical solution of the Navier-Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L 2 least-squares functional and L 2 error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier-Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation

  1. Simultaneous determination of penicillin G salts by infrared spectroscopy: Evaluation of combining orthogonal signal correction with radial basis function-partial least squares regression

    Science.gov (United States)

    Talebpour, Zahra; Tavallaie, Roya; Ahmadi, Seyyed Hamid; Abdollahpour, Assem

    2010-09-01

    In this study, a new method for the simultaneous determination of penicillin G salts in pharmaceutical mixture via FT-IR spectroscopy combined with chemometrics was investigated. The mixture of penicillin G salts is a complex system due to similar analytical characteristics of components. Partial least squares (PLS) and radial basis function-partial least squares (RBF-PLS) were used to develop the linear and nonlinear relation between spectra and components, respectively. The orthogonal signal correction (OSC) preprocessing method was used to correct unexpected information, such as spectral overlapping and scattering effects. In order to compare the influence of OSC on PLS and RBF-PLS models, the optimal linear (PLS) and nonlinear (RBF-PLS) models based on conventional and OSC preprocessed spectra were established and compared. The obtained results demonstrated that OSC clearly enhanced the performance of both RBF-PLS and PLS calibration models. Also in the case of some nonlinear relation between spectra and component, OSC-RBF-PLS gave satisfactory results than OSC-PLS model which indicated that the OSC was helpful to remove extrinsic deviations from linearity without elimination of nonlinear information related to component. The chemometric models were tested on an external dataset and finally applied to the analysis commercialized injection product of penicillin G salts.

  2. Estimating the kinetic parameters of activated sludge storage using weighted non-linear least-squares and accelerating genetic algorithm.

    Science.gov (United States)

    Fang, Fang; Ni, Bing-Jie; Yu, Han-Qing

    2009-06-01

    In this study, weighted non-linear least-squares analysis and accelerating genetic algorithm are integrated to estimate the kinetic parameters of substrate consumption and storage product formation of activated sludge. A storage product formation equation is developed and used to construct the objective function for the determination of its production kinetics. The weighted least-squares analysis is employed to calculate the differences in the storage product concentration between the model predictions and the experimental data as the sum of squared weighted errors. The kinetic parameters for the substrate consumption and the storage product formation are estimated to be the maximum heterotrophic growth rate of 0.121/h, the yield coefficient of 0.44 mg CODX/mg CODS (COD, chemical oxygen demand) and the substrate half saturation constant of 16.9 mg/L, respectively, by minimizing the objective function using a real-coding-based accelerating genetic algorithm. Also, the fraction of substrate electrons diverted to the storage product formation is estimated to be 0.43 mg CODSTO/mg CODS. The validity of our approach is confirmed by the results of independent tests and the kinetic parameter values reported in literature, suggesting that this approach could be useful to evaluate the product formation kinetics of mixed cultures like activated sludge. More importantly, as this integrated approach could estimate the kinetic parameters rapidly and accurately, it could be applied to other biological processes.

  3. Newton-Gauss Algorithm of Robust Weighted Total Least Squares Model

    Directory of Open Access Journals (Sweden)

    WANG Bin

    2015-06-01

    Full Text Available Based on the Newton-Gauss iterative algorithm of weighted total least squares (WTLS, a robust WTLS (RWTLS model is presented. The model utilizes the standardized residuals to construct the weight factor function and the square root of the variance component estimator with robustness is obtained by introducing the median method. Therefore, the robustness in both the observation and structure spaces can be simultaneously achieved. To obtain standardized residuals, the linearly approximate cofactor propagation law is employed to derive the expression of the cofactor matrix of WTLS residuals. The iterative calculation steps for RWTLS are also described. The experiment indicates that the model proposed in this paper exhibits satisfactory robustness for gross errors handling problem of WTLS, the obtained parameters have no significant difference with the results of WTLS without gross errors. Therefore, it is superior to the robust weighted total least squares model directly constructed with residuals.

  4. Wind Tunnel Strain-Gage Balance Calibration Data Analysis Using a Weighted Least Squares Approach

    Science.gov (United States)

    Ulbrich, N.; Volden, T.

    2017-01-01

    A new approach is presented that uses a weighted least squares fit to analyze wind tunnel strain-gage balance calibration data. The weighted least squares fit is specifically designed to increase the influence of single-component loadings during the regression analysis. The weighted least squares fit also reduces the impact of calibration load schedule asymmetries on the predicted primary sensitivities of the balance gages. A weighting factor between zero and one is assigned to each calibration data point that depends on a simple count of its intentionally loaded load components or gages. The greater the number of a data point's intentionally loaded load components or gages is, the smaller its weighting factor becomes. The proposed approach is applicable to both the Iterative and Non-Iterative Methods that are used for the analysis of strain-gage balance calibration data in the aerospace testing community. The Iterative Method uses a reasonable estimate of the tare corrected load set as input for the determination of the weighting factors. The Non-Iterative Method, on the other hand, uses gage output differences relative to the natural zeros as input for the determination of the weighting factors. Machine calibration data of a six-component force balance is used to illustrate benefits of the proposed weighted least squares fit. In addition, a detailed derivation of the PRESS residuals associated with a weighted least squares fit is given in the appendices of the paper as this information could not be found in the literature. These PRESS residuals may be needed to evaluate the predictive capabilities of the final regression models that result from a weighted least squares fit of the balance calibration data.

  5. A Two-Layer Least Squares Support Vector Machine Approach to Credit Risk Assessment

    Science.gov (United States)

    Liu, Jingli; Li, Jianping; Xu, Weixuan; Shi, Yong

    Least squares support vector machine (LS-SVM) is a revised version of support vector machine (SVM) and has been proved to be a useful tool for pattern recognition. LS-SVM had excellent generalization performance and low computational cost. In this paper, we propose a new method called two-layer least squares support vector machine which combines kernel principle component analysis (KPCA) and linear programming form of least square support vector machine. With this method sparseness and robustness is obtained while solving large dimensional and large scale database. A U.S. commercial credit card database is used to test the efficiency of our method and the result proved to be a satisfactory one.

  6. A Trajectory Regression Clustering Technique Combining a Novel Fuzzy C-Means Clustering Algorithm with the Least Squares Method

    Directory of Open Access Journals (Sweden)

    Xiangbing Zhou

    2018-04-01

    Full Text Available Rapidly growing GPS (Global Positioning System trajectories hide much valuable information, such as city road planning, urban travel demand, and population migration. In order to mine the hidden information and to capture better clustering results, a trajectory regression clustering method (an unsupervised trajectory clustering method is proposed to reduce local information loss of the trajectory and to avoid getting stuck in the local optimum. Using this method, we first define our new concept of trajectory clustering and construct a novel partitioning (angle-based partitioning method of line segments; second, the Lagrange-based method and Hausdorff-based K-means++ are integrated in fuzzy C-means (FCM clustering, which are used to maintain the stability and the robustness of the clustering process; finally, least squares regression model is employed to achieve regression clustering of the trajectory. In our experiment, the performance and effectiveness of our method is validated against real-world taxi GPS data. When comparing our clustering algorithm with the partition-based clustering algorithms (K-means, K-median, and FCM, our experimental results demonstrate that the presented method is more effective and generates a more reasonable trajectory.

  7. Efficient design of gain-flattened multi-pump Raman fiber amplifiers using least squares support vector regression

    Science.gov (United States)

    Chen, Jing; Qiu, Xiaojie; Yin, Cunyi; Jiang, Hao

    2018-02-01

    An efficient method to design the broadband gain-flattened Raman fiber amplifier with multiple pumps is proposed based on least squares support vector regression (LS-SVR). A multi-input multi-output LS-SVR model is introduced to replace the complicated solving process of the nonlinear coupled Raman amplification equation. The proposed approach contains two stages: offline training stage and online optimization stage. During the offline stage, the LS-SVR model is trained. Owing to the good generalization capability of LS-SVR, the net gain spectrum can be directly and accurately obtained when inputting any combination of the pump wavelength and power to the well-trained model. During the online stage, we incorporate the LS-SVR model into the particle swarm optimization algorithm to find the optimal pump configuration. The design results demonstrate that the proposed method greatly shortens the computation time and enhances the efficiency of the pump parameter optimization for Raman fiber amplifier design.

  8. A robust regression based on weighted LSSVM and penalized trimmed squares

    International Nuclear Information System (INIS)

    Liu, Jianyong; Wang, Yong; Fu, Chengqun; Guo, Jie; Yu, Qin

    2016-01-01

    Least squares support vector machine (LS-SVM) for nonlinear regression is sensitive to outliers in the field of machine learning. Weighted LS-SVM (WLS-SVM) overcomes this drawback by adding weight to each training sample. However, as the number of outliers increases, the accuracy of WLS-SVM may decrease. In order to improve the robustness of WLS-SVM, a new robust regression method based on WLS-SVM and penalized trimmed squares (WLSSVM–PTS) has been proposed. The algorithm comprises three main stages. The initial parameters are obtained by least trimmed squares at first. Then, the significant outliers are identified and eliminated by the Fast-PTS algorithm. The remaining samples with little outliers are estimated by WLS-SVM at last. The statistical tests of experimental results carried out on numerical datasets and real-world datasets show that the proposed WLSSVM–PTS is significantly robust than LS-SVM, WLS-SVM and LSSVM–LTS.

  9. Recursive least squares method of regression coefficients estimation as a special case of Kalman filter

    Science.gov (United States)

    Borodachev, S. M.

    2016-06-01

    The simple derivation of recursive least squares (RLS) method equations is given as special case of Kalman filter estimation of a constant system state under changing observation conditions. A numerical example illustrates application of RLS to multicollinearity problem.

  10. Deformation analysis with Total Least Squares

    Directory of Open Access Journals (Sweden)

    M. Acar

    2006-01-01

    Full Text Available Deformation analysis is one of the main research fields in geodesy. Deformation analysis process comprises measurement and analysis phases. Measurements can be collected using several techniques. The output of the evaluation of the measurements is mainly point positions. In the deformation analysis phase, the coordinate changes in the point positions are investigated. Several models or approaches can be employed for the analysis. One approach is based on a Helmert or similarity coordinate transformation where the displacements and the respective covariance matrix are transformed into a unique datum. Traditionally a Least Squares (LS technique is used for the transformation procedure. Another approach that could be introduced as an alternative methodology is the Total Least Squares (TLS that is considerably a new approach in geodetic applications. In this study, in order to determine point displacements, 3-D coordinate transformations based on the Helmert transformation model were carried out individually by the Least Squares (LS and the Total Least Squares (TLS, respectively. The data used in this study was collected by GPS technique in a landslide area located nearby Istanbul. The results obtained from these two approaches have been compared.

  11. Particle swarm optimization-based least squares support vector regression for critical heat flux prediction

    International Nuclear Information System (INIS)

    Jiang, B.T.; Zhao, F.Y.

    2013-01-01

    Highlights: ► CHF data are collected from the published literature. ► Less training data are used to train the LSSVR model. ► PSO is adopted to optimize the key parameters to improve the model precision. ► The reliability of LSSVR is proved through parametric trends analysis. - Abstract: In view of practical importance of critical heat flux (CHF) for design and safety of nuclear reactors, accurate prediction of CHF is of utmost significance. This paper presents a novel approach using least squares support vector regression (LSSVR) and particle swarm optimization (PSO) to predict CHF. Two available published datasets are used to train and test the proposed algorithm, in which PSO is employed to search for the best parameters involved in LSSVR model. The CHF values obtained by the LSSVR model are compared with the corresponding experimental values and those of a previous method, adaptive neuro fuzzy inference system (ANFIS). This comparison is also carried out in the investigation of parametric trends of CHF. It is found that the proposed method can achieve the desired performance and yields a more satisfactory fit with experimental results than ANFIS. Therefore, LSSVR method is likely to be suitable for other parameters processing such as CHF

  12. Robust regularized least-squares beamforming approach to signal estimation

    KAUST Repository

    Suliman, Mohamed Abdalla Elhag

    2017-05-12

    In this paper, we address the problem of robust adaptive beamforming of signals received by a linear array. The challenge associated with the beamforming problem is twofold. Firstly, the process requires the inversion of the usually ill-conditioned covariance matrix of the received signals. Secondly, the steering vector pertaining to the direction of arrival of the signal of interest is not known precisely. To tackle these two challenges, the standard capon beamformer is manipulated to a form where the beamformer output is obtained as a scaled version of the inner product of two vectors. The two vectors are linearly related to the steering vector and the received signal snapshot, respectively. The linear operator, in both cases, is the square root of the covariance matrix. A regularized least-squares (RLS) approach is proposed to estimate these two vectors and to provide robustness without exploiting prior information. Simulation results show that the RLS beamformer using the proposed regularization algorithm outperforms state-of-the-art beamforming algorithms, as well as another RLS beamformers using a standard regularization approaches.

  13. A constrained robust least squares approach for contaminant release history identification

    Science.gov (United States)

    Sun, Alexander Y.; Painter, Scott L.; Wittmeyer, Gordon W.

    2006-04-01

    Contaminant source identification is an important type of inverse problem in groundwater modeling and is subject to both data and model uncertainty. Model uncertainty was rarely considered in the previous studies. In this work, a robust framework for solving contaminant source recovery problems is introduced. The contaminant source identification problem is first cast into one of solving uncertain linear equations, where the response matrix is constructed using a superposition technique. The formulation presented here is general and is applicable to any porous media flow and transport solvers. The robust least squares (RLS) estimator, which originated in the field of robust identification, directly accounts for errors arising from model uncertainty and has been shown to significantly reduce the sensitivity of the optimal solution to perturbations in model and data. In this work, a new variant of RLS, the constrained robust least squares (CRLS), is formulated for solving uncertain linear equations. CRLS allows for additional constraints, such as nonnegativity, to be imposed. The performance of CRLS is demonstrated through one- and two-dimensional test problems. When the system is ill-conditioned and uncertain, it is found that CRLS gave much better performance than its classical counterpart, the nonnegative least squares. The source identification framework developed in this work thus constitutes a reliable tool for recovering source release histories in real applications.

  14. Least-squares reverse time migration of multiples

    KAUST Repository

    Zhang, Dongliang; Schuster, Gerard T.

    2013-01-01

    The theory of least-squares reverse time migration of multiples (RTMM) is presented. In this method, least squares migration (LSM) is used to image free-surface multiples where the recorded traces are used as the time histories of the virtual

  15. Least Squares Inference on Integrated Volatility and the Relationship between Efficient Prices and Noise

    DEFF Research Database (Denmark)

    Nolte, Ingmar; Voev, Valeri

    The expected value of sums of squared intraday returns (realized variance) gives rise to a least squares regression which adapts itself to the assumptions of the noise process and allows for a joint inference on integrated volatility (IV), noise moments and price-noise relations. In the iid noise...

  16. Gauss’s, Cholesky’s and Banachiewicz’s Contributions to Least Squares

    DEFF Research Database (Denmark)

    Gustavson, Fred G.; Wasniewski, Jerzy

    This paper describes historically Gauss’s contributions to the area of Least Squares. Also mentioned are Cholesky’s and Banachiewicz’s contributions to linear algebra. The material given is backup information to a Tutorial given at PPAM 2011 to honor Cholesky on the hundred anniversary of his...

  17. Least Squares Inference on Integrated Volatility and the Relationship between Efficient Prices and Noise

    OpenAIRE

    Nolte, Ingmar; Voev, Valeri

    2009-01-01

    The expected value of sums of squared intraday returns (realized variance)gives rise to a least squares regression which adapts itself to the assumptions ofthe noise process and allows for a joint inference on integrated volatility (IV),noise moments and price-noise relations. In the iid noise case we derive theasymptotic variance of the regression parameter estimating the IV, show thatit is consistent and compare its asymptotic efficiency against alternative consistentIV measures. In case of...

  18. A new stabilized least-squares imaging condition

    International Nuclear Information System (INIS)

    Vivas, Flor A; Pestana, Reynam C; Ursin, Bjørn

    2009-01-01

    The classical deconvolution imaging condition consists of dividing the upgoing wave field by the downgoing wave field and summing over all frequencies and sources. The least-squares imaging condition consists of summing the cross-correlation of the upgoing and downgoing wave fields over all frequencies and sources, and dividing the result by the total energy of the downgoing wave field. This procedure is more stable than using the classical imaging condition, but it still requires stabilization in zones where the energy of the downgoing wave field is small. To stabilize the least-squares imaging condition, the energy of the downgoing wave field is replaced by its average value computed in a horizontal plane in poorly illuminated regions. Applications to the Marmousi and Sigsbee2A data sets show that the stabilized least-squares imaging condition produces better images than the least-squares and cross-correlation imaging conditions

  19. Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations

    KAUST Repository

    Carlberg, Kevin

    2010-10-28

    A Petrov-Galerkin projection method is proposed for reducing the dimension of a discrete non-linear static or dynamic computational model in view of enabling its processing in real time. The right reduced-order basis is chosen to be invariant and is constructed using the Proper Orthogonal Decomposition method. The left reduced-order basis is selected to minimize the two-norm of the residual arising at each Newton iteration. Thus, this basis is iteration-dependent, enables capturing of non-linearities, and leads to the globally convergent Gauss-Newton method. To avoid the significant computational cost of assembling the reduced-order operators, the residual and action of the Jacobian on the right reduced-order basis are each approximated by the product of an invariant, large-scale matrix, and an iteration-dependent, smaller one. The invariant matrix is computed using a data compression procedure that meets proposed consistency requirements. The iteration-dependent matrix is computed to enable the least-squares reconstruction of some entries of the approximated quantities. The results obtained for the solution of a turbulent flow problem and several non-linear structural dynamics problems highlight the merit of the proposed consistency requirements. They also demonstrate the potential of this method to significantly reduce the computational cost associated with high-dimensional non-linear models while retaining their accuracy. © 2010 John Wiley & Sons, Ltd.

  20. Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations

    KAUST Repository

    Carlberg, Kevin; Bou-Mosleh, Charbel; Farhat, Charbel

    2010-01-01

    A Petrov-Galerkin projection method is proposed for reducing the dimension of a discrete non-linear static or dynamic computational model in view of enabling its processing in real time. The right reduced-order basis is chosen to be invariant and is constructed using the Proper Orthogonal Decomposition method. The left reduced-order basis is selected to minimize the two-norm of the residual arising at each Newton iteration. Thus, this basis is iteration-dependent, enables capturing of non-linearities, and leads to the globally convergent Gauss-Newton method. To avoid the significant computational cost of assembling the reduced-order operators, the residual and action of the Jacobian on the right reduced-order basis are each approximated by the product of an invariant, large-scale matrix, and an iteration-dependent, smaller one. The invariant matrix is computed using a data compression procedure that meets proposed consistency requirements. The iteration-dependent matrix is computed to enable the least-squares reconstruction of some entries of the approximated quantities. The results obtained for the solution of a turbulent flow problem and several non-linear structural dynamics problems highlight the merit of the proposed consistency requirements. They also demonstrate the potential of this method to significantly reduce the computational cost associated with high-dimensional non-linear models while retaining their accuracy. © 2010 John Wiley & Sons, Ltd.

  1. Fruit fly optimization based least square support vector regression for blind image restoration

    Science.gov (United States)

    Zhang, Jiao; Wang, Rui; Li, Junshan; Yang, Yawei

    2014-11-01

    The goal of image restoration is to reconstruct the original scene from a degraded observation. It is a critical and challenging task in image processing. Classical restorations require explicit knowledge of the point spread function and a description of the noise as priors. However, it is not practical for many real image processing. The recovery processing needs to be a blind image restoration scenario. Since blind deconvolution is an ill-posed problem, many blind restoration methods need to make additional assumptions to construct restrictions. Due to the differences of PSF and noise energy, blurring images can be quite different. It is difficult to achieve a good balance between proper assumption and high restoration quality in blind deconvolution. Recently, machine learning techniques have been applied to blind image restoration. The least square support vector regression (LSSVR) has been proven to offer strong potential in estimating and forecasting issues. Therefore, this paper proposes a LSSVR-based image restoration method. However, selecting the optimal parameters for support vector machine is essential to the training result. As a novel meta-heuristic algorithm, the fruit fly optimization algorithm (FOA) can be used to handle optimization problems, and has the advantages of fast convergence to the global optimal solution. In the proposed method, the training samples are created from a neighborhood in the degraded image to the central pixel in the original image. The mapping between the degraded image and the original image is learned by training LSSVR. The two parameters of LSSVR are optimized though FOA. The fitness function of FOA is calculated by the restoration error function. With the acquired mapping, the degraded image can be recovered. Experimental results show the proposed method can obtain satisfactory restoration effect. Compared with BP neural network regression, SVR method and Lucy-Richardson algorithm, it speeds up the restoration rate and

  2. Plane-wave least-squares reverse-time migration

    KAUST Repository

    Dai, Wei

    2013-06-03

    A plane-wave least-squares reverse-time migration (LSRTM) is formulated with a new parameterization, where the migration image of each shot gather is updated separately and an ensemble of prestack images is produced along with common image gathers. The merits of plane-wave prestack LSRTM are the following: (1) plane-wave prestack LSRTM can sometimes offer stable convergence even when the migration velocity has bulk errors of up to 5%; (2) to significantly reduce computation cost, linear phase-shift encoding is applied to hundreds of shot gathers to produce dozens of plane waves. Unlike phase-shift encoding with random time shifts applied to each shot gather, plane-wave encoding can be effectively applied to data with a marine streamer geometry. (3) Plane-wave prestack LSRTM can provide higher-quality images than standard reverse-time migration. Numerical tests on the Marmousi2 model and a marine field data set are performed to illustrate the benefits of plane-wave LSRTM. Empirical results show that LSRTM in the plane-wave domain, compared to standard reversetime migration, produces images efficiently with fewer artifacts and better spatial resolution. Moreover, the prestack image ensemble accommodates more unknowns to makes it more robust than conventional least-squares migration in the presence of migration velocity errors. © 2013 Society of Exploration Geophysicists.

  3. Uncertainty analysis of pollutant build-up modelling based on a Bayesian weighted least squares approach

    International Nuclear Information System (INIS)

    Haddad, Khaled; Egodawatta, Prasanna; Rahman, Ataur; Goonetilleke, Ashantha

    2013-01-01

    Reliable pollutant build-up prediction plays a critical role in the accuracy of urban stormwater quality modelling outcomes. However, water quality data collection is resource demanding compared to streamflow data monitoring, where a greater quantity of data is generally available. Consequently, available water quality datasets span only relatively short time scales unlike water quantity data. Therefore, the ability to take due consideration of the variability associated with pollutant processes and natural phenomena is constrained. This in turn gives rise to uncertainty in the modelling outcomes as research has shown that pollutant loadings on catchment surfaces and rainfall within an area can vary considerably over space and time scales. Therefore, the assessment of model uncertainty is an essential element of informed decision making in urban stormwater management. This paper presents the application of a range of regression approaches such as ordinary least squares regression, weighted least squares regression and Bayesian weighted least squares regression for the estimation of uncertainty associated with pollutant build-up prediction using limited datasets. The study outcomes confirmed that the use of ordinary least squares regression with fixed model inputs and limited observational data may not provide realistic estimates. The stochastic nature of the dependent and independent variables need to be taken into consideration in pollutant build-up prediction. It was found that the use of the Bayesian approach along with the Monte Carlo simulation technique provides a powerful tool, which attempts to make the best use of the available knowledge in prediction and thereby presents a practical solution to counteract the limitations which are otherwise imposed on water quality modelling. - Highlights: ► Water quality data spans short time scales leading to significant model uncertainty. ► Assessment of uncertainty essential for informed decision making in water

  4. Squares of Random Linear Codes

    DEFF Research Database (Denmark)

    Cascudo Pueyo, Ignacio; Cramer, Ronald; Mirandola, Diego

    2015-01-01

    a positive answer, for codes of dimension $k$ and length roughly $\\frac{1}{2}k^2$ or smaller. Moreover, the convergence speed is exponential if the difference $k(k+1)/2-n$ is at least linear in $k$. The proof uses random coding and combinatorial arguments, together with algebraic tools involving the precise......Given a linear code $C$, one can define the $d$-th power of $C$ as the span of all componentwise products of $d$ elements of $C$. A power of $C$ may quickly fill the whole space. Our purpose is to answer the following question: does the square of a code ``typically'' fill the whole space? We give...

  5. Comparison of l₁-Norm SVR and Sparse Coding Algorithms for Linear Regression.

    Science.gov (United States)

    Zhang, Qingtian; Hu, Xiaolin; Zhang, Bo

    2015-08-01

    Support vector regression (SVR) is a popular function estimation technique based on Vapnik's concept of support vector machine. Among many variants, the l1-norm SVR is known to be good at selecting useful features when the features are redundant. Sparse coding (SC) is a technique widely used in many areas and a number of efficient algorithms are available. Both l1-norm SVR and SC can be used for linear regression. In this brief, the close connection between the l1-norm SVR and SC is revealed and some typical algorithms are compared for linear regression. The results show that the SC algorithms outperform the Newton linear programming algorithm, an efficient l1-norm SVR algorithm, in efficiency. The algorithms are then used to design the radial basis function (RBF) neural networks. Experiments on some benchmark data sets demonstrate the high efficiency of the SC algorithms. In particular, one of the SC algorithms, the orthogonal matching pursuit is two orders of magnitude faster than a well-known RBF network designing algorithm, the orthogonal least squares algorithm.

  6. Non-destructive and rapid prediction of moisture content in red pepper (Capsicum annuum L.) powder using near-infrared spectroscopy and a partial least squares regression model

    Science.gov (United States)

    Purpose: The aim of this study was to develop a technique for the non-destructive and rapid prediction of the moisture content in red pepper powder using near-infrared (NIR) spectroscopy and a partial least squares regression (PLSR) model. Methods: Three red pepper powder products were separated in...

  7. Performance improvement of shunt active power filter based on non-linear least-square approach

    DEFF Research Database (Denmark)

    Terriche, Yacine

    2018-01-01

    Nowadays, the shunt active power filters (SAPFs) have become a popular solution for power quality issues. A crucial issue in controlling the SAPFs which is highly correlated with their accuracy, flexibility and dynamic behavior, is generating the reference compensating current (RCC). The synchron......Nowadays, the shunt active power filters (SAPFs) have become a popular solution for power quality issues. A crucial issue in controlling the SAPFs which is highly correlated with their accuracy, flexibility and dynamic behavior, is generating the reference compensating current (RCC......). The synchronous reference frame (SRF) approach is widely used for generating the RCC due to its simplicity and computation efficiency. However, the SRF approach needs precise information of the voltage phase which becomes a challenge under adverse grid conditions. A typical solution to answer this need....... This paper proposes an improved open loop strategy which is unconditionally stable and flexible. The proposed method which is based on non-linear least square (NLS) approach can extract the fundamental voltage and estimates its phase within only half cycle, even in the presence of odd harmonics and dc offset...

  8. The Total Least Squares Problem in AX approximate to B: A New Classification with the Relationship to the Classical Works

    Czech Academy of Sciences Publication Activity Database

    Hnětynková, I.; Plešinger, Martin; Sima, D.M.; Strakoš, Z.; Huffel van, S.

    2011-01-01

    Roč. 32, č. 3 (2011), s. 748-770 ISSN 0895-4798 R&D Projects: GA AV ČR IAA100300802 Grant - others:GA ČR(CZ) GA201/09/0917 Program:GA Institutional research plan: CEZ:AV0Z10300504 Keywords : total least squares * multiple right-hand sides * linear approximation problems * orthogonally invariant problems * orthogonal regression * errors-in-variables modeling Subject RIV: BA - General Mathematics Impact factor: 1.368, year: 2011

  9. COLOR IMAGE RETRIEVAL BASED ON FEATURE FUSION THROUGH MULTIPLE LINEAR REGRESSION ANALYSIS

    Directory of Open Access Journals (Sweden)

    K. Seetharaman

    2015-08-01

    Full Text Available This paper proposes a novel technique based on feature fusion using multiple linear regression analysis, and the least-square estimation method is employed to estimate the parameters. The given input query image is segmented into various regions according to the structure of the image. The color and texture features are extracted on each region of the query image, and the features are fused together using the multiple linear regression model. The estimated parameters of the model, which is modeled based on the features, are formed as a vector called a feature vector. The Canberra distance measure is adopted to compare the feature vectors of the query and target images. The F-measure is applied to evaluate the performance of the proposed technique. The obtained results expose that the proposed technique is comparable to the other existing techniques.

  10. Fast Combinatorial Algorithm for the Solution of Linearly Constrained Least Squares Problems

    Science.gov (United States)

    Van Benthem, Mark H.; Keenan, Michael R.

    2008-11-11

    A fast combinatorial algorithm can significantly reduce the computational burden when solving general equality and inequality constrained least squares problems with large numbers of observation vectors. The combinatorial algorithm provides a mathematically rigorous solution and operates at great speed by reorganizing the calculations to take advantage of the combinatorial nature of the problems to be solved. The combinatorial algorithm exploits the structure that exists in large-scale problems in order to minimize the number of arithmetic operations required to obtain a solution.

  11. The comparison of partial least squares and principal component regression in simultaneous spectrophotometric determination of ascorbic acid, dopamine and uric acid in real samples

    Directory of Open Access Journals (Sweden)

    Habiboallah Khajehsharifi

    2017-05-01

    Full Text Available Partial least squares (PLS1 and principal component regression (PCR are two multivariate calibration methods that allow simultaneous determination of several analytes in spite of their overlapping spectra. In this research, a spectrophotometric method using PLS1 is proposed for the simultaneous determination of ascorbic acid (AA, dopamine (DA and uric acid (UA. The linear concentration ranges for AA, DA and UA were 1.76–47.55, 0.57–22.76 and 1.68–28.58 (in μg mL−1, respectively. However, PLS1 and PCR were applied to design calibration set based on absorption spectra in the 250–320 nm range for 36 different mixtures of AA, DA and UA, in all cases, the PLS1 calibration method showed more quantitative prediction ability than PCR method. Cross validation method was used to select the optimum number of principal components (NPC. The NPC for AA, DA and UA was found to be 4 by PLS1 and 5, 12, 8 by PCR. Prediction error sum of squares (PRESS of AA, DA and UA were 1.2461, 1.1144, 2.3104 for PLS1 and 11.0563, 1.3819, 4.0956 for PCR, respectively. Satisfactory results were achieved for the simultaneous determination of AA, DA and UA in some real samples such as human urine, serum and pharmaceutical formulations.

  12. Linear support vector regression and partial least squares chemometric models for determination of Hydrochlorothiazide and Benazepril hydrochloride in presence of related impurities: A comparative study

    Science.gov (United States)

    Naguib, Ibrahim A.; Abdelaleem, Eglal A.; Draz, Mohammed E.; Zaazaa, Hala E.

    2014-09-01

    Partial least squares regression (PLSR) and support vector regression (SVR) are two popular chemometric models that are being subjected to a comparative study in the presented work. The comparison shows their characteristics via applying them to analyze Hydrochlorothiazide (HCZ) and Benazepril hydrochloride (BZ) in presence of HCZ impurities; Chlorothiazide (CT) and Salamide (DSA) as a case study. The analysis results prove to be valid for analysis of the two active ingredients in raw materials and pharmaceutical dosage form through handling UV spectral data in range (220-350 nm). For proper analysis a 4 factor 4 level experimental design was established resulting in a training set consisting of 16 mixtures containing different ratios of interfering species. An independent test set consisting of 8 mixtures was used to validate the prediction ability of the suggested models. The results presented indicate the ability of mentioned multivariate calibration models to analyze HCZ and BZ in presence of HCZ impurities CT and DSA with high selectivity and accuracy of mean percentage recoveries of (101.01 ± 0.80) and (100.01 ± 0.87) for HCZ and BZ respectively using PLSR model and of (99.78 ± 0.80) and (99.85 ± 1.08) for HCZ and BZ respectively using SVR model. The analysis results of the dosage form were statistically compared to the reference HPLC method with no significant differences regarding accuracy and precision. SVR model gives more accurate results compared to PLSR model and show high generalization ability, however, PLSR still keeps the advantage of being fast to optimize and implement.

  13. Precision PEP-II optics measurement with an SVD-enhanced Least-Square fitting

    Science.gov (United States)

    Yan, Y. T.; Cai, Y.

    2006-03-01

    A singular value decomposition (SVD)-enhanced Least-Square fitting technique is discussed. By automatic identifying, ordering, and selecting dominant SVD modes of the derivative matrix that responds to the variations of the variables, the converging process of the Least-Square fitting is significantly enhanced. Thus the fitting speed can be fast enough for a fairly large system. This technique has been successfully applied to precision PEP-II optics measurement in which we determine all quadrupole strengths (both normal and skew components) and sextupole feed-downs as well as all BPM gains and BPM cross-plane couplings through Least-Square fitting of the phase advances and the Local Green's functions as well as the coupling ellipses among BPMs. The local Green's functions are specified by 4 local transfer matrix components R12, R34, R32, R14. These measurable quantities (the Green's functions, the phase advances and the coupling ellipse tilt angles and axis ratios) are obtained by analyzing turn-by-turn Beam Position Monitor (BPM) data with a high-resolution model-independent analysis (MIA). Once all of the quadrupoles and sextupole feed-downs are determined, we obtain a computer virtual accelerator which matches the real accelerator in linear optics. Thus, beta functions, linear coupling parameters, and interaction point (IP) optics characteristics can be measured and displayed.

  14. On structure-exploiting trust-region regularized nonlinear least squares algorithms for neural-network learning.

    Science.gov (United States)

    Mizutani, Eiji; Demmel, James W

    2003-01-01

    This paper briefly introduces our numerical linear algebra approaches for solving structured nonlinear least squares problems arising from 'multiple-output' neural-network (NN) models. Our algorithms feature trust-region regularization, and exploit sparsity of either the 'block-angular' residual Jacobian matrix or the 'block-arrow' Gauss-Newton Hessian (or Fisher information matrix in statistical sense) depending on problem scale so as to render a large class of NN-learning algorithms 'efficient' in both memory and operation costs. Using a relatively large real-world nonlinear regression application, we shall explain algorithmic strengths and weaknesses, analyzing simulation results obtained by both direct and iterative trust-region algorithms with two distinct NN models: 'multilayer perceptrons' (MLP) and 'complementary mixtures of MLP-experts' (or neuro-fuzzy modular networks).

  15. Handbook of Partial Least Squares Concepts, Methods and Applications

    CERN Document Server

    Vinzi, Vincenzo Esposito; Henseler, Jörg

    2010-01-01

    This handbook provides a comprehensive overview of Partial Least Squares (PLS) methods with specific reference to their use in marketing and with a discussion of the directions of current research and perspectives. It covers the broad area of PLS methods, from regression to structural equation modeling applications, software and interpretation of results. The handbook serves both as an introduction for those without prior knowledge of PLS and as a comprehensive reference for researchers and practitioners interested in the most recent advances in PLS methodology.

  16. On Solution of Total Least Squares Problems with Multiple Right-hand Sides

    Czech Academy of Sciences Publication Activity Database

    Hnětynková, I.; Plešinger, Martin; Strakoš, Zdeněk

    2008-01-01

    Roč. 8, č. 1 (2008), s. 10815-10816 ISSN 1617-7061 R&D Projects: GA AV ČR IAA100300802 Institutional research plan: CEZ:AV0Z10300504 Keywords : total least squares problem * multiple right-hand sides * linear approximation problem Subject RIV: BA - General Mathematics

  17. Implicit collinearity effect in linear regression: Application to basal ...

    African Journals Online (AJOL)

    Collinearity of predictor variables is a severe problem in the least square regression analysis. It contributes to the instability of regression coefficients and leads to a wrong prediction accuracy. Despite these problems, studies are conducted with a large number of observed and derived variables linked with a response ...

  18. A graphical method to evaluate spectral preprocessing in multivariate regression calibrations: example with Savitzky-Golay filters and partial least squares regression.

    Science.gov (United States)

    Delwiche, Stephen R; Reeves, James B

    2010-01-01

    In multivariate regression analysis of spectroscopy data, spectral preprocessing is often performed to reduce unwanted background information (offsets, sloped baselines) or accentuate absorption features in intrinsically overlapping bands. These procedures, also known as pretreatments, are commonly smoothing operations or derivatives. While such operations are often useful in reducing the number of latent variables of the actual decomposition and lowering residual error, they also run the risk of misleading the practitioner into accepting calibration equations that are poorly adapted to samples outside of the calibration. The current study developed a graphical method to examine this effect on partial least squares (PLS) regression calibrations of near-infrared (NIR) reflection spectra of ground wheat meal with two analytes, protein content and sodium dodecyl sulfate sedimentation (SDS) volume (an indicator of the quantity of the gluten proteins that contribute to strong doughs). These two properties were chosen because of their differing abilities to be modeled by NIR spectroscopy: excellent for protein content, fair for SDS sedimentation volume. To further demonstrate the potential pitfalls of preprocessing, an artificial component, a randomly generated value, was included in PLS regression trials. Savitzky-Golay (digital filter) smoothing, first-derivative, and second-derivative preprocess functions (5 to 25 centrally symmetric convolution points, derived from quadratic polynomials) were applied to PLS calibrations of 1 to 15 factors. The results demonstrated the danger of an over reliance on preprocessing when (1) the number of samples used in a multivariate calibration is low (<50), (2) the spectral response of the analyte is weak, and (3) the goodness of the calibration is based on the coefficient of determination (R(2)) rather than a term based on residual error. The graphical method has application to the evaluation of other preprocess functions and various

  19. Quantitative analysis of Fe and Co in Co-substituted magnetite using XPS: The application of non-linear least squares fitting (NLLSF)

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Hongmei, E-mail: hmliu@gig.ac.cn [CAS Key Laboratory of Mineralogy and Metallogeny/Guangdong Provincial Key Laboratory of Mineral Physics and Materials, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou, 510640 (China); Wei, Gaoling [Guangdong Key Laboratory of Agricultural Environment Pollution Integrated Control, Guangdong Institute of Eco-Environmental and Soil Sciences, Guangzhou, 510650 (China); Xu, Zhen [School of Materials Science and Engineering, Central South University, Changsha, 410012 (China); Liu, Peng; Li, Ying [CAS Key Laboratory of Mineralogy and Metallogeny/Guangdong Provincial Key Laboratory of Mineral Physics and Materials, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou, 510640 (China); University of Chinese Academy of Sciences, Beijing, 100049 (China)

    2016-12-15

    Highlights: • XPS and Auger peak overlapping complicates Co-substituted magnetite quantification. • Disrurbance of Auger peaks was eliminated by non-linear least squares fitting. • Fitting greatly improved the accuracy of quantification for Co and Fe. • Catalytic activity of magnetite was enhanced with the increase of Co substitution. - Abstract: Quantitative analysis of Co and Fe using X-ray photoelectron spectroscopy (XPS) is of important for the evaluation of the catalytic ability of Co-substituted magnetite. However, the overlap of XPS peaks and Auger peaks for Co and Fe complicate quantification. In this study, non-linear least squares fitting (NLLSF) was used to calculate the relative Co and Fe contents of a series of synthesized Co-substituted magnetite samples with different Co doping levels. NLLSF separated the XPS peaks of Co 2p and Fe 2p from the Auger peaks of Fe and Co, respectively. Compared with a control group without fitting, the accuracy of quantification of Co and Fe was greatly improved after elimination by NLLSF of the disturbance of Auger peaks. A catalysis study confirmed that the catalytic activity of magnetite was enhanced with the increase of Co substitution. This study confirms the effectiveness and accuracy of the NLLSF method in XPS quantitative calculation of Fe and Co coexisting in a material.

  20. Fuzzy Linear Regression for the Time Series Data which is Fuzzified with SMRGT Method

    Directory of Open Access Journals (Sweden)

    Seçil YALAZ

    2016-10-01

    Full Text Available Our work on regression and classification provides a new contribution to the analysis of time series used in many areas for years. Owing to the fact that convergence could not obtained with the methods used in autocorrelation fixing process faced with time series regression application, success is not met or fall into obligation of changing the models’ degree. Changing the models’ degree may not be desirable in every situation. In our study, recommended for these situations, time series data was fuzzified by using the simple membership function and fuzzy rule generation technique (SMRGT and to estimate future an equation has created by applying fuzzy least square regression (FLSR method which is a simple linear regression method to this data. Although SMRGT has success in determining the flow discharge in open channels and can be used confidently for flow discharge modeling in open canals, as well as in pipe flow with some modifications, there is no clue about that this technique is successful in fuzzy linear regression modeling. Therefore, in order to address the luck of such a modeling, a new hybrid model has been described within this study. In conclusion, to demonstrate our methods’ efficiency, classical linear regression for time series data and linear regression for fuzzy time series data were applied to two different data sets, and these two approaches performances were compared by using different measures.

  1. Direct-on-Filter α-Quartz Estimation in Respirable Coal Mine Dust Using Transmission Fourier Transform Infrared Spectrometry and Partial Least Squares Regression.

    Science.gov (United States)

    Miller, Arthur L; Weakley, Andrew Todd; Griffiths, Peter R; Cauda, Emanuele G; Bayman, Sean

    2017-05-01

    In order to help reduce silicosis in miners, the National Institute for Occupational Health and Safety (NIOSH) is developing field-portable methods for measuring airborne respirable crystalline silica (RCS), specifically the polymorph α-quartz, in mine dusts. In this study we demonstrate the feasibility of end-of-shift measurement of α-quartz using a direct-on-filter (DoF) method to analyze coal mine dust samples deposited onto polyvinyl chloride filters. The DoF method is potentially amenable for on-site analyses, but deviates from the current regulatory determination of RCS for coal mines by eliminating two sample preparation steps: ashing the sampling filter and redepositing the ash prior to quantification by Fourier transform infrared (FT-IR) spectrometry. In this study, the FT-IR spectra of 66 coal dust samples from active mines were used, and the RCS was quantified by using: (1) an ordinary least squares (OLS) calibration approach that utilizes standard silica material as done in the Mine Safety and Health Administration's P7 method; and (2) a partial least squares (PLS) regression approach. Both were capable of accounting for kaolinite, which can confound the IR analysis of silica. The OLS method utilized analytical standards for silica calibration and kaolin correction, resulting in a good linear correlation with P7 results and minimal bias but with the accuracy limited by the presence of kaolinite. The PLS approach also produced predictions well-correlated to the P7 method, as well as better accuracy in RCS prediction, and no bias due to variable kaolinite mass. Besides decreased sensitivity to mineral or substrate confounders, PLS has the advantage that the analyst is not required to correct for the presence of kaolinite or background interferences related to the substrate, making the method potentially viable for automated RCS prediction in the field. This study demonstrated the efficacy of FT-IR transmission spectrometry for silica determination in

  2. FPGA-based electrocardiography (ECG signal analysis system using least-square linear phase finite impulse response (FIR filter

    Directory of Open Access Journals (Sweden)

    Mohamed G. Egila

    2016-12-01

    Full Text Available This paper presents a proposed design for analyzing electrocardiography (ECG signals. This methodology employs highpass least-square linear phase Finite Impulse Response (FIR filtering technique to filter out the baseline wander noise embedded in the input ECG signal to the system. Discrete Wavelet Transform (DWT was utilized as a feature extraction methodology to extract the reduced feature set from the input ECG signal. The design uses back propagation neural network classifier to classify the input ECG signal. The system is implemented on Xilinx 3AN-XC3S700AN Field Programming Gate Array (FPGA board. A system simulation has been done. The design is compared with some other designs achieving total accuracy of 97.8%, and achieving reduction in utilizing resources on FPGA implementation.

  3. A Bayesian least squares support vector machines based framework for fault diagnosis and failure prognosis

    Science.gov (United States)

    Khawaja, Taimoor Saleem

    A high-belief low-overhead Prognostics and Health Management (PHM) system is desired for online real-time monitoring of complex non-linear systems operating in a complex (possibly non-Gaussian) noise environment. This thesis presents a Bayesian Least Squares Support Vector Machine (LS-SVM) based framework for fault diagnosis and failure prognosis in nonlinear non-Gaussian systems. The methodology assumes the availability of real-time process measurements, definition of a set of fault indicators and the existence of empirical knowledge (or historical data) to characterize both nominal and abnormal operating conditions. An efficient yet powerful Least Squares Support Vector Machine (LS-SVM) algorithm, set within a Bayesian Inference framework, not only allows for the development of real-time algorithms for diagnosis and prognosis but also provides a solid theoretical framework to address key concepts related to classification for diagnosis and regression modeling for prognosis. SVM machines are founded on the principle of Structural Risk Minimization (SRM) which tends to find a good trade-off between low empirical risk and small capacity. The key features in SVM are the use of non-linear kernels, the absence of local minima, the sparseness of the solution and the capacity control obtained by optimizing the margin. The Bayesian Inference framework linked with LS-SVMs allows a probabilistic interpretation of the results for diagnosis and prognosis. Additional levels of inference provide the much coveted features of adaptability and tunability of the modeling parameters. The two main modules considered in this research are fault diagnosis and failure prognosis. With the goal of designing an efficient and reliable fault diagnosis scheme, a novel Anomaly Detector is suggested based on the LS-SVM machines. The proposed scheme uses only baseline data to construct a 1-class LS-SVM machine which, when presented with online data is able to distinguish between normal behavior

  4. An Adaptive Noise Cancellation System Based on Linear and Widely Linear Complex Valued Least Mean Square Algorithms for Removing Electrooculography Artifacts from Electroencephalography Signals

    Directory of Open Access Journals (Sweden)

    Engin Cemal MENGÜÇ

    2018-03-01

    Full Text Available In this study, an adaptive noise cancellation (ANC system based on linear and widely linear (WL complex valued least mean square (LMS algorithms is designed for removing electrooculography (EOG artifacts from electroencephalography (EEG signals. The real valued EOG and EEG signals (Fp1 and Fp2 given in dataset are primarily expressed as a complex valued signal in the complex domain. Then, using the proposed ANC system, the EOG artifacts are eliminated in the complex domain from the EEG signals. Expression of these signals in the complex domain allows us to remove EOG artifacts from two EEG channels simultaneously. Moreover, in this study, it has been shown that the complex valued EEG signal exhibits noncircular behavior, and in the case, the WL-CLMS algorithm enhances the performance of the ANC system compared to real-valued LMS and CLMS algorithms. Simulation results support the proposed approach.

  5. Linear regression based on Minimum Covariance Determinant (MCD) and TELBS methods on the productivity of phytoplankton

    Science.gov (United States)

    Gusriani, N.; Firdaniza

    2018-03-01

    The existence of outliers on multiple linear regression analysis causes the Gaussian assumption to be unfulfilled. If the Least Square method is forcedly used on these data, it will produce a model that cannot represent most data. For that, we need a robust regression method against outliers. This paper will compare the Minimum Covariance Determinant (MCD) method and the TELBS method on secondary data on the productivity of phytoplankton, which contains outliers. Based on the robust determinant coefficient value, MCD method produces a better model compared to TELBS method.

  6. Feasibility study on the least square method for fitting non-Gaussian noise data

    Science.gov (United States)

    Xu, Wei; Chen, Wen; Liang, Yingjie

    2018-02-01

    This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, Lévy and stretched Gaussian noises, to exact value of the selected functions including linear equations, polynomial and exponential equations, and the maximum absolute and the mean square errors are calculated for the different cases. Lévy and stretched Gaussian distributions have many applications in fractional and fractal calculus. It is observed that the non-Gaussian noises are less accurately fitted than the Gaussian noise, but the stretched Gaussian cases appear to perform better than the Lévy noise cases. It is stressed that the least-squares method is inapplicable to the non-Gaussian noise cases when the noise level is larger than 5%.

  7. Discrimination of Transgenic Rice Based on Near Infrared Reflectance Spectroscopy and Partial Least Squares Regression Discriminant Analysis

    Directory of Open Access Journals (Sweden)

    ZHANG Long

    2015-09-01

    Full Text Available Near infrared reflectance spectroscopy (NIRS, a non-destructive measurement technique, was combined with partial least squares regression discrimiant analysis (PLS-DA to discriminate the transgenic (TCTP and mi166 and wild type (Zhonghua 11 rice. Furthermore, rice lines transformed with protein gene (OsTCTP and regulation gene (Osmi166 were also discriminated by the NIRS method. The performances of PLS-DA in spectral ranges of 4 000–8 000 cm-1 and 4 000–10 000 cm-1 were compared to obtain the optimal spectral range. As a result, the transgenic and wild type rice were distinguished from each other in the range of 4 000–10 000 cm-1, and the correct classification rate was 100.0% in the validation test. The transgenic rice TCTP and mi166 were also distinguished from each other in the range of 4 000–10 000 cm-1, and the correct classification rate was also 100.0%. In conclusion, NIRS combined with PLS-DA can be used for the discrimination of transgenic rice.

  8. Development of nondestructive detection method for adulterated powder products using Raman spectroscopy and partial least squares regression

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Sang Dae; Lohumi, Santosh; Cho, Byoung Kwan [Dept. of Biosystems Machinery Engineering, Chungnam National University, Daejeon (Korea, Republic of); Kim, Moon Sung [United States Department of Agriculture Agricultural Research Service, Washington (United States); Lee, Soo Hee [Life and Technology Co.,Ltd., Hwasung (Korea, Republic of)

    2014-08-15

    This study was conducted to develop a non-destructive detection method for adulterated powder products using Raman spectroscopy and partial least squares regression(PLSR). Garlic and ginger powder, which are used as natural seasoning and in health supplement foods, were selected for this experiment. Samples were adulterated with corn starch in concentrations of 5-35%. PLSR models for adulterated garlic and ginger powders were developed and their performances evaluated using cross validation. The R{sup 2}{sub c} and SEC of an optimal PLSR model were 0.99 and 2.16 for the garlic powder samples, and 0.99 and 0.84 for the ginger samples, respectively. The variable importance in projection (VIP) score is a useful and simple tool for the evaluation of the importance of each variable in a PLSR model. After the VIP scores were taken pre-selection, the Raman spectrum data was reduced by one third. New PLSR models, based on a reduced number of wavelengths selected by the VIP scores technique, gave good predictions for the adulterated garlic and ginger powder samples.

  9. Development of nondestructive detection method for adulterated powder products using Raman spectroscopy and partial least squares regression

    International Nuclear Information System (INIS)

    Lee, Sang Dae; Lohumi, Santosh; Cho, Byoung Kwan; Kim, Moon Sung; Lee, Soo Hee

    2014-01-01

    This study was conducted to develop a non-destructive detection method for adulterated powder products using Raman spectroscopy and partial least squares regression(PLSR). Garlic and ginger powder, which are used as natural seasoning and in health supplement foods, were selected for this experiment. Samples were adulterated with corn starch in concentrations of 5-35%. PLSR models for adulterated garlic and ginger powders were developed and their performances evaluated using cross validation. The R 2 c and SEC of an optimal PLSR model were 0.99 and 2.16 for the garlic powder samples, and 0.99 and 0.84 for the ginger samples, respectively. The variable importance in projection (VIP) score is a useful and simple tool for the evaluation of the importance of each variable in a PLSR model. After the VIP scores were taken pre-selection, the Raman spectrum data was reduced by one third. New PLSR models, based on a reduced number of wavelengths selected by the VIP scores technique, gave good predictions for the adulterated garlic and ginger powder samples.

  10. Linear Regression Based Real-Time Filtering

    Directory of Open Access Journals (Sweden)

    Misel Batmend

    2013-01-01

    Full Text Available This paper introduces real time filtering method based on linear least squares fitted line. Method can be used in case that a filtered signal is linear. This constraint narrows a band of potential applications. Advantage over Kalman filter is that it is computationally less expensive. The paper further deals with application of introduced method on filtering data used to evaluate a position of engraved material with respect to engraving machine. The filter was implemented to the CNC engraving machine control system. Experiments showing its performance are included.

  11. Iterative least-squares solvers for the Navier-Stokes equations

    Energy Technology Data Exchange (ETDEWEB)

    Bochev, P. [Univ. of Texas, Arlington, TX (United States)

    1996-12-31

    In the recent years finite element methods of least-squares type have attracted considerable attention from both mathematicians and engineers. This interest has been motivated, to a large extent, by several valuable analytic and computational properties of least-squares variational principles. In particular, finite element methods based on such principles circumvent Ladyzhenskaya-Babuska-Brezzi condition and lead to symmetric and positive definite algebraic systems. Thus, it is not surprising that numerical solution of fluid flow problems has been among the most promising and successful applications of least-squares methods. In this context least-squares methods offer significant theoretical and practical advantages in the algorithmic design, which makes resulting methods suitable, among other things, for large-scale numerical simulations.

  12. Controlling attribute effect in linear regression

    KAUST Repository

    Calders, Toon; Karim, Asim A.; Kamiran, Faisal; Ali, Wasif Mohammad; Zhang, Xiangliang

    2013-01-01

    In data mining we often have to learn from biased data, because, for instance, data comes from different batches or there was a gender or racial bias in the collection of social data. In some applications it may be necessary to explicitly control this bias in the models we learn from the data. This paper is the first to study learning linear regression models under constraints that control the biasing effect of a given attribute such as gender or batch number. We show how propensity modeling can be used for factoring out the part of the bias that can be justified by externally provided explanatory attributes. Then we analytically derive linear models that minimize squared error while controlling the bias by imposing constraints on the mean outcome or residuals of the models. Experiments with discrimination-aware crime prediction and batch effect normalization tasks show that the proposed techniques are successful in controlling attribute effects in linear regression models. © 2013 IEEE.

  13. Controlling attribute effect in linear regression

    KAUST Repository

    Calders, Toon

    2013-12-01

    In data mining we often have to learn from biased data, because, for instance, data comes from different batches or there was a gender or racial bias in the collection of social data. In some applications it may be necessary to explicitly control this bias in the models we learn from the data. This paper is the first to study learning linear regression models under constraints that control the biasing effect of a given attribute such as gender or batch number. We show how propensity modeling can be used for factoring out the part of the bias that can be justified by externally provided explanatory attributes. Then we analytically derive linear models that minimize squared error while controlling the bias by imposing constraints on the mean outcome or residuals of the models. Experiments with discrimination-aware crime prediction and batch effect normalization tasks show that the proposed techniques are successful in controlling attribute effects in linear regression models. © 2013 IEEE.

  14. Evaluation of linear regression techniques for atmospheric applications: the importance of appropriate weighting

    Directory of Open Access Journals (Sweden)

    C. Wu

    2018-03-01

    Full Text Available Linear regression techniques are widely used in atmospheric science, but they are often improperly applied due to lack of consideration or inappropriate handling of measurement uncertainty. In this work, numerical experiments are performed to evaluate the performance of five linear regression techniques, significantly extending previous works by Chu and Saylor. The five techniques are ordinary least squares (OLS, Deming regression (DR, orthogonal distance regression (ODR, weighted ODR (WODR, and York regression (YR. We first introduce a new data generation scheme that employs the Mersenne twister (MT pseudorandom number generator. The numerical simulations are also improved by (a refining the parameterization of nonlinear measurement uncertainties, (b inclusion of a linear measurement uncertainty, and (c inclusion of WODR for comparison. Results show that DR, WODR and YR produce an accurate slope, but the intercept by WODR and YR is overestimated and the degree of bias is more pronounced with a low R2 XY dataset. The importance of a properly weighting parameter λ in DR is investigated by sensitivity tests, and it is found that an improper λ in DR can lead to a bias in both the slope and intercept estimation. Because the λ calculation depends on the actual form of the measurement error, it is essential to determine the exact form of measurement error in the XY data during the measurement stage. If a priori error in one of the variables is unknown, or the measurement error described cannot be trusted, DR, WODR and YR can provide the least biases in slope and intercept among all tested regression techniques. For these reasons, DR, WODR and YR are recommended for atmospheric studies when both X and Y data have measurement errors. An Igor Pro-based program (Scatter Plot was developed to facilitate the implementation of error-in-variables regressions.

  15. Evaluation of linear regression techniques for atmospheric applications: the importance of appropriate weighting

    Science.gov (United States)

    Wu, Cheng; Zhen Yu, Jian

    2018-03-01

    Linear regression techniques are widely used in atmospheric science, but they are often improperly applied due to lack of consideration or inappropriate handling of measurement uncertainty. In this work, numerical experiments are performed to evaluate the performance of five linear regression techniques, significantly extending previous works by Chu and Saylor. The five techniques are ordinary least squares (OLS), Deming regression (DR), orthogonal distance regression (ODR), weighted ODR (WODR), and York regression (YR). We first introduce a new data generation scheme that employs the Mersenne twister (MT) pseudorandom number generator. The numerical simulations are also improved by (a) refining the parameterization of nonlinear measurement uncertainties, (b) inclusion of a linear measurement uncertainty, and (c) inclusion of WODR for comparison. Results show that DR, WODR and YR produce an accurate slope, but the intercept by WODR and YR is overestimated and the degree of bias is more pronounced with a low R2 XY dataset. The importance of a properly weighting parameter λ in DR is investigated by sensitivity tests, and it is found that an improper λ in DR can lead to a bias in both the slope and intercept estimation. Because the λ calculation depends on the actual form of the measurement error, it is essential to determine the exact form of measurement error in the XY data during the measurement stage. If a priori error in one of the variables is unknown, or the measurement error described cannot be trusted, DR, WODR and YR can provide the least biases in slope and intercept among all tested regression techniques. For these reasons, DR, WODR and YR are recommended for atmospheric studies when both X and Y data have measurement errors. An Igor Pro-based program (Scatter Plot) was developed to facilitate the implementation of error-in-variables regressions.

  16. Quantitative structure-retention relationship studies with immobilized artificial membrane chromatography II: partial least squares regression.

    Science.gov (United States)

    Li, Jie; Sun, Jin; He, Zhonggui

    2007-01-26

    We aimed to establish quantitative structure-retention relationship (QSRR) with immobilized artificial membrane (IAM) chromatography using easily understood and obtained physicochemical molecular descriptors and to elucidate which descriptors are critical to affect the interaction process between solutes and immobilized phospholipid membranes. The retention indices (logk(IAM)) of 55 structurally diverse drugs were determined on an immobilized artificial membrane column (IAM.PC.DD2) directly or obtained by extrapolation method for highly hydrophobic compounds. Ten simple physicochemical property descriptors (clogP, rings, rotatory bond, hydro-bond counting, etc.) of these drugs were collected and used to establish QSRR and predict the retention data by partial least squares regression (PLSR). Five descriptors, clogP, rotatory bond (RotB), rings, molecular weight (MW) and total surface area (TSA), were reserved by using the Variable Importance for Projection (VIP) values as criterion to build the final PLSR model. An external test set was employed to verify the QSRR based on the training set with the five variables, and QSRR by PLSR exhibited a satisfying predictive ability with R(p)=0.902 and RMSE(p)=0.400. Comparison of coefficients of centered and scaled variables by PLSR demonstrated that, for the descriptors studied, clogP and TSA have the most significant positive effect but the rotatable bond has significant negative effect on drug IAM chromatographic retention.

  17. Lattice Designs in Standard and Simple Implicit Multi-linear Regression

    OpenAIRE

    Wooten, Rebecca D.

    2016-01-01

    Statisticians generally use ordinary least squares to minimize the random error in a subject response with respect to independent explanatory variable. However, Wooten shows illustrates how ordinary least squares can be used to minimize the random error in the system without defining a subject response. Using lattice design Wooten shows that non-response analysis is a superior alternative rotation of the pyramidal relationship between random variables and parameter estimates in multi-linear r...

  18. A land use regression model for ambient ultrafine particles in Montreal, Canada: A comparison of linear regression and a machine learning approach.

    Science.gov (United States)

    Weichenthal, Scott; Ryswyk, Keith Van; Goldstein, Alon; Bagg, Scott; Shekkarizfard, Maryam; Hatzopoulou, Marianne

    2016-04-01

    Existing evidence suggests that ambient ultrafine particles (UFPs) (regression model for UFPs in Montreal, Canada using mobile monitoring data collected from 414 road segments during the summer and winter months between 2011 and 2012. Two different approaches were examined for model development including standard multivariable linear regression and a machine learning approach (kernel-based regularized least squares (KRLS)) that learns the functional form of covariate impacts on ambient UFP concentrations from the data. The final models included parameters for population density, ambient temperature and wind speed, land use parameters (park space and open space), length of local roads and rail, and estimated annual average NOx emissions from traffic. The final multivariable linear regression model explained 62% of the spatial variation in ambient UFP concentrations whereas the KRLS model explained 79% of the variance. The KRLS model performed slightly better than the linear regression model when evaluated using an external dataset (R(2)=0.58 vs. 0.55) or a cross-validation procedure (R(2)=0.67 vs. 0.60). In general, our findings suggest that the KRLS approach may offer modest improvements in predictive performance compared to standard multivariable linear regression models used to estimate spatial variations in ambient UFPs. However, differences in predictive performance were not statistically significant when evaluated using the cross-validation procedure. Crown Copyright © 2015. Published by Elsevier Inc. All rights reserved.

  19. Comparison of partial least squares and lasso regression techniques as applied to laser-induced breakdown spectroscopy of geological samples

    International Nuclear Information System (INIS)

    Dyar, M.D.; Carmosino, M.L.; Breves, E.A.; Ozanne, M.V.; Clegg, S.M.; Wiens, R.C.

    2012-01-01

    A remote laser-induced breakdown spectrometer (LIBS) designed to simulate the ChemCam instrument on the Mars Science Laboratory Rover Curiosity was used to probe 100 geologic samples at a 9-m standoff distance. ChemCam consists of an integrated remote LIBS instrument that will probe samples up to 7 m from the mast of the rover and a remote micro-imager (RMI) that will record context images. The elemental compositions of 100 igneous and highly-metamorphosed rocks are determined with LIBS using three variations of multivariate analysis, with a goal of improving the analytical accuracy. Two forms of partial least squares (PLS) regression are employed with finely-tuned parameters: PLS-1 regresses a single response variable (elemental concentration) against the observation variables (spectra, or intensity at each of 6144 spectrometer channels), while PLS-2 simultaneously regresses multiple response variables (concentrations of the ten major elements in rocks) against the observation predictor variables, taking advantage of natural correlations between elements. Those results are contrasted with those from the multivariate regression technique of the least absolute shrinkage and selection operator (lasso), which is a penalized shrunken regression method that selects the specific channels for each element that explain the most variance in the concentration of that element. To make this comparison, we use results of cross-validation and of held-out testing, and employ unscaled and uncentered spectral intensity data because all of the input variables are already in the same units. Results demonstrate that the lasso, PLS-1, and PLS-2 all yield comparable results in terms of accuracy for this dataset. However, the interpretability of these methods differs greatly in terms of fundamental understanding of LIBS emissions. PLS techniques generate principal components, linear combinations of intensities at any number of spectrometer channels, which explain as much variance in the

  20. A Newton Algorithm for Multivariate Total Least Squares Problems

    Directory of Open Access Journals (Sweden)

    WANG Leyang

    2016-04-01

    Full Text Available In order to improve calculation efficiency of parameter estimation, an algorithm for multivariate weighted total least squares adjustment based on Newton method is derived. The relationship between the solution of this algorithm and that of multivariate weighted total least squares adjustment based on Lagrange multipliers method is analyzed. According to propagation of cofactor, 16 computational formulae of cofactor matrices of multivariate total least squares adjustment are also listed. The new algorithm could solve adjustment problems containing correlation between observation matrix and coefficient matrix. And it can also deal with their stochastic elements and deterministic elements with only one cofactor matrix. The results illustrate that the Newton algorithm for multivariate total least squares problems could be practiced and have higher convergence rate.

  1. Distribución de las transformaciones lineales de los residuos mínimos cuadrados studentizados internamente = Distribution of linear transformations of internally studentized least squares residuals

    Directory of Open Access Journals (Sweden)

    Seppo Pynnönem

    2012-03-01

    that the resulting ratio, U/S, has a distribution that is free of from the nuisance unknown scale parameter. External Studentization refers to a ratio in which the nominator and denominator are independent, while internal Studentization refers to a ratio in which these are dependent. The advantage of the internal Studentization is that typically one can use a single common scale estimator, while in the external Studentization every single residual is scaled by different scale estimator to gain the independence. With normal regression errors the joint distribution of an arbitrary (linearly independent subset of internally Studentized residuals is well documented. However, in some applications a linear combination of internally Studentized residuals may be useful. The boundedness of them is well documented, but the distribution seems not be derived in the literature. This paper contributes to the existing literature by deriving the joint distribution of an arbitrary linear transformation of internally Studentized residuals from ordinary least squares regression with spherical error distribution. All major versions of commonly utilized internally Studentized regression residuals in literature are obtained as special cases of the linear transformation

  2. Using the Ridge Regression Procedures to Estimate the Multiple Linear Regression Coefficients

    Science.gov (United States)

    Gorgees, HazimMansoor; Mahdi, FatimahAssim

    2018-05-01

    This article concerns with comparing the performance of different types of ordinary ridge regression estimators that have been already proposed to estimate the regression parameters when the near exact linear relationships among the explanatory variables is presented. For this situations we employ the data obtained from tagi gas filling company during the period (2008-2010). The main result we reached is that the method based on the condition number performs better than other methods since it has smaller mean square error (MSE) than the other stated methods.

  3. Elastic least-squares reverse time migration

    KAUST Repository

    Feng, Zongcai

    2017-03-08

    We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTMsolves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional leastsquares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTMwill produce migration noise stronger than that seen in the RTM images.

  4. Elastic least-squares reverse time migration

    KAUST Repository

    Feng, Zongcai; Schuster, Gerard T.

    2017-01-01

    We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTMsolves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional leastsquares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTMwill produce migration noise stronger than that seen in the RTM images.

  5. Space-time coupled spectral/hp least-squares finite element formulation for the incompressible Navier-Stokes equations

    International Nuclear Information System (INIS)

    Pontaza, J.P.; Reddy, J.N.

    2004-01-01

    We consider least-squares finite element models for the numerical solution of the non-stationary Navier-Stokes equations governing viscous incompressible fluid flows. The paper presents a formulation where the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space-time decoupled formulation where a least-squares minimization procedure is performed in space at each time step. The formulation is first presented for the linear advection-diffusion equation and then extended to the Navier-Stokes equations. The formulation has no time step stability restrictions and is spectrally accurate in both space and time. To allow the use of practical C 0 element expansions in the resulting finite element model, the Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity as an additional independent variable and the least-squares method is used to develop the finite element model of the governing equations. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix-free form. Spectral convergence of the L 2 least-squares functional and L 2 error norms in space-time is verified using a smooth solution to the two-dimensional non-stationary incompressible Navier-Stokes equations. Numerical results are presented for impulsively started lid-driven cavity flow, oscillatory lid-driven cavity flow, transient flow over a backward-facing step, and flow around a circular cylinder; the results demonstrate the predictive capability and robustness of the proposed formulation. Even though the space-time coupled formulation is emphasized, we also present the formulation and numerical results for least-squares

  6. Least-squares variance component estimation

    NARCIS (Netherlands)

    Teunissen, P.J.G.; Amiri-Simkooei, A.R.

    2007-01-01

    Least-squares variance component estimation (LS-VCE) is a simple, flexible and attractive method for the estimation of unknown variance and covariance components. LS-VCE is simple because it is based on the well-known principle of LS; it is flexible because it works with a user-defined weight

  7. [From clinical judgment to linear regression model.

    Science.gov (United States)

    Palacios-Cruz, Lino; Pérez, Marcela; Rivas-Ruiz, Rodolfo; Talavera, Juan O

    2013-01-01

    When we think about mathematical models, such as linear regression model, we think that these terms are only used by those engaged in research, a notion that is far from the truth. Legendre described the first mathematical model in 1805, and Galton introduced the formal term in 1886. Linear regression is one of the most commonly used regression models in clinical practice. It is useful to predict or show the relationship between two or more variables as long as the dependent variable is quantitative and has normal distribution. Stated in another way, the regression is used to predict a measure based on the knowledge of at least one other variable. Linear regression has as it's first objective to determine the slope or inclination of the regression line: Y = a + bx, where "a" is the intercept or regression constant and it is equivalent to "Y" value when "X" equals 0 and "b" (also called slope) indicates the increase or decrease that occurs when the variable "x" increases or decreases in one unit. In the regression line, "b" is called regression coefficient. The coefficient of determination (R 2 ) indicates the importance of independent variables in the outcome.

  8. Microprocessor-controlled system for automatic acquisition of potentiometric data and their non-linear least-squares fit in equilibrium studies.

    Science.gov (United States)

    Gampp, H; Maeder, M; Zuberbühler, A D; Kaden, T A

    1980-06-01

    A microprocessor-controlled potentiometric titration apparatus for equilibrium studies is described. The microprocessor controls the stepwise addition of reagent, monitors the pH until it becomes constant and stores the constant value. The data are recorded on magnetic tape by a cassette recorder with an RS232 input-output interface. A non-linear least-squares program based on Marquardt's modification of the Newton-Gauss method is discussed and its performance in the calculation of equilibrium constants is exemplified. An HP 9821 desk-top computer accepts the data from the magnetic tape recorder. In addition to a fully automatic fitting procedure, the program allows manual adjustment of the parameters. Three examples are discussed with regard to performance and reproducibility.

  9. Rapid Quantitative Analysis of Forest Biomass Using Fourier Transform Infrared Spectroscopy and Partial Least Squares Regression

    Directory of Open Access Journals (Sweden)

    Gifty E. Acquah

    2016-01-01

    Full Text Available Fourier transform infrared reflectance (FTIR spectroscopy has been used to predict properties of forest logging residue, a very heterogeneous feedstock material. Properties studied included the chemical composition, thermal reactivity, and energy content. The ability to rapidly determine these properties is vital in the optimization of conversion technologies for the successful commercialization of biobased products. Partial least squares regression of first derivative treated FTIR spectra had good correlations with the conventionally measured properties. For the chemical composition, constructed models generally did a better job of predicting the extractives and lignin content than the carbohydrates. In predicting the thermochemical properties, models for volatile matter and fixed carbon performed very well (i.e., R2 > 0.80, RPD > 2.0. The effect of reducing the wavenumber range to the fingerprint region for PLS modeling and the relationship between the chemical composition and higher heating value of logging residue were also explored. This study is new and different in that it is the first to use FTIR spectroscopy to quantitatively analyze forest logging residue, an abundant resource that can be used as a feedstock in the emerging low carbon economy. Furthermore, it provides a complete and systematic characterization of this heterogeneous raw material.

  10. Trend analysis by a piecewise linear regression model applied to surface air temperatures in Southeastern Spain (1973–2014)

    OpenAIRE

    Campra, Pablo; Morales, Maria

    2016-01-01

    The magnitude of the trends of environmental and climatic changes is mostly derived from the slopes of the linear trends using ordinary least-square fitting. An alternative flexible fitting model, piecewise regression, has been applied here to surface air temperature records in southeastern Spain for the recent warming period (1973–2014) to gain accuracy in the description of the inner structure of change, dividing the time series into linear segments with different slopes. Breakpoint y...

  11. Recursive N-way partial least squares for brain-computer interface.

    Directory of Open Access Journals (Sweden)

    Andrey Eliseyev

    Full Text Available In the article tensor-input/tensor-output blockwise Recursive N-way Partial Least Squares (RNPLS regression is considered. It combines the multi-way tensors decomposition with a consecutive calculation scheme and allows blockwise treatment of tensor data arrays with huge dimensions, as well as the adaptive modeling of time-dependent processes with tensor variables. In the article the numerical study of the algorithm is undertaken. The RNPLS algorithm demonstrates fast and stable convergence of regression coefficients. Applied to Brain Computer Interface system calibration, the algorithm provides an efficient adjustment of the decoding model. Combining the online adaptation with easy interpretation of results, the method can be effectively applied in a variety of multi-modal neural activity flow modeling tasks.

  12. An Incremental Weighted Least Squares Approach to Surface Lights Fields

    Science.gov (United States)

    Coombe, Greg; Lastra, Anselmo

    An Image-Based Rendering (IBR) approach to appearance modelling enables the capture of a wide variety of real physical surfaces with complex reflectance behaviour. The challenges with this approach are handling the large amount of data, rendering the data efficiently, and previewing the model as it is being constructed. In this paper, we introduce the Incremental Weighted Least Squares approach to the representation and rendering of spatially and directionally varying illumination. Each surface patch consists of a set of Weighted Least Squares (WLS) node centers, which are low-degree polynomial representations of the anisotropic exitant radiance. During rendering, the representations are combined in a non-linear fashion to generate a full reconstruction of the exitant radiance. The rendering algorithm is fast, efficient, and implemented entirely on the GPU. The construction algorithm is incremental, which means that images are processed as they arrive instead of in the traditional batch fashion. This human-in-the-loop process enables the user to preview the model as it is being constructed and to adapt to over-sampling and under-sampling of the surface appearance.

  13. Fast Dating Using Least-Squares Criteria and Algorithms.

    Science.gov (United States)

    To, Thu-Hien; Jung, Matthieu; Lycett, Samantha; Gascuel, Olivier

    2016-01-01

    Phylogenies provide a useful way to understand the evolutionary history of genetic samples, and data sets with more than a thousand taxa are becoming increasingly common, notably with viruses (e.g., human immunodeficiency virus (HIV)). Dating ancestral events is one of the first, essential goals with such data. However, current sophisticated probabilistic approaches struggle to handle data sets of this size. Here, we present very fast dating algorithms, based on a Gaussian model closely related to the Langley-Fitch molecular-clock model. We show that this model is robust to uncorrelated violations of the molecular clock. Our algorithms apply to serial data, where the tips of the tree have been sampled through times. They estimate the substitution rate and the dates of all ancestral nodes. When the input tree is unrooted, they can provide an estimate for the root position, thus representing a new, practical alternative to the standard rooting methods (e.g., midpoint). Our algorithms exploit the tree (recursive) structure of the problem at hand, and the close relationships between least-squares and linear algebra. We distinguish between an unconstrained setting and the case where the temporal precedence constraint (i.e., an ancestral node must be older that its daughter nodes) is accounted for. With rooted trees, the former is solved using linear algebra in linear computing time (i.e., proportional to the number of taxa), while the resolution of the latter, constrained setting, is based on an active-set method that runs in nearly linear time. With unrooted trees the computing time becomes (nearly) quadratic (i.e., proportional to the square of the number of taxa). In all cases, very large input trees (>10,000 taxa) can easily be processed and transformed into time-scaled trees. We compare these algorithms to standard methods (root-to-tip, r8s version of Langley-Fitch method, and BEAST). Using simulated data, we show that their estimation accuracy is similar to that

  14. Application of new least-squares methods for the quantitative infrared analysis of multicomponent samples

    International Nuclear Information System (INIS)

    Haaland, D.M.; Easterling, R.G.

    1982-01-01

    Improvements have been made in previous least-squares regression analyses of infrared spectra for the quantitative estimation of concentrations of multicomponent mixtures. Spectral baselines are fitted by least-squares methods, and overlapping spectral features are accounted for in the fitting procedure. Selection of peaks above a threshold value reduces computation time and data storage requirements. Four weighted least-squares methods incorporating different baseline assumptions were investigated using FT-IR spectra of the three pure xylene isomers and their mixtures. By fitting only regions of the spectra that follow Beer's Law, accurate results can be obtained using three of the fitting methods even when baselines are not corrected to zero. Accurate results can also be obtained using one of the fits even in the presence of Beer's Law deviations. This is a consequence of pooling the weighted results for each spectral peak such that the greatest weighting is automatically given to those peaks that adhere to Beer's Law. It has been shown with the xylene spectra that semiquantitative results can be obtained even when all the major components are not known or when expected components are not present. This improvement over previous methods greatly expands the utility of quantitative least-squares analyses

  15. Strong source heat transfer simulations based on a GalerKin/Gradient - least - squares method

    International Nuclear Information System (INIS)

    Franca, L.P.; Carmo, E.G.D. do.

    1989-05-01

    Heat conduction problems with temperature-dependent strong sources are modeled by an equation with a laplacian term, a linear term and a given source distribution term. When the linear-temperature-dependent source term is much larger than the laplacian term, we have a singular perturbation problem. In this case, boundary layers are formed to satisfy the Dirichlet boundary conditions. Although this is an elliptic equation, the standard Galerkin method solution is contaminated by spurious oscillations in the neighborhood of the boundary layers. Herein we employ a Galerkin/Gradient-least-squares method which eliminates all pathological phenomena of the Galerkin method. The method is constructed by adding to the Galerkin method a mesh-dependent term obtained by the least-squares form of the gradient of the Euler-Lagrange equation. Error estimates, numerical simulations in one-and multi-dimensions are given that attest the good stability and accuracy properties of the method [pt

  16. An improved conjugate gradient scheme to the solution of least squares SVM.

    Science.gov (United States)

    Chu, Wei; Ong, Chong Jin; Keerthi, S Sathiya

    2005-03-01

    The least square support vector machines (LS-SVM) formulation corresponds to the solution of a linear system of equations. Several approaches to its numerical solutions have been proposed in the literature. In this letter, we propose an improved method to the numerical solution of LS-SVM and show that the problem can be solved using one reduced system of linear equations. Compared with the existing algorithm for LS-SVM, the approach used in this letter is about twice as efficient. Numerical results using the proposed method are provided for comparisons with other existing algorithms.

  17. On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

    Science.gov (United States)

    Schaffrin, Burkhard; Felus, Yaron A.

    2008-06-01

    The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model ( Y- E Y = ( X- E X ) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E Y and E X . Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem by using the nonlinear Euler-Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition. For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335-342). The differences between the standard least-squares and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion matrix of the estimated parameters.

  18. Advanced statistics: linear regression, part II: multiple linear regression.

    Science.gov (United States)

    Marill, Keith A

    2004-01-01

    The applications of simple linear regression in medical research are limited, because in most situations, there are multiple relevant predictor variables. Univariate statistical techniques such as simple linear regression use a single predictor variable, and they often may be mathematically correct but clinically misleading. Multiple linear regression is a mathematical technique used to model the relationship between multiple independent predictor variables and a single dependent outcome variable. It is used in medical research to model observational data, as well as in diagnostic and therapeutic studies in which the outcome is dependent on more than one factor. Although the technique generally is limited to data that can be expressed with a linear function, it benefits from a well-developed mathematical framework that yields unique solutions and exact confidence intervals for regression coefficients. Building on Part I of this series, this article acquaints the reader with some of the important concepts in multiple regression analysis. These include multicollinearity, interaction effects, and an expansion of the discussion of inference testing, leverage, and variable transformations to multivariate models. Examples from the first article in this series are expanded on using a primarily graphic, rather than mathematical, approach. The importance of the relationships among the predictor variables and the dependence of the multivariate model coefficients on the choice of these variables are stressed. Finally, concepts in regression model building are discussed.

  19. note: The least square nucleolus is a general nucleolus

    OpenAIRE

    Elisenda Molina; Juan Tejada

    2000-01-01

    This short note proves that the least square nucleolus (Ruiz et al. (1996)) and the lexicographical solution (Sakawa and Nishizaki (1994)) select the same imputation in each game with nonempty imputation set. As a consequence the least square nucleolus is a general nucleolus (Maschler et al. (1992)).

  20. Polynomial regression analysis and significance test of the regression function

    International Nuclear Information System (INIS)

    Gao Zhengming; Zhao Juan; He Shengping

    2012-01-01

    In order to analyze the decay heating power of a certain radioactive isotope per kilogram with polynomial regression method, the paper firstly demonstrated the broad usage of polynomial function and deduced its parameters with ordinary least squares estimate. Then significance test method of polynomial regression function is derived considering the similarity between the polynomial regression model and the multivariable linear regression model. Finally, polynomial regression analysis and significance test of the polynomial function are done to the decay heating power of the iso tope per kilogram in accord with the authors' real work. (authors)

  1. Application of least-squares method to decay heat evaluation

    International Nuclear Information System (INIS)

    Schmittroth, F.; Schenter, R.E.

    1976-01-01

    Generalized least-squares methods are applied to decay-heat experiments and summation calculations to arrive at evaluated values and uncertainties for the fission-product decay-heat from the thermal fission of 235 U. Emphasis is placed on a proper treatment of both statistical and correlated uncertainties in the least-squares method

  2. Multivariat least-squares methods applied to the quantitative spectral analysis of multicomponent samples

    International Nuclear Information System (INIS)

    Haaland, D.M.; Easterling, R.G.; Vopicka, D.A.

    1985-01-01

    In an extension of earlier work, weighted multivariate least-squares methods of quantitative FT-IR analysis have been developed. A linear least-squares approximation to nonlinearities in the Beer-Lambert law is made by allowing the reference spectra to be a set of known mixtures, The incorporation of nonzero intercepts in the relation between absorbance and concentration further improves the approximation of nonlinearities while simultaneously accounting for nonzero spectra baselines. Pathlength variations are also accommodated in the analysis, and under certain conditions, unknown sample pathlengths can be determined. All spectral data are used to improve the precision and accuracy of the estimated concentrations. During the calibration phase of the analysis, pure component spectra are estimated from the standard mixture spectra. These can be compared with the measured pure component spectra to determine which vibrations experience nonlinear behavior. In the predictive phase of the analysis, the calculated spectra are used in our previous least-squares analysis to estimate sample component concentrations. These methods were applied to the analysis of the IR spectra of binary mixtures of esters. Even with severely overlapping spectral bands and nonlinearities in the Beer-Lambert law, the average relative error in the estimated concentration was <1%

  3. Multiples least-squares reverse time migration

    KAUST Repository

    Zhang, Dongliang; Zhan, Ge; Dai, Wei; Schuster, Gerard T.

    2013-01-01

    To enhance the image quality, we propose multiples least-squares reverse time migration (MLSRTM) that transforms each hydrophone into a virtual point source with a time history equal to that of the recorded data. Since each recorded trace is treated

  4. Least-squares Minimization Approaches to Interpret Total Magnetic Anomalies Due to Spheres

    Science.gov (United States)

    Abdelrahman, E. M.; El-Araby, T. M.; Soliman, K. S.; Essa, K. S.; Abo-Ezz, E. R.

    2007-05-01

    We have developed three different least-squares approaches to determine successively: the depth, magnetic angle, and amplitude coefficient of a buried sphere from a total magnetic anomaly. By defining the anomaly value at the origin and the nearest zero-anomaly distance from the origin on the profile, the problem of depth determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(z)=0. Knowing the depth and applying the least-squares method, the magnetic angle and amplitude coefficient are determined using two simple linear equations. In this way, the depth, magnetic angle, and amplitude coefficient are determined individually from all observed total magnetic data. The method is applied to synthetic examples with and without random errors and tested on a field example from Senegal, West Africa. In all cases, the depth solutions are in good agreement with the actual ones.

  5. Application of least square support vector machine and multivariate adaptive regression spline models in long term prediction of river water pollution

    Science.gov (United States)

    Kisi, Ozgur; Parmar, Kulwinder Singh

    2016-03-01

    This study investigates the accuracy of least square support vector machine (LSSVM), multivariate adaptive regression splines (MARS) and M5 model tree (M5Tree) in modeling river water pollution. Various combinations of water quality parameters, Free Ammonia (AMM), Total Kjeldahl Nitrogen (TKN), Water Temperature (WT), Total Coliform (TC), Fecal Coliform (FC) and Potential of Hydrogen (pH) monitored at Nizamuddin, Delhi Yamuna River in India were used as inputs to the applied models. Results indicated that the LSSVM and MARS models had almost same accuracy and they performed better than the M5Tree model in modeling monthly chemical oxygen demand (COD). The average root mean square error (RMSE) of the LSSVM and M5Tree models was decreased by 1.47% and 19.1% using MARS model, respectively. Adding TC input to the models did not increase their accuracy in modeling COD while adding FC and pH inputs to the models generally decreased the accuracy. The overall results indicated that the MARS and LSSVM models could be successfully used in estimating monthly river water pollution level by using AMM, TKN and WT parameters as inputs.

  6. Least-squares dual characterization for ROI assessment in emission tomography

    International Nuclear Information System (INIS)

    Ben Bouallègue, F; Mariano-Goulart, D; Crouzet, J F; Dubois, A; Buvat, I

    2013-01-01

    Our aim is to describe an original method for estimating the statistical properties of regions of interest (ROIs) in emission tomography. Drawn upon the works of Louis on the approximate inverse, we propose a dual formulation of the ROI estimation problem to derive the ROI activity and variance directly from the measured data without any image reconstruction. The method requires the definition of an ROI characteristic function that can be extracted from a co-registered morphological image. This characteristic function can be smoothed to optimize the resolution-variance tradeoff. An iterative procedure is detailed for the solution of the dual problem in the least-squares sense (least-squares dual (LSD) characterization), and a linear extrapolation scheme is described to compensate for sampling partial volume effect and reduce the estimation bias (LSD-ex). LSD and LSD-ex are compared with classical ROI estimation using pixel summation after image reconstruction and with Huesman's method. For this comparison, we used Monte Carlo simulations (GATE simulation tool) of 2D PET data of a Hoffman brain phantom containing three small uniform high-contrast ROIs and a large non-uniform low-contrast ROI. Our results show that the performances of LSD characterization are at least as good as those of the classical methods in terms of root mean square (RMS) error. For the three small tumor regions, LSD-ex allows a reduction in the estimation bias by up to 14%, resulting in a reduction in the RMS error of up to 8.5%, compared with the optimal classical estimation. For the large non-specific region, LSD using appropriate smoothing could intuitively and efficiently handle the resolution-variance tradeoff. (paper)

  7. Least-squares dual characterization for ROI assessment in emission tomography

    Science.gov (United States)

    Ben Bouallègue, F.; Crouzet, J. F.; Dubois, A.; Buvat, I.; Mariano-Goulart, D.

    2013-06-01

    Our aim is to describe an original method for estimating the statistical properties of regions of interest (ROIs) in emission tomography. Drawn upon the works of Louis on the approximate inverse, we propose a dual formulation of the ROI estimation problem to derive the ROI activity and variance directly from the measured data without any image reconstruction. The method requires the definition of an ROI characteristic function that can be extracted from a co-registered morphological image. This characteristic function can be smoothed to optimize the resolution-variance tradeoff. An iterative procedure is detailed for the solution of the dual problem in the least-squares sense (least-squares dual (LSD) characterization), and a linear extrapolation scheme is described to compensate for sampling partial volume effect and reduce the estimation bias (LSD-ex). LSD and LSD-ex are compared with classical ROI estimation using pixel summation after image reconstruction and with Huesman's method. For this comparison, we used Monte Carlo simulations (GATE simulation tool) of 2D PET data of a Hoffman brain phantom containing three small uniform high-contrast ROIs and a large non-uniform low-contrast ROI. Our results show that the performances of LSD characterization are at least as good as those of the classical methods in terms of root mean square (RMS) error. For the three small tumor regions, LSD-ex allows a reduction in the estimation bias by up to 14%, resulting in a reduction in the RMS error of up to 8.5%, compared with the optimal classical estimation. For the large non-specific region, LSD using appropriate smoothing could intuitively and efficiently handle the resolution-variance tradeoff.

  8. Comparison of partial least squares and lasso regression techniques as applied to laser-induced breakdown spectroscopy of geological samples

    Energy Technology Data Exchange (ETDEWEB)

    Dyar, M.D., E-mail: mdyar@mtholyoke.edu [Dept. of Astronomy, Mount Holyoke College, 50 College St., South Hadley, MA 01075 (United States); Carmosino, M.L.; Breves, E.A.; Ozanne, M.V. [Dept. of Astronomy, Mount Holyoke College, 50 College St., South Hadley, MA 01075 (United States); Clegg, S.M.; Wiens, R.C. [Los Alamos National Laboratory, P.O. Box 1663, MS J565, Los Alamos, NM 87545 (United States)

    2012-04-15

    A remote laser-induced breakdown spectrometer (LIBS) designed to simulate the ChemCam instrument on the Mars Science Laboratory Rover Curiosity was used to probe 100 geologic samples at a 9-m standoff distance. ChemCam consists of an integrated remote LIBS instrument that will probe samples up to 7 m from the mast of the rover and a remote micro-imager (RMI) that will record context images. The elemental compositions of 100 igneous and highly-metamorphosed rocks are determined with LIBS using three variations of multivariate analysis, with a goal of improving the analytical accuracy. Two forms of partial least squares (PLS) regression are employed with finely-tuned parameters: PLS-1 regresses a single response variable (elemental concentration) against the observation variables (spectra, or intensity at each of 6144 spectrometer channels), while PLS-2 simultaneously regresses multiple response variables (concentrations of the ten major elements in rocks) against the observation predictor variables, taking advantage of natural correlations between elements. Those results are contrasted with those from the multivariate regression technique of the least absolute shrinkage and selection operator (lasso), which is a penalized shrunken regression method that selects the specific channels for each element that explain the most variance in the concentration of that element. To make this comparison, we use results of cross-validation and of held-out testing, and employ unscaled and uncentered spectral intensity data because all of the input variables are already in the same units. Results demonstrate that the lasso, PLS-1, and PLS-2 all yield comparable results in terms of accuracy for this dataset. However, the interpretability of these methods differs greatly in terms of fundamental understanding of LIBS emissions. PLS techniques generate principal components, linear combinations of intensities at any number of spectrometer channels, which explain as much variance in the

  9. Robust anti-synchronization of uncertain chaotic systems based on multiple-kernel least squares support vector machine modeling

    International Nuclear Information System (INIS)

    Chen Qiang; Ren Xuemei; Na Jing

    2011-01-01

    Highlights: Model uncertainty of the system is approximated by multiple-kernel LSSVM. Approximation errors and disturbances are compensated in the controller design. Asymptotical anti-synchronization is achieved with model uncertainty and disturbances. Abstract: In this paper, we propose a robust anti-synchronization scheme based on multiple-kernel least squares support vector machine (MK-LSSVM) modeling for two uncertain chaotic systems. The multiple-kernel regression, which is a linear combination of basic kernels, is designed to approximate system uncertainties by constructing a multiple-kernel Lagrangian function and computing the corresponding regression parameters. Then, a robust feedback control based on MK-LSSVM modeling is presented and an improved update law is employed to estimate the unknown bound of the approximation error. The proposed control scheme can guarantee the asymptotic convergence of the anti-synchronization errors in the presence of system uncertainties and external disturbances. Numerical examples are provided to show the effectiveness of the proposed method.

  10. Time-domain least-squares migration using the Gaussian beam summation method

    Science.gov (United States)

    Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

    2018-04-01

    With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modeling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modeling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a preconditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

  11. LSL: a logarithmic least-squares adjustment method

    International Nuclear Information System (INIS)

    Stallmann, F.W.

    1982-01-01

    To meet regulatory requirements, spectral unfolding codes must not only provide reliable estimates for spectral parameters, but must also be able to determine the uncertainties associated with these parameters. The newer codes, which are more appropriately called adjustment codes, use the least squares principle to determine estimates and uncertainties. The principle is simple and straightforward, but there are several different mathematical models to describe the unfolding problem. In addition to a sound mathematical model, ease of use and range of options are important considerations in the construction of adjustment codes. Based on these considerations, a least squares adjustment code for neutron spectrum unfolding has been constructed some time ago and tentatively named LSL

  12. Healthcare Expenditures Associated with Depression Among Individuals with Osteoarthritis: Post-Regression Linear Decomposition Approach.

    Science.gov (United States)

    Agarwal, Parul; Sambamoorthi, Usha

    2015-12-01

    Depression is common among individuals with osteoarthritis and leads to increased healthcare burden. The objective of this study was to examine excess total healthcare expenditures associated with depression among individuals with osteoarthritis in the US. Adults with self-reported osteoarthritis (n = 1881) were identified using data from the 2010 Medical Expenditure Panel Survey (MEPS). Among those with osteoarthritis, chi-square tests and ordinary least square regressions (OLS) were used to examine differences in healthcare expenditures between those with and without depression. Post-regression linear decomposition technique was used to estimate the relative contribution of different constructs of the Anderson's behavioral model, i.e., predisposing, enabling, need, personal healthcare practices, and external environment factors, to the excess expenditures associated with depression among individuals with osteoarthritis. All analysis accounted for the complex survey design of MEPS. Depression coexisted among 20.6 % of adults with osteoarthritis. The average total healthcare expenditures were $13,684 among adults with depression compared to $9284 among those without depression. Multivariable OLS regression revealed that adults with depression had 38.8 % higher healthcare expenditures (p regression linear decomposition analysis indicated that 50 % of differences in expenditures among adults with and without depression can be explained by differences in need factors. Among individuals with coexisting osteoarthritis and depression, excess healthcare expenditures associated with depression were mainly due to comorbid anxiety, chronic conditions and poor health status. These expenditures may potentially be reduced by providing timely intervention for need factors or by providing care under a collaborative care model.

  13. Applied linear regression

    CERN Document Server

    Weisberg, Sanford

    2013-01-01

    Praise for the Third Edition ""...this is an excellent book which could easily be used as a course text...""-International Statistical Institute The Fourth Edition of Applied Linear Regression provides a thorough update of the basic theory and methodology of linear regression modeling. Demonstrating the practical applications of linear regression analysis techniques, the Fourth Edition uses interesting, real-world exercises and examples. Stressing central concepts such as model building, understanding parameters, assessing fit and reliability, and drawing conclusions, the new edition illus

  14. Sparse least-squares reverse time migration using seislets

    KAUST Repository

    Dutta, Gaurav

    2015-08-19

    We propose sparse least-squares reverse time migration (LSRTM) using seislets as a basis for the reflectivity distribution. This basis is used along with a dip-constrained preconditioner that emphasizes image updates only along prominent dips during the iterations. These dips can be estimated from the standard migration image or from the gradient using plane-wave destruction filters or structural tensors. Numerical tests on synthetic datasets demonstrate the benefits of this method for mitigation of aliasing artifacts and crosstalk noise in multisource least-squares migration.

  15. Quantized kernel least mean square algorithm.

    Science.gov (United States)

    Chen, Badong; Zhao, Songlin; Zhu, Pingping; Príncipe, José C

    2012-01-01

    In this paper, we propose a quantization approach, as an alternative of sparsification, to curb the growth of the radial basis function structure in kernel adaptive filtering. The basic idea behind this method is to quantize and hence compress the input (or feature) space. Different from sparsification, the new approach uses the "redundant" data to update the coefficient of the closest center. In particular, a quantized kernel least mean square (QKLMS) algorithm is developed, which is based on a simple online vector quantization method. The analytical study of the mean square convergence has been carried out. The energy conservation relation for QKLMS is established, and on this basis we arrive at a sufficient condition for mean square convergence, and a lower and upper bound on the theoretical value of the steady-state excess mean square error. Static function estimation and short-term chaotic time-series prediction examples are presented to demonstrate the excellent performance.

  16. Least-squares methods for identifying biochemical regulatory networks from noisy measurements

    Directory of Open Access Journals (Sweden)

    Heslop-Harrison Pat

    2007-01-01

    Full Text Available Abstract Background We consider the problem of identifying the dynamic interactions in biochemical networks from noisy experimental data. Typically, approaches for solving this problem make use of an estimation algorithm such as the well-known linear Least-Squares (LS estimation technique. We demonstrate that when time-series measurements are corrupted by white noise and/or drift noise, more accurate and reliable identification of network interactions can be achieved by employing an estimation algorithm known as Constrained Total Least Squares (CTLS. The Total Least Squares (TLS technique is a generalised least squares method to solve an overdetermined set of equations whose coefficients are noisy. The CTLS is a natural extension of TLS to the case where the noise components of the coefficients are correlated, as is usually the case with time-series measurements of concentrations and expression profiles in gene networks. Results The superior performance of the CTLS method in identifying network interactions is demonstrated on three examples: a genetic network containing four genes, a network describing p53 activity and mdm2 messenger RNA interactions, and a recently proposed kinetic model for interleukin (IL-6 and (IL-12b messenger RNA expression as a function of ATF3 and NF-κB promoter binding. For the first example, the CTLS significantly reduces the errors in the estimation of the Jacobian for the gene network. For the second, the CTLS reduces the errors from the measurements that are corrupted by white noise and the effect of neglected kinetics. For the third, it allows the correct identification, from noisy data, of the negative regulation of (IL-6 and (IL-12b by ATF3. Conclusion The significant improvements in performance demonstrated by the CTLS method under the wide range of conditions tested here, including different levels and types of measurement noise and different numbers of data points, suggests that its application will enable

  17. Corporate Social Responsibility and Financial Performance: A Two Least Regression Approach

    Directory of Open Access Journals (Sweden)

    Alexander Olawumi Dabor

    2017-12-01

    Full Text Available The objective of this study is to investigate the casuality between corporate social responsibility and firm financial performance. The study employed two least square regression approaches. Fifty-two firms were selected using the scientific method. The findings revealed that corporate social responsibility and firm performance in manufacturing sector are mutually related at 5%. The study recommended that management of manufacturing companies in Nigeria should expend on CSR to boost profitability and corporate image.

  18. Internal displacement and strain measurement using digital volume correlation: a least-squares framework

    International Nuclear Information System (INIS)

    Pan, Bing; Wu, Dafang; Wang, Zhaoyang

    2012-01-01

    As a novel tool for quantitative 3D internal deformation measurement throughout the interior of a material or tissue, digital volume correlation (DVC) has increasingly gained attention and application in the fields of experimental mechanics, material research and biomedical engineering. However, the practical implementation of DVC involves important challenges such as implementation complexity, calculation accuracy and computational efficiency. In this paper, a least-squares framework is presented for 3D internal displacement and strain field measurement using DVC. The proposed DVC combines a practical linear-intensity-change model with an easy-to-implement iterative least-squares (ILS) algorithm to retrieve 3D internal displacement vector field with sub-voxel accuracy. Because the linear-intensity-change model is capable of accounting for both the possible intensity changes and the relative geometric transform of the target subvolume, the presented DVC thus provides the highest sub-voxel registration accuracy and widest applicability. Furthermore, as the ILS algorithm uses only first-order spatial derivatives of the deformed volumetric image, the developed DVC thus significantly reduces computational complexity. To further extract 3D strain distributions from the 3D discrete displacement vectors obtained by the ILS algorithm, the presented DVC employs a pointwise least-squares algorithm to estimate the strain components for each measurement point. Computer-simulated volume images with controlled displacements are employed to investigate the performance of the proposed DVC method in terms of mean bias error and standard deviation error. Results reveal that the present technique is capable of providing accurate measurements in an easy-to-implement manner, and can be applied to practical 3D internal displacement and strain calculation. (paper)

  19. Optimistic semi-supervised least squares classification

    DEFF Research Database (Denmark)

    Krijthe, Jesse H.; Loog, Marco

    2017-01-01

    The goal of semi-supervised learning is to improve supervised classifiers by using additional unlabeled training examples. In this work we study a simple self-learning approach to semi-supervised learning applied to the least squares classifier. We show that a soft-label and a hard-label variant ...

  20. Two-step superresolution approach for surveillance face image through radial basis function-partial least squares regression and locality-induced sparse representation

    Science.gov (United States)

    Jiang, Junjun; Hu, Ruimin; Han, Zhen; Wang, Zhongyuan; Chen, Jun

    2013-10-01

    Face superresolution (SR), or face hallucination, refers to the technique of generating a high-resolution (HR) face image from a low-resolution (LR) one with the help of a set of training examples. It aims at transcending the limitations of electronic imaging systems. Applications of face SR include video surveillance, in which the individual of interest is often far from cameras. A two-step method is proposed to infer a high-quality and HR face image from a low-quality and LR observation. First, we establish the nonlinear relationship between LR face images and HR ones, according to radial basis function and partial least squares (RBF-PLS) regression, to transform the LR face into the global face space. Then, a locality-induced sparse representation (LiSR) approach is presented to enhance the local facial details once all the global faces for each LR training face are constructed. A comparison of some state-of-the-art SR methods shows the superiority of the proposed two-step approach, RBF-PLS global face regression followed by LiSR-based local patch reconstruction. Experiments also demonstrate the effectiveness under both simulation conditions and some real conditions.

  1. Modelling daily dissolved oxygen concentration using least square support vector machine, multivariate adaptive regression splines and M5 model tree

    Science.gov (United States)

    Heddam, Salim; Kisi, Ozgur

    2018-04-01

    In the present study, three types of artificial intelligence techniques, least square support vector machine (LSSVM), multivariate adaptive regression splines (MARS) and M5 model tree (M5T) are applied for modeling daily dissolved oxygen (DO) concentration using several water quality variables as inputs. The DO concentration and water quality variables data from three stations operated by the United States Geological Survey (USGS) were used for developing the three models. The water quality data selected consisted of daily measured of water temperature (TE, °C), pH (std. unit), specific conductance (SC, μS/cm) and discharge (DI cfs), are used as inputs to the LSSVM, MARS and M5T models. The three models were applied for each station separately and compared to each other. According to the results obtained, it was found that: (i) the DO concentration could be successfully estimated using the three models and (ii) the best model among all others differs from one station to another.

  2. Outlier detection algorithms for least squares time series regression

    DEFF Research Database (Denmark)

    Johansen, Søren; Nielsen, Bent

    We review recent asymptotic results on some robust methods for multiple regression. The regressors include stationary and non-stationary time series as well as polynomial terms. The methods include the Huber-skip M-estimator, 1-step Huber-skip M-estimators, in particular the Impulse Indicator Sat...

  3. Multilevel weighted least squares polynomial approximation

    KAUST Repository

    Haji-Ali, Abdul-Lateef

    2017-06-30

    Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.

  4. Application of Least-Squares Spectral Element Methods to Polynomial Chaos

    NARCIS (Netherlands)

    Vos, P.E.J.; Gerritsma, M.I.

    2006-01-01

    This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conventional Galerkin projection.

  5. Multi-source least-squares reverse time migration

    KAUST Repository

    Dai, Wei

    2012-06-15

    Least-squares migration has been shown to improve image quality compared to the conventional migration method, but its computational cost is often too high to be practical. In this paper, we develop two numerical schemes to implement least-squares migration with the reverse time migration method and the blended source processing technique to increase computation efficiency. By iterative migration of supergathers, which consist in a sum of many phase-encoded shots, the image quality is enhanced and the crosstalk noise associated with the encoded shots is reduced. Numerical tests on 2D HESS VTI data show that the multisource least-squares reverse time migration (LSRTM) algorithm suppresses migration artefacts, balances the amplitudes, improves image resolution and reduces crosstalk noise associated with the blended shot gathers. For this example, the multisource LSRTM is about three times faster than the conventional RTM method. For the 3D example of the SEG/EAGE salt model, with a comparable computational cost, multisource LSRTM produces images with more accurate amplitudes, better spatial resolution and fewer migration artefacts compared to conventional RTM. The empirical results suggest that multisource LSRTM can produce more accurate reflectivity images than conventional RTM does with a similar or less computational cost. The caveat is that the LSRTM image is sensitive to large errors in the migration velocity model. © 2012 European Association of Geoscientists & Engineers.

  6. Multi-source least-squares reverse time migration

    KAUST Repository

    Dai, Wei; Fowler, Paul J.; Schuster, Gerard T.

    2012-01-01

    Least-squares migration has been shown to improve image quality compared to the conventional migration method, but its computational cost is often too high to be practical. In this paper, we develop two numerical schemes to implement least-squares migration with the reverse time migration method and the blended source processing technique to increase computation efficiency. By iterative migration of supergathers, which consist in a sum of many phase-encoded shots, the image quality is enhanced and the crosstalk noise associated with the encoded shots is reduced. Numerical tests on 2D HESS VTI data show that the multisource least-squares reverse time migration (LSRTM) algorithm suppresses migration artefacts, balances the amplitudes, improves image resolution and reduces crosstalk noise associated with the blended shot gathers. For this example, the multisource LSRTM is about three times faster than the conventional RTM method. For the 3D example of the SEG/EAGE salt model, with a comparable computational cost, multisource LSRTM produces images with more accurate amplitudes, better spatial resolution and fewer migration artefacts compared to conventional RTM. The empirical results suggest that multisource LSRTM can produce more accurate reflectivity images than conventional RTM does with a similar or less computational cost. The caveat is that the LSRTM image is sensitive to large errors in the migration velocity model. © 2012 European Association of Geoscientists & Engineers.

  7. Evaluation of Ordinary Least Square (OLS) and Geographically Weighted Regression (GWR) for Water Quality Monitoring: A Case Study for the Estimation of Salinity

    Science.gov (United States)

    Nazeer, Majid; Bilal, Muhammad

    2018-04-01

    Landsat-5 Thematic Mapper (TM) dataset have been used to estimate salinity in the coastal area of Hong Kong. Four adjacent Landsat TM images were used in this study, which was atmospherically corrected using the Second Simulation of the Satellite Signal in the Solar Spectrum (6S) radiative transfer code. The atmospherically corrected images were further used to develop models for salinity using Ordinary Least Square (OLS) regression and Geographically Weighted Regression (GWR) based on in situ data of October 2009. Results show that the coefficient of determination ( R 2) of 0.42 between the OLS estimated and in situ measured salinity is much lower than that of the GWR model, which is two times higher ( R 2 = 0.86). It indicates that the GWR model has more ability than the OLS regression model to predict salinity and show its spatial heterogeneity better. It was observed that the salinity was high in Deep Bay (north-western part of Hong Kong) which might be due to the industrial waste disposal, whereas the salinity was estimated to be constant (32 practical salinity units) towards the open sea.

  8. Multi-source least-squares migration of marine data

    KAUST Repository

    Wang, Xin

    2012-11-04

    Kirchhoff based multi-source least-squares migration (MSLSM) is applied to marine streamer data. To suppress the crosstalk noise from the excitation of multiple sources, a dynamic encoding function (including both time-shifts and polarity changes) is applied to the receiver side traces. Results show that the MSLSM images are of better quality than the standard Kirchhoff migration and reverse time migration images; moreover, the migration artifacts are reduced and image resolution is significantly improved. The computational cost of MSLSM is about the same as conventional least-squares migration, but its IO cost is significantly decreased.

  9. Least-squares methods involving the H{sup -1} inner product

    Energy Technology Data Exchange (ETDEWEB)

    Pasciak, J.

    1996-12-31

    Least-squares methods are being shown to be an effective technique for the solution of elliptic boundary value problems. However, the methods differ depending on the norms in which they are formulated. For certain problems, it is much more natural to consider least-squares functionals involving the H{sup -1} norm. Such norms give rise to improved convergence estimates and better approximation to problems with low regularity solutions. In addition, fewer new variables need to be added and less stringent boundary conditions need to be imposed. In this talk, I will describe some recent developments involving least-squares methods utilizing the H{sup -1} inner product.

  10. Optimization Method of Fusing Model Tree into Partial Least Squares

    Directory of Open Access Journals (Sweden)

    Yu Fang

    2017-01-01

    Full Text Available Partial Least Square (PLS can’t adapt to the characteristics of the data of many fields due to its own features multiple independent variables, multi-dependent variables and non-linear. However, Model Tree (MT has a good adaptability to nonlinear function, which is made up of many multiple linear segments. Based on this, a new method combining PLS and MT to analysis and predict the data is proposed, which build MT through the main ingredient and the explanatory variables(the dependent variable extracted from PLS, and extract residual information constantly to build Model Tree until well-pleased accuracy condition is satisfied. Using the data of the maxingshigan decoction of the monarch drug to treat the asthma or cough and two sample sets in the UCI Machine Learning Repository, the experimental results show that, the ability of explanation and predicting get improved in the new method.

  11. Two biased estimation techniques in linear regression: Application to aircraft

    Science.gov (United States)

    Klein, Vladislav

    1988-01-01

    Several ways for detection and assessment of collinearity in measured data are discussed. Because data collinearity usually results in poor least squares estimates, two estimation techniques which can limit a damaging effect of collinearity are presented. These two techniques, the principal components regression and mixed estimation, belong to a class of biased estimation techniques. Detection and assessment of data collinearity and the two biased estimation techniques are demonstrated in two examples using flight test data from longitudinal maneuvers of an experimental aircraft. The eigensystem analysis and parameter variance decomposition appeared to be a promising tool for collinearity evaluation. The biased estimators had far better accuracy than the results from the ordinary least squares technique.

  12. Prediction of Biomass Production and Nutrient Uptake in Land Application Using Partial Least Squares Regression Analysis

    Directory of Open Access Journals (Sweden)

    Vasileios A. Tzanakakis

    2014-12-01

    Full Text Available Partial Least Squares Regression (PLSR can integrate a great number of variables and overcome collinearity problems, a fact that makes it suitable for intensive agronomical practices such as land application. In the present study a PLSR model was developed to predict important management goals, including biomass production and nutrient recovery (i.e., nitrogen and phosphorus, associated with treatment potential, environmental impacts, and economic benefits. Effluent loading and a considerable number of soil parameters commonly monitored in effluent irrigated lands were considered as potential predictor variables during the model development. All data were derived from a three year field trial including plantations of four different plant species (Acacia cyanophylla, Eucalyptus camaldulensis, Populus nigra, and Arundo donax, irrigated with pre-treated domestic effluent. PLSR method was very effective despite the small sample size and the wide nature of data set (with many highly correlated inputs and several highly correlated responses. Through PLSR method the number of initial predictor variables was reduced and only several variables were remained and included in the final PLSR model. The important input variables maintained were: Effluent loading, electrical conductivity (EC, available phosphorus (Olsen-P, Na+, Ca2+, Mg2+, K2+, SAR, and NO3−-N. Among these variables, effluent loading, EC, and nitrates had the greater contribution to the final PLSR model. PLSR is highly compatible with intensive agronomical practices such as land application, in which a large number of highly collinear and noisy input variables is monitored to assess plant species performance and to detect impacts on the environment.

  13. Effective Surfactants Blend Concentration Determination for O/W Emulsion Stabilization by Two Nonionic Surfactants by Simple Linear Regression.

    Science.gov (United States)

    Hassan, A K

    2015-01-01

    In this work, O/W emulsion sets were prepared by using different concentrations of two nonionic surfactants. The two surfactants, tween 80(HLB=15.0) and span 80(HLB=4.3) were used in a fixed proportions equal to 0.55:0.45 respectively. HLB value of the surfactants blends were fixed at 10.185. The surfactants blend concentration is starting from 3% up to 19%. For each O/W emulsion set the conductivity was measured at room temperature (25±2°), 40, 50, 60, 70 and 80°. Applying the simple linear regression least squares method statistical analysis to the temperature-conductivity obtained data determines the effective surfactants blend concentration required for preparing the most stable O/W emulsion. These results were confirmed by applying the physical stability centrifugation testing and the phase inversion temperature range measurements. The results indicated that, the relation which represents the most stable O/W emulsion has the strongest direct linear relationship between temperature and conductivity. This relationship is linear up to 80°. This work proves that, the most stable O/W emulsion is determined via the determination of the maximum R² value by applying of the simple linear regression least squares method to the temperature-conductivity obtained data up to 80°, in addition to, the true maximum slope is represented by the equation which has the maximum R² value. Because the conditions would be changed in a more complex formulation, the method of the determination of the effective surfactants blend concentration was verified by applying it for more complex formulations of 2% O/W miconazole nitrate cream and the results indicate its reproducibility.

  14. PENGGUNAAN PARTIAL LEAST SQUARE REGRESSION (PLSR UNTUK MENGATASI MULTIKOLINEARITAS DALAM ESTIMASI KLOROFIL DAUN TANAMAN PADI DENGAN CITRA HIPERSPEKTRAL

    Directory of Open Access Journals (Sweden)

    Abdi Sukmono

    2015-02-01

    Full Text Available Klorofil merupakan pigmen yang paling penting dalam proses fotosintesis. Tanaman sehat yang mampu tumbuh maksimum umumnya  memiliki jumlah klorofil yang lebih besar daripada tanaman yang tidak sehat. Dalam Estimasi kandungan klorofil tanaman padi dengan airborne hiperspektral dibutuhkan model khusus untuk mendaaptkan akurasi yang baik. Citra Hhiperspektral mempunyai ratusan band dan julat yang sempit pada setiap bandnya, sehingga mempunyai kemampuan yang cukup baik untuk estimasi klorofil. Akan tetapi karena julat yang cukup sempit ini menyebabkan adanya efek multikolinearitas. Objek dari penelitian ini mengembangkan reflektan in situ menjadi model  estimasi kandungan klorofil tanaman padi untuk citra airborne hiperspektral dengan menggunakan metode partial least square regression untuk menghilangkan efek multikolinearitas.  Dalam penelitian ini dengan menggunakan teknik hubungan reflektan dan klorofil dipilih band-band yang berhungan dan efektif untuk estimasi klorofil. Dari hasil seleksi tersebut terpilih 44 band yang efektif untuk estimasi kandungan klorofil daun tanaman padi. Hasil dari penelitian ini menunjukkan mertode PLSR dapat menghasilkan model yang cukup baik untuk estimasi kandungan klorofil tanaman padi dengan nilai Koefisien determinasi (R2 mencapai 0.75 pada PC no 11 dan mempunyai RMSE sebesar 1.44 SPAD unit. Validasi menggunakan data citra airborne hiperspektral menghasilkan RMSE sebesar 1.07 SPAD Unit.

  15. Regularized plane-wave least-squares Kirchhoff migration

    KAUST Repository

    Wang, Xin; Dai, Wei; Schuster, Gerard T.

    2013-01-01

    A Kirchhoff least-squares migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images. A regularization term is included that accounts for mispositioning of reflectors due to errors in the velocity

  16. Least squares reverse time migration of controlled order multiples

    Science.gov (United States)

    Liu, Y.

    2016-12-01

    Imaging using the reverse time migration of multiples generates inherent crosstalk artifacts due to the interference among different order multiples. Traditionally, least-square fitting has been used to address this issue by seeking the best objective function to measure the amplitude differences between the predicted and observed data. We have developed an alternative objective function by decomposing multiples into different orders to minimize the difference between Born modeling predicted multiples and specific-order multiples from observational data in order to attenuate the crosstalk. This method is denoted as the least-squares reverse time migration of controlled order multiples (LSRTM-CM). Our numerical examples demonstrated that the LSRTM-CM can significantly improve image quality compared with reverse time migration of multiples and least-square reverse time migration of multiples. Acknowledgments This research was funded by the National Nature Science Foundation of China (Grant Nos. 41430321 and 41374138).

  17. Two Enhancements of the Logarithmic Least-Squares Method for Analyzing Subjective Comparisons

    Science.gov (United States)

    1989-03-25

    error term. 1 For this model, the total sum of squares ( SSTO ), defined as n 2 SSTO = E (yi y) i=1 can be partitioned into error and regression sums...of the regression line around the mean value. Mathematically, for the model given by equation A.4, SSTO = SSE + SSR (A.6) A-4 where SSTO is the total...sum of squares (i.e., the variance of the yi’s), SSE is error sum of squares, and SSR is the regression sum of squares. SSTO , SSE, and SSR are given

  18. On the null distribution of Bayes factors in linear regression

    Science.gov (United States)

    We show that under the null, the 2 log (Bayes factor) is asymptotically distributed as a weighted sum of chi-squared random variables with a shifted mean. This claim holds for Bayesian multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma prior, the g-prior, and...

  19. Accurate human limb angle measurement: sensor fusion through Kalman, least mean squares and recursive least-squares adaptive filtering

    Science.gov (United States)

    Olivares, A.; Górriz, J. M.; Ramírez, J.; Olivares, G.

    2011-02-01

    Inertial sensors are widely used in human body motion monitoring systems since they permit us to determine the position of the subject's limbs. Limb angle measurement is carried out through the integration of the angular velocity measured by a rate sensor and the decomposition of the components of static gravity acceleration measured by an accelerometer. Different factors derived from the sensors' nature, such as the angle random walk and dynamic bias, lead to erroneous measurements. Dynamic bias effects can be reduced through the use of adaptive filtering based on sensor fusion concepts. Most existing published works use a Kalman filtering sensor fusion approach. Our aim is to perform a comparative study among different adaptive filters. Several least mean squares (LMS), recursive least squares (RLS) and Kalman filtering variations are tested for the purpose of finding the best method leading to a more accurate and robust limb angle measurement. A new angle wander compensation sensor fusion approach based on LMS and RLS filters has been developed.

  20. Accurate human limb angle measurement: sensor fusion through Kalman, least mean squares and recursive least-squares adaptive filtering

    International Nuclear Information System (INIS)

    Olivares, A; Olivares, G; Górriz, J M; Ramírez, J

    2011-01-01

    Inertial sensors are widely used in human body motion monitoring systems since they permit us to determine the position of the subject's limbs. Limb angle measurement is carried out through the integration of the angular velocity measured by a rate sensor and the decomposition of the components of static gravity acceleration measured by an accelerometer. Different factors derived from the sensors' nature, such as the angle random walk and dynamic bias, lead to erroneous measurements. Dynamic bias effects can be reduced through the use of adaptive filtering based on sensor fusion concepts. Most existing published works use a Kalman filtering sensor fusion approach. Our aim is to perform a comparative study among different adaptive filters. Several least mean squares (LMS), recursive least squares (RLS) and Kalman filtering variations are tested for the purpose of finding the best method leading to a more accurate and robust limb angle measurement. A new angle wander compensation sensor fusion approach based on LMS and RLS filters has been developed

  1. Iterative methods for weighted least-squares

    Energy Technology Data Exchange (ETDEWEB)

    Bobrovnikova, E.Y.; Vavasis, S.A. [Cornell Univ., Ithaca, NY (United States)

    1996-12-31

    A weighted least-squares problem with a very ill-conditioned weight matrix arises in many applications. Because of round-off errors, the standard conjugate gradient method for solving this system does not give the correct answer even after n iterations. In this paper we propose an iterative algorithm based on a new type of reorthogonalization that converges to the solution.

  2. A Generalized Autocovariance Least-Squares Method for Covariance Estimation

    DEFF Research Database (Denmark)

    Åkesson, Bernt Magnus; Jørgensen, John Bagterp; Poulsen, Niels Kjølstad

    2007-01-01

    A generalization of the autocovariance least- squares method for estimating noise covariances is presented. The method can estimate mutually correlated system and sensor noise and can be used with both the predicting and the filtering form of the Kalman filter.......A generalization of the autocovariance least- squares method for estimating noise covariances is presented. The method can estimate mutually correlated system and sensor noise and can be used with both the predicting and the filtering form of the Kalman filter....

  3. Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Qiqi, E-mail: qiqi@mit.edu; Hu, Rui, E-mail: hurui@mit.edu; Blonigan, Patrick, E-mail: blonigan@mit.edu

    2014-06-15

    The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged quantity. This failure is known to be caused by ill-conditioned initial value problems. This paper overcomes this failure by replacing the initial value problem with the well-conditioned “least squares shadowing (LSS) problem”. The LSS problem is then linearized in our sensitivity analysis algorithm, which computes a derivative that converges to the derivative of the infinitely long time average. We demonstrate our algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations.

  4. A high order compact least-squares reconstructed discontinuous Galerkin method for the steady-state compressible flows on hybrid grids

    Science.gov (United States)

    Cheng, Jian; Zhang, Fan; Liu, Tiegang

    2018-06-01

    In this paper, a class of new high order reconstructed DG (rDG) methods based on the compact least-squares (CLS) reconstruction [23,24] is developed for simulating the two dimensional steady-state compressible flows on hybrid grids. The proposed method combines the advantages of the DG discretization with the flexibility of the compact least-squares reconstruction, which exhibits its superior potential in enhancing the level of accuracy and reducing the computational cost compared to the underlying DG methods with respect to the same number of degrees of freedom. To be specific, a third-order compact least-squares rDG(p1p2) method and a fourth-order compact least-squares rDG(p2p3) method are developed and investigated in this work. In this compact least-squares rDG method, the low order degrees of freedom are evolved through the underlying DG(p1) method and DG(p2) method, respectively, while the high order degrees of freedom are reconstructed through the compact least-squares reconstruction, in which the constitutive relations are built by requiring the reconstructed polynomial and its spatial derivatives on the target cell to conserve the cell averages and the corresponding spatial derivatives on the face-neighboring cells. The large sparse linear system resulted by the compact least-squares reconstruction can be solved relatively efficient when it is coupled with the temporal discretization in the steady-state simulations. A number of test cases are presented to assess the performance of the high order compact least-squares rDG methods, which demonstrates their potential to be an alternative approach for the high order numerical simulations of steady-state compressible flows.

  5. Measurement of food colour in L*a*b* units from RGB digital image using least squares support vector machine regression

    Directory of Open Access Journals (Sweden)

    Roberto Romaniello

    2015-12-01

    Full Text Available The aim of this work is to evaluate the potential of least squares support vector machine (LS-SVM regression to develop an efficient method to measure the colour of food materials in L*a*b* units by means of a computer vision systems (CVS. A laboratory CVS, based on colour digital camera (CDC, was implemented and three LS-SVM models were trained and validated, one for each output variables (L*, a*, and b* required by this problem, using the RGB signals generated by the CDC as input variables to these models. The colour target-based approach was used to camera characterization and a standard reference target of 242 colour samples was acquired using the CVS and a colorimeter. This data set was split in two sets of equal sizes, for training and validating the LS-SVM models. An effective two-stage grid search process on the parameters space was performed in MATLAB to tune the regularization parameters γ and the kernel parameters σ2 of the three LS-SVM models. A 3-8-3 multilayer feed-forward neural network (MFNN, according to the research conducted by León et al. (2006, was also trained in order to compare its performance with those of LS-SVM models. The LS-SVM models developed in this research have been shown better generalization capability then the MFNN, allowed to obtain high correlations between L*a*b* data acquired using the colorimeter and the corresponding data obtained by transformation of the RGB data acquired by the CVS. In particular, for the validation set, R2 values equal to 0.9989, 0.9987, and 0.9994 for L*, a* and b* parameters were obtained. The root mean square error values were 0.6443, 0.3226, and 0.2702 for L*, a*, and b* respectively, and the average of colour differences ΔEab was 0.8232±0.5033 units. Thus, LS-SVM regression seems to be a useful tool to measurement of food colour using a low cost CVS.

  6. Weighted least squares phase unwrapping based on the wavelet transform

    Science.gov (United States)

    Chen, Jiafeng; Chen, Haiqin; Yang, Zhengang; Ren, Haixia

    2007-01-01

    The weighted least squares phase unwrapping algorithm is a robust and accurate method to solve phase unwrapping problem. This method usually leads to a large sparse linear equation system. Gauss-Seidel relaxation iterative method is usually used to solve this large linear equation. However, this method is not practical due to its extremely slow convergence. The multigrid method is an efficient algorithm to improve convergence rate. However, this method needs an additional weight restriction operator which is very complicated. For this reason, the multiresolution analysis method based on the wavelet transform is proposed. By applying the wavelet transform, the original system is decomposed into its coarse and fine resolution levels and an equivalent equation system with better convergence condition can be obtained. Fast convergence in separate coarse resolution levels speeds up the overall system convergence rate. The simulated experiment shows that the proposed method converges faster and provides better result than the multigrid method.

  7. Linear least squares approach for evaluating crack tip fracture parameters using isochromatic and isoclinic data from digital photoelasticity

    Science.gov (United States)

    Patil, Prataprao; Vyasarayani, C. P.; Ramji, M.

    2017-06-01

    In this work, digital photoelasticity technique is used to estimate the crack tip fracture parameters for different crack configurations. Conventionally, only isochromatic data surrounding the crack tip is used for SIF estimation, but with the advent of digital photoelasticity, pixel-wise availability of both isoclinic and isochromatic data could be exploited for SIF estimation in a novel way. A linear least square approach is proposed to estimate the mixed-mode crack tip fracture parameters by solving the multi-parameter stress field equation. The stress intensity factor (SIF) is extracted from those estimated fracture parameters. The isochromatic and isoclinic data around the crack tip is estimated using the ten-step phase shifting technique. To get the unwrapped data, the adaptive quality guided phase unwrapping algorithm (AQGPU) has been used. The mixed mode fracture parameters, especially SIF are estimated for specimen configurations like single edge notch (SEN), center crack and straight crack ahead of inclusion using the proposed algorithm. The experimental SIF values estimated using the proposed method are compared with analytical/finite element analysis (FEA) results, and are found to be in good agreement.

  8. Least Square Fast Learning Network for modeling the combustion efficiency of a 300WM coal-fired boiler.

    Science.gov (United States)

    Li, Guoqiang; Niu, Peifeng; Wang, Huaibao; Liu, Yongchao

    2014-03-01

    This paper presents a novel artificial neural network with a very fast learning speed, all of whose weights and biases are determined by the twice Least Square method, so it is called Least Square Fast Learning Network (LSFLN). In addition, there is another difference from conventional neural networks, which is that the output neurons of LSFLN not only receive the information from the hidden layer neurons, but also receive the external information itself directly from the input neurons. In order to test the validity of LSFLN, it is applied to 6 classical regression applications, and also employed to build the functional relation between the combustion efficiency and operating parameters of a 300WM coal-fired boiler. Experimental results show that, compared with other methods, LSFLN with very less hidden neurons could achieve much better regression precision and generalization ability at a much faster learning speed. Copyright © 2013 Elsevier Ltd. All rights reserved.

  9. Solution of Large Systems of Linear Equations in the Presence of Errors. A Constructive Criticism of the Least Squares Method

    Energy Technology Data Exchange (ETDEWEB)

    Nygaard, K

    1968-09-15

    From the point of view that no mathematical method can ever minimise or alter errors already made in a physical measurement, the classical least squares method has severe limitations which makes it unsuitable for the statistical analysis of many physical measurements. Based on the assumptions that the experimental errors are characteristic for each single experiment and that the errors must be properly estimated rather than minimised, a new method for solving large systems of linear equations is developed. The new method exposes the entire range of possible solutions before the decision is taken which of the possible solutions should be chosen as a representative one. The choice is based on physical considerations which (in two examples, curve fitting and unfolding of a spectrum) are presented in such a form that a computer is able to make the decision, A description of the computation is given. The method described is a tool for removing uncertainties due to conventional mathematical formulations (zero determinant, linear dependence) and which are not inherent in the physical problem as such. The method is therefore especially well fitted for unfolding of spectra.

  10. Solution of Large Systems of Linear Equations in the Presence of Errors. A Constructive Criticism of the Least Squares Method

    International Nuclear Information System (INIS)

    Nygaard, K.

    1968-09-01

    From the point of view that no mathematical method can ever minimise or alter errors already made in a physical measurement, the classical least squares method has severe limitations which makes it unsuitable for the statistical analysis of many physical measurements. Based on the assumptions that the experimental errors are characteristic for each single experiment and that the errors must be properly estimated rather than minimised, a new method for solving large systems of linear equations is developed. The new method exposes the entire range of possible solutions before the decision is taken which of the possible solutions should be chosen as a representative one. The choice is based on physical considerations which (in two examples, curve fitting and unfolding of a spectrum) are presented in such a form that a computer is able to make the decision, A description of the computation is given. The method described is a tool for removing uncertainties due to conventional mathematical formulations (zero determinant, linear dependence) and which are not inherent in the physical problem as such. The method is therefore especially well fitted for unfolding of spectra

  11. Linear regression

    CERN Document Server

    Olive, David J

    2017-01-01

    This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response trans...

  12. Prediction of aged red wine aroma properties from aroma chemical composition. Partial least squares regression models.

    Science.gov (United States)

    Aznar, Margarita; López, Ricardo; Cacho, Juan; Ferreira, Vicente

    2003-04-23

    Partial least squares regression (PLSR) models able to predict some of the wine aroma nuances from its chemical composition have been developed. The aromatic sensory characteristics of 57 Spanish aged red wines were determined by 51 experts from the wine industry. The individual descriptions given by the experts were recorded, and the frequency with which a sensory term was used to define a given wine was taken as a measurement of its intensity. The aromatic chemical composition of the wines was determined by already published gas chromatography (GC)-flame ionization detector and GC-mass spectrometry methods. In the whole, 69 odorants were analyzed. Both matrixes, the sensory and chemical data, were simplified by grouping and rearranging correlated sensory terms or chemical compounds and by the exclusion of secondary aroma terms or of weak aroma chemicals. Finally, models were developed for 18 sensory terms and 27 chemicals or groups of chemicals. Satisfactory models, explaining more than 45% of the original variance, could be found for nine of the most important sensory terms (wood-vanillin-cinnamon, animal-leather-phenolic, toasted-coffee, old wood-reduction, vegetal-pepper, raisin-flowery, sweet-candy-cacao, fruity, and berry fruit). For this set of terms, the correlation coefficients between the measured and predicted Y (determined by cross-validation) ranged from 0.62 to 0.81. Models confirmed the existence of complex multivariate relationships between chemicals and odors. In general, pleasant descriptors were positively correlated to chemicals with pleasant aroma, such as vanillin, beta damascenone, or (E)-beta-methyl-gamma-octalactone, and negatively correlated to compounds showing less favorable odor properties, such as 4-ethyl and vinyl phenols, 3-(methylthio)-1-propanol, or phenylacetaldehyde.

  13. Least Squares Methods for Equidistant Tree Reconstruction

    OpenAIRE

    Fahey, Conor; Hosten, Serkan; Krieger, Nathan; Timpe, Leslie

    2008-01-01

    UPGMA is a heuristic method identifying the least squares equidistant phylogenetic tree given empirical distance data among $n$ taxa. We study this classic algorithm using the geometry of the space of all equidistant trees with $n$ leaves, also known as the Bergman complex of the graphical matroid for the complete graph $K_n$. We show that UPGMA performs an orthogonal projection of the data onto a maximal cell of the Bergman complex. We also show that the equidistant tree with the least (Eucl...

  14. Optimally weighted least-squares steganalysis

    Science.gov (United States)

    Ker, Andrew D.

    2007-02-01

    Quantitative steganalysis aims to estimate the amount of payload in a stego object, and such estimators seem to arise naturally in steganalysis of Least Significant Bit (LSB) replacement in digital images. However, as with all steganalysis, the estimators are subject to errors, and their magnitude seems heavily dependent on properties of the cover. In very recent work we have given the first derivation of estimation error, for a certain method of steganalysis (the Least-Squares variant of Sample Pairs Analysis) of LSB replacement steganography in digital images. In this paper we make use of our theoretical results to find an improved estimator and detector. We also extend the theoretical analysis to another (more accurate) steganalysis estimator (Triples Analysis) and hence derive an improved version of that estimator too. Experimental results show that the new steganalyzers have improved accuracy, particularly in the difficult case of never-compressed covers.

  15. Data-adapted moving least squares method for 3-D image interpolation

    International Nuclear Information System (INIS)

    Jang, Sumi; Lee, Yeon Ju; Jeong, Byeongseon; Nam, Haewon; Lee, Rena; Yoon, Jungho

    2013-01-01

    In this paper, we present a nonlinear three-dimensional interpolation scheme for gray-level medical images. The scheme is based on the moving least squares method but introduces a fundamental modification. For a given evaluation point, the proposed method finds the local best approximation by reproducing polynomials of a certain degree. In particular, in order to obtain a better match to the local structures of the given image, we employ locally data-adapted least squares methods that can improve the classical one. Some numerical experiments are presented to demonstrate the performance of the proposed method. Five types of data sets are used: MR brain, MR foot, MR abdomen, CT head, and CT foot. From each of the five types, we choose five volumes. The scheme is compared with some well-known linear methods and other recently developed nonlinear methods. For quantitative comparison, we follow the paradigm proposed by Grevera and Udupa (1998). (Each slice is first assumed to be unknown then interpolated by each method. The performance of each interpolation method is assessed statistically.) The PSNR results for the estimated volumes are also provided. We observe that the new method generates better results in both quantitative and visual quality comparisons. (paper)

  16. Multilevel solvers of first-order system least-squares for Stokes equations

    Energy Technology Data Exchange (ETDEWEB)

    Lai, Chen-Yao G. [National Chung Cheng Univ., Chia-Yi (Taiwan, Province of China)

    1996-12-31

    Recently, The use of first-order system least squares principle for the approximate solution of Stokes problems has been extensively studied by Cai, Manteuffel, and McCormick. In this paper, we study multilevel solvers of first-order system least-squares method for the generalized Stokes equations based on the velocity-vorticity-pressure formulation in three dimensions. The least-squares functionals is defined to be the sum of the L{sup 2}-norms of the residuals, which is weighted appropriately by the Reynolds number. We develop convergence analysis for additive and multiplicative multilevel methods applied to the resulting discrete equations.

  17. Elastic least-squares reverse time migration

    KAUST Repository

    Feng, Zongcai; Schuster, Gerard T.

    2016-01-01

    Elastic least-squares reverse time migration (LSRTM) is used to invert synthetic particle-velocity data and crosswell pressure field data. The migration images consist of both the P- and Svelocity perturbation images. Numerical tests on synthetic and field data illustrate the advantages of elastic LSRTM over elastic reverse time migration (RTM). In addition, elastic LSRTM images are better focused and have better reflector continuity than do the acoustic LSRTM images.

  18. Elastic least-squares reverse time migration

    KAUST Repository

    Feng, Zongcai

    2016-09-06

    Elastic least-squares reverse time migration (LSRTM) is used to invert synthetic particle-velocity data and crosswell pressure field data. The migration images consist of both the P- and Svelocity perturbation images. Numerical tests on synthetic and field data illustrate the advantages of elastic LSRTM over elastic reverse time migration (RTM). In addition, elastic LSRTM images are better focused and have better reflector continuity than do the acoustic LSRTM images.

  19. Daily Suspended Sediment Discharge Prediction Using Multiple Linear Regression and Artificial Neural Network

    Science.gov (United States)

    Uca; Toriman, Ekhwan; Jaafar, Othman; Maru, Rosmini; Arfan, Amal; Saleh Ahmar, Ansari

    2018-01-01

    Prediction of suspended sediment discharge in a catchments area is very important because it can be used to evaluation the erosion hazard, management of its water resources, water quality, hydrology project management (dams, reservoirs, and irrigation) and to determine the extent of the damage that occurred in the catchments. Multiple Linear Regression analysis and artificial neural network can be used to predict the amount of daily suspended sediment discharge. Regression analysis using the least square method, whereas artificial neural networks using Radial Basis Function (RBF) and feedforward multilayer perceptron with three learning algorithms namely Levenberg-Marquardt (LM), Scaled Conjugate Descent (SCD) and Broyden-Fletcher-Goldfarb-Shanno Quasi-Newton (BFGS). The number neuron of hidden layer is three to sixteen, while in output layer only one neuron because only one output target. The mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R2 ) and coefficient of efficiency (CE) of the multiple linear regression (MLRg) value Model 2 (6 input variable independent) has the lowest the value of MAE and RMSE (0.0000002 and 13.6039) and highest R2 and CE (0.9971 and 0.9971). When compared between LM, SCG and RBF, the BFGS model structure 3-7-1 is the better and more accurate to prediction suspended sediment discharge in Jenderam catchment. The performance value in testing process, MAE and RMSE (13.5769 and 17.9011) is smallest, meanwhile R2 and CE (0.9999 and 0.9998) is the highest if it compared with the another BFGS Quasi-Newton model (6-3-1, 9-10-1 and 12-12-1). Based on the performance statistics value, MLRg, LM, SCG, BFGS and RBF suitable and accurately for prediction by modeling the non-linear complex behavior of suspended sediment responses to rainfall, water depth and discharge. The comparison between artificial neural network (ANN) and MLRg, the MLRg Model 2 accurately for to prediction suspended sediment discharge (kg

  20. Modelling subject-specific childhood growth using linear mixed-effect models with cubic regression splines.

    Science.gov (United States)

    Grajeda, Laura M; Ivanescu, Andrada; Saito, Mayuko; Crainiceanu, Ciprian; Jaganath, Devan; Gilman, Robert H; Crabtree, Jean E; Kelleher, Dermott; Cabrera, Lilia; Cama, Vitaliano; Checkley, William

    2016-01-01

    Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration. We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific random intercepts and slopes and residual autocorrelation. We then compared cubic regression splines vis-à-vis linear piecewise splines, and with varying number of knots and positions. Statistical code is provided to ensure reproducibility and improve dissemination of methods. Models are applied to longitudinal height measurements in a cohort of 215 Peruvian children followed from birth until their fourth year of life. Unexplained variability, as measured by the variance of the regression model, was reduced from 7.34 when using ordinary least squares to 0.81 (p linear mixed-effect models with random slopes and a first order continuous autoregressive error term. There was substantial heterogeneity in both the intercept (p modeled with a first order continuous autoregressive error term as evidenced by the variogram of the residuals and by a lack of association among residuals. The final model provides a parametric linear regression equation for both estimation and prediction of population- and individual-level growth in height. We show that cubic regression splines are superior to linear regression splines for the case of a small number of knots in both estimation and prediction with the full linear mixed effect model (AIC 19,352 vs. 19

  1. Method validation using weighted linear regression models for quantification of UV filters in water samples.

    Science.gov (United States)

    da Silva, Claudia Pereira; Emídio, Elissandro Soares; de Marchi, Mary Rosa Rodrigues

    2015-01-01

    This paper describes the validation of a method consisting of solid-phase extraction followed by gas chromatography-tandem mass spectrometry for the analysis of the ultraviolet (UV) filters benzophenone-3, ethylhexyl salicylate, ethylhexyl methoxycinnamate and octocrylene. The method validation criteria included evaluation of selectivity, analytical curve, trueness, precision, limits of detection and limits of quantification. The non-weighted linear regression model has traditionally been used for calibration, but it is not necessarily the optimal model in all cases. Because the assumption of homoscedasticity was not met for the analytical data in this work, a weighted least squares linear regression was used for the calibration method. The evaluated analytical parameters were satisfactory for the analytes and showed recoveries at four fortification levels between 62% and 107%, with relative standard deviations less than 14%. The detection limits ranged from 7.6 to 24.1 ng L(-1). The proposed method was used to determine the amount of UV filters in water samples from water treatment plants in Araraquara and Jau in São Paulo, Brazil. Copyright © 2014 Elsevier B.V. All rights reserved.

  2. Constrained least squares regularization in PET

    International Nuclear Information System (INIS)

    Choudhury, K.R.; O'Sullivan, F.O.

    1996-01-01

    Standard reconstruction methods used in tomography produce images with undesirable negative artifacts in background and in areas of high local contrast. While sophisticated statistical reconstruction methods can be devised to correct for these artifacts, their computational implementation is excessive for routine operational use. This work describes a technique for rapid computation of approximate constrained least squares regularization estimates. The unique feature of the approach is that it involves no iterative projection or backprojection steps. This contrasts with the familiar computationally intensive algorithms based on algebraic reconstruction (ART) or expectation-maximization (EM) methods. Experimentation with the new approach for deconvolution and mixture analysis shows that the root mean square error quality of estimators based on the proposed algorithm matches and usually dominates that of more elaborate maximum likelihood, at a fraction of the computational effort

  3. A Technique of Fuzzy C-Mean in Multiple Linear Regression Model toward Paddy Yield

    Science.gov (United States)

    Syazwan Wahab, Nur; Saifullah Rusiman, Mohd; Mohamad, Mahathir; Amira Azmi, Nur; Che Him, Norziha; Ghazali Kamardan, M.; Ali, Maselan

    2018-04-01

    In this paper, we propose a hybrid model which is a combination of multiple linear regression model and fuzzy c-means method. This research involved a relationship between 20 variates of the top soil that are analyzed prior to planting of paddy yields at standard fertilizer rates. Data used were from the multi-location trials for rice carried out by MARDI at major paddy granary in Peninsular Malaysia during the period from 2009 to 2012. Missing observations were estimated using mean estimation techniques. The data were analyzed using multiple linear regression model and a combination of multiple linear regression model and fuzzy c-means method. Analysis of normality and multicollinearity indicate that the data is normally scattered without multicollinearity among independent variables. Analysis of fuzzy c-means cluster the yield of paddy into two clusters before the multiple linear regression model can be used. The comparison between two method indicate that the hybrid of multiple linear regression model and fuzzy c-means method outperform the multiple linear regression model with lower value of mean square error.

  4. A least-squares minimization approach for model parameters estimate by using a new magnetic anomaly formula

    Science.gov (United States)

    Abo-Ezz, E. R.; Essa, K. S.

    2016-04-01

    A new linear least-squares approach is proposed to interpret magnetic anomalies of the buried structures by using a new magnetic anomaly formula. This approach depends on solving different sets of algebraic linear equations in order to invert the depth ( z), amplitude coefficient ( K), and magnetization angle ( θ) of buried structures using magnetic data. The utility and validity of the new proposed approach has been demonstrated through various reliable synthetic data sets with and without noise. In addition, the method has been applied to field data sets from USA and India. The best-fitted anomaly has been delineated by estimating the root-mean squared (rms). Judging satisfaction of this approach is done by comparing the obtained results with other available geological or geophysical information.

  5. Estimation of active pharmaceutical ingredients content using locally weighted partial least squares and statistical wavelength selection.

    Science.gov (United States)

    Kim, Sanghong; Kano, Manabu; Nakagawa, Hiroshi; Hasebe, Shinji

    2011-12-15

    Development of quality estimation models using near infrared spectroscopy (NIRS) and multivariate analysis has been accelerated as a process analytical technology (PAT) tool in the pharmaceutical industry. Although linear regression methods such as partial least squares (PLS) are widely used, they cannot always achieve high estimation accuracy because physical and chemical properties of a measuring object have a complex effect on NIR spectra. In this research, locally weighted PLS (LW-PLS) which utilizes a newly defined similarity between samples is proposed to estimate active pharmaceutical ingredient (API) content in granules for tableting. In addition, a statistical wavelength selection method which quantifies the effect of API content and other factors on NIR spectra is proposed. LW-PLS and the proposed wavelength selection method were applied to real process data provided by Daiichi Sankyo Co., Ltd., and the estimation accuracy was improved by 38.6% in root mean square error of prediction (RMSEP) compared to the conventional PLS using wavelengths selected on the basis of variable importance on the projection (VIP). The results clearly show that the proposed calibration modeling technique is useful for API content estimation and is superior to the conventional one. Copyright © 2011 Elsevier B.V. All rights reserved.

  6. Dual stacked partial least squares for analysis of near-infrared spectra

    Energy Technology Data Exchange (ETDEWEB)

    Bi, Yiming [Institute of Automation, Chinese Academy of Sciences, 100190 Beijing (China); Xie, Qiong, E-mail: yimbi@163.com [Institute of Automation, Chinese Academy of Sciences, 100190 Beijing (China); Peng, Silong; Tang, Liang; Hu, Yong; Tan, Jie [Institute of Automation, Chinese Academy of Sciences, 100190 Beijing (China); Zhao, Yuhui [School of Economics and Business, Northeastern University at Qinhuangdao, 066000 Qinhuangdao City (China); Li, Changwen [Food Research Institute of Tianjin Tasly Group, 300410 Tianjin (China)

    2013-08-20

    Graphical abstract: -- Highlights: •Dual stacking steps are used for multivariate calibration of near-infrared spectra. •A selective weighting strategy is introduced that only a subset of all available sub-models is used for model fusion. •Using two public near-infrared datasets, the proposed method achieved competitive results. •The method can be widely applied in many fields, such as Mid-infrared spectra data and Raman spectra data. -- Abstract: A new ensemble learning algorithm is presented for quantitative analysis of near-infrared spectra. The algorithm contains two steps of stacked regression and Partial Least Squares (PLS), termed Dual Stacked Partial Least Squares (DSPLS) algorithm. First, several sub-models were generated from the whole calibration set. The inner-stack step was implemented on sub-intervals of the spectrum. Then the outer-stack step was used to combine these sub-models. Several combination rules of the outer-stack step were analyzed for the proposed DSPLS algorithm. In addition, a novel selective weighting rule was also involved to select a subset of all available sub-models. Experiments on two public near-infrared datasets demonstrate that the proposed DSPLS with selective weighting rule provided superior prediction performance and outperformed the conventional PLS algorithm. Compared with the single model, the new ensemble model can provide more robust prediction result and can be considered an alternative choice for quantitative analytical applications.

  7. Dual stacked partial least squares for analysis of near-infrared spectra

    International Nuclear Information System (INIS)

    Bi, Yiming; Xie, Qiong; Peng, Silong; Tang, Liang; Hu, Yong; Tan, Jie; Zhao, Yuhui; Li, Changwen

    2013-01-01

    Graphical abstract: -- Highlights: •Dual stacking steps are used for multivariate calibration of near-infrared spectra. •A selective weighting strategy is introduced that only a subset of all available sub-models is used for model fusion. •Using two public near-infrared datasets, the proposed method achieved competitive results. •The method can be widely applied in many fields, such as Mid-infrared spectra data and Raman spectra data. -- Abstract: A new ensemble learning algorithm is presented for quantitative analysis of near-infrared spectra. The algorithm contains two steps of stacked regression and Partial Least Squares (PLS), termed Dual Stacked Partial Least Squares (DSPLS) algorithm. First, several sub-models were generated from the whole calibration set. The inner-stack step was implemented on sub-intervals of the spectrum. Then the outer-stack step was used to combine these sub-models. Several combination rules of the outer-stack step were analyzed for the proposed DSPLS algorithm. In addition, a novel selective weighting rule was also involved to select a subset of all available sub-models. Experiments on two public near-infrared datasets demonstrate that the proposed DSPLS with selective weighting rule provided superior prediction performance and outperformed the conventional PLS algorithm. Compared with the single model, the new ensemble model can provide more robust prediction result and can be considered an alternative choice for quantitative analytical applications

  8. Method for nonlinear exponential regression analysis

    Science.gov (United States)

    Junkin, B. G.

    1972-01-01

    Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.

  9. Algorithms for non-linear M-estimation

    DEFF Research Database (Denmark)

    Madsen, Kaj; Edlund, O; Ekblom, H

    1997-01-01

    In non-linear regression, the least squares method is most often used. Since this estimator is highly sensitive to outliers in the data, alternatives have became increasingly popular during the last decades. We present algorithms for non-linear M-estimation. A trust region approach is used, where...

  10. Multi-source least-squares migration of marine data

    KAUST Repository

    Wang, Xin; Schuster, Gerard T.

    2012-01-01

    Kirchhoff based multi-source least-squares migration (MSLSM) is applied to marine streamer data. To suppress the crosstalk noise from the excitation of multiple sources, a dynamic encoding function (including both time-shifts and polarity changes

  11. Cointegrating MiDaS Regressions and a MiDaS Test

    OpenAIRE

    J. Isaac Miller

    2011-01-01

    This paper introduces cointegrating mixed data sampling (CoMiDaS) regressions, generalizing nonlinear MiDaS regressions in the extant literature. Under a linear mixed-frequency data-generating process, MiDaS regressions provide a parsimoniously parameterized nonlinear alternative when the linear forecasting model is over-parameterized and may be infeasible. In spite of potential correlation of the error term both serially and with the regressors, I find that nonlinear least squares consistent...

  12. Weighted least-squares criteria for electrical impedance tomography

    International Nuclear Information System (INIS)

    Kallman, J.S.; Berryman, J.G.

    1992-01-01

    Methods are developed for design of electrical impedance tomographic reconstruction algorithms with specified properties. Assuming a starting model with constant conductivity or some other specified background distribution, an algorithm with the following properties is found: (1) the optimum constant for the starting model is determined automatically; (2) the weighted least-squares error between the predicted and measured power dissipation data is as small as possible; (3) the variance of the reconstructed conductivity from the starting model is minimized; (4) potential distributions with the largest volume integral of gradient squared have the least influence on the reconstructed conductivity, and therefore distributions most likely to be corrupted by contact impedance effects are deemphasized; (5) cells that dissipate the most power during the current injection tests tend to deviate least from the background value. The resulting algorithm maps the reconstruction problem into a vector space where the contribution to the inversion from the background conductivity remains invariant, while the optimum contributions in orthogonal directions are found. For a starting model with nonconstant conductivity, the reconstruction algorithm has analogous properties

  13. 3D plane-wave least-squares Kirchhoff migration

    KAUST Repository

    Wang, Xin; Dai, Wei; Huang, Yunsong; Schuster, Gerard T.

    2014-01-01

    A three dimensional least-squares Kirchhoff migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images and the computational efficiency. Due to the limitation of current 3D marine acquisition

  14. Decision-Directed Recursive Least Squares MIMO Channels Tracking

    Directory of Open Access Journals (Sweden)

    Karami Ebrahim

    2006-01-01

    Full Text Available A new approach for joint data estimation and channel tracking for multiple-input multiple-output (MIMO channels is proposed based on the decision-directed recursive least squares (DD-RLS algorithm. RLS algorithm is commonly used for equalization and its application in channel estimation is a novel idea. In this paper, after defining the weighted least squares cost function it is minimized and eventually the RLS MIMO channel estimation algorithm is derived. The proposed algorithm combined with the decision-directed algorithm (DDA is then extended for the blind mode operation. From the computational complexity point of view being versus the number of transmitter and receiver antennas, the proposed algorithm is very efficient. Through various simulations, the mean square error (MSE of the tracking of the proposed algorithm for different joint detection algorithms is compared with Kalman filtering approach which is one of the most well-known channel tracking algorithms. It is shown that the performance of the proposed algorithm is very close to Kalman estimator and that in the blind mode operation it presents a better performance with much lower complexity irrespective of the need to know the channel model.

  15. Independent contrasts and PGLS regression estimators are equivalent.

    Science.gov (United States)

    Blomberg, Simon P; Lefevre, James G; Wells, Jessie A; Waterhouse, Mary

    2012-05-01

    We prove that the slope parameter of the ordinary least squares regression of phylogenetically independent contrasts (PICs) conducted through the origin is identical to the slope parameter of the method of generalized least squares (GLSs) regression under a Brownian motion model of evolution. This equivalence has several implications: 1. Understanding the structure of the linear model for GLS regression provides insight into when and why phylogeny is important in comparative studies. 2. The limitations of the PIC regression analysis are the same as the limitations of the GLS model. In particular, phylogenetic covariance applies only to the response variable in the regression and the explanatory variable should be regarded as fixed. Calculation of PICs for explanatory variables should be treated as a mathematical idiosyncrasy of the PIC regression algorithm. 3. Since the GLS estimator is the best linear unbiased estimator (BLUE), the slope parameter estimated using PICs is also BLUE. 4. If the slope is estimated using different branch lengths for the explanatory and response variables in the PIC algorithm, the estimator is no longer the BLUE, so this is not recommended. Finally, we discuss whether or not and how to accommodate phylogenetic covariance in regression analyses, particularly in relation to the problem of phylogenetic uncertainty. This discussion is from both frequentist and Bayesian perspectives.

  16. Least squares analysis of fission neutron standard fields

    International Nuclear Information System (INIS)

    Griffin, P.J.; Williams, J.G.

    1997-01-01

    A least squares analysis of fission neutron standard fields has been performed using the latest dosimetry cross sections. Discrepant nuclear data are identified and adjusted spectra for 252 Cf spontaneous fission and 235 U thermal fission fields are presented

  17. Fragility estimation for seismically isolated nuclear structures by high confidence low probability of failure values and bi-linear regression

    International Nuclear Information System (INIS)

    Carausu, A.

    1996-01-01

    A method for the fragility estimation of seismically isolated nuclear power plant structure is proposed. The relationship between the ground motion intensity parameter (e.g. peak ground velocity or peak ground acceleration) and the response of isolated structures is expressed in terms of a bi-linear regression line, whose coefficients are estimated by the least-square method in terms of available data on seismic input and structural response. The notion of high confidence low probability of failure (HCLPF) value is also used for deriving compound fragility curves for coupled subsystems. (orig.)

  18. Least-squares finite element discretizations of neutron transport equations in 3 dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Manteuffel, T.A [Univ. of Colorado, Boulder, CO (United States); Ressel, K.J. [Interdisciplinary Project Center for Supercomputing, Zurich (Switzerland); Starkes, G. [Universtaet Karlsruhe (Germany)

    1996-12-31

    The least-squares finite element framework to the neutron transport equation introduced in is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. Here we report on some practical aspects of this approach for neutron transport calculations in three space dimensions. The systems of partial differential equations resulting from a P{sub 1} and P{sub 2} approximation of the angular dependence are derived. In the diffusive limit, the system is essentially a Poisson equation for zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. We report on the numerical results obtained for the minimum of the least-squares functional augmented by an additional boundary term using trilinear finite elements on a uniform tesselation into cubes.

  19. On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs

    Energy Technology Data Exchange (ETDEWEB)

    Amini, Nina H. [Stanford University, Edward L. Ginzton Laboratory, Stanford, CA (United States); CNRS, Laboratoire des Signaux et Systemes (L2S) CentraleSupelec, Gif-sur-Yvette (France); Miao, Zibo; Pan, Yu; James, Matthew R. [Australian National University, ARC Centre for Quantum Computation and Communication Technology, Research School of Engineering, Canberra, ACT (Australia); Mabuchi, Hideo [Stanford University, Edward L. Ginzton Laboratory, Stanford, CA (United States)

    2015-12-15

    The purpose of this paper is to study the problem of generalizing the Belavkin-Kalman filter to the case where the classical measurement signal is replaced by a fully quantum non-commutative output signal. We formulate a least mean squares estimation problem that involves a non-commutative system as the filter processing the non-commutative output signal. We solve this estimation problem within the framework of non-commutative probability. Also, we find the necessary and sufficient conditions which make these non-commutative estimators physically realizable. These conditions are restrictive in practice. (orig.)

  20. SECOND ORDER LEAST SQUARE ESTIMATION ON ARCH(1 MODEL WITH BOX-COX TRANSFORMED DEPENDENT VARIABLE

    Directory of Open Access Journals (Sweden)

    Herni Utami

    2014-03-01

    Full Text Available Box-Cox transformation is often used to reduce heterogeneity and to achieve a symmetric distribution of response variable. In this paper, we estimate the parameters of Box-Cox transformed ARCH(1 model using second-order leastsquare method and then we study the consistency and asymptotic normality for second-order least square (SLS estimators. The SLS estimation was introduced byWang (2003, 2004 to estimate the parameters of nonlinear regression models with independent and identically distributed errors

  1. Recursive Algorithm For Linear Regression

    Science.gov (United States)

    Varanasi, S. V.

    1988-01-01

    Order of model determined easily. Linear-regression algorithhm includes recursive equations for coefficients of model of increased order. Algorithm eliminates duplicative calculations, facilitates search for minimum order of linear-regression model fitting set of data satisfactory.

  2. Facial Expression Recognition via Non-Negative Least-Squares Sparse Coding

    Directory of Open Access Journals (Sweden)

    Ying Chen

    2014-05-01

    Full Text Available Sparse coding is an active research subject in signal processing, computer vision, and pattern recognition. A novel method of facial expression recognition via non-negative least squares (NNLS sparse coding is presented in this paper. The NNLS sparse coding is used to form a facial expression classifier. To testify the performance of the presented method, local binary patterns (LBP and the raw pixels are extracted for facial feature representation. Facial expression recognition experiments are conducted on the Japanese Female Facial Expression (JAFFE database. Compared with other widely used methods such as linear support vector machines (SVM, sparse representation-based classifier (SRC, nearest subspace classifier (NSC, K-nearest neighbor (KNN and radial basis function neural networks (RBFNN, the experiment results indicate that the presented NNLS method performs better than other used methods on facial expression recognition tasks.

  3. Moving least squares simulation of free surface flows

    DEFF Research Database (Denmark)

    Felter, C. L.; Walther, Jens Honore; Henriksen, Christian

    2014-01-01

    In this paper a Moving Least Squares method (MLS) for the simulation of 2D free surface flows is presented. The emphasis is on the governing equations, the boundary conditions, and the numerical implementation. The compressible viscous isothermal Navier–Stokes equations are taken as the starting ...

  4. Multivariate calibration with least-squares support vector machines.

    NARCIS (Netherlands)

    Thissen, U.M.J.; Ustun, B.; Melssen, W.J.; Buydens, L.M.C.

    2004-01-01

    This paper proposes the use of least-squares support vector machines (LS-SVMs) as a relatively new nonlinear multivariate calibration method, capable of dealing with ill-posed problems. LS-SVMs are an extension of "traditional" SVMs that have been introduced recently in the field of chemistry and

  5. Synthesis of linear regression coefficients by recovering the within-study covariance matrix from summary statistics.

    Science.gov (United States)

    Yoneoka, Daisuke; Henmi, Masayuki

    2017-06-01

    Recently, the number of regression models has dramatically increased in several academic fields. However, within the context of meta-analysis, synthesis methods for such models have not been developed in a commensurate trend. One of the difficulties hindering the development is the disparity in sets of covariates among literature models. If the sets of covariates differ across models, interpretation of coefficients will differ, thereby making it difficult to synthesize them. Moreover, previous synthesis methods for regression models, such as multivariate meta-analysis, often have problems because covariance matrix of coefficients (i.e. within-study correlations) or individual patient data are not necessarily available. This study, therefore, proposes a brief explanation regarding a method to synthesize linear regression models under different covariate sets by using a generalized least squares method involving bias correction terms. Especially, we also propose an approach to recover (at most) threecorrelations of covariates, which is required for the calculation of the bias term without individual patient data. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

  6. Source allocation by least-squares hydrocarbon fingerprint matching

    Energy Technology Data Exchange (ETDEWEB)

    William A. Burns; Stephen M. Mudge; A. Edward Bence; Paul D. Boehm; John S. Brown; David S. Page; Keith R. Parker [W.A. Burns Consulting Services LLC, Houston, TX (United States)

    2006-11-01

    There has been much controversy regarding the origins of the natural polycyclic aromatic hydrocarbon (PAH) and chemical biomarker background in Prince William Sound (PWS), Alaska, site of the 1989 Exxon Valdez oil spill. Different authors have attributed the sources to various proportions of coal, natural seep oil, shales, and stream sediments. The different probable bioavailabilities of hydrocarbons from these various sources can affect environmental damage assessments from the spill. This study compares two different approaches to source apportionment with the same data (136 PAHs and biomarkers) and investigate whether increasing the number of coal source samples from one to six increases coal attributions. The constrained least-squares (CLS) source allocation method that fits concentrations meets geologic and chemical constraints better than partial least-squares (PLS) which predicts variance. The field data set was expanded to include coal samples reported by others, and CLS fits confirm earlier findings of low coal contributions to PWS. 15 refs., 5 figs.

  7. Least-Square Prediction for Backward Adaptive Video Coding

    Directory of Open Access Journals (Sweden)

    Li Xin

    2006-01-01

    Full Text Available Almost all existing approaches towards video coding exploit the temporal redundancy by block-matching-based motion estimation and compensation. Regardless of its popularity, block matching still reflects an ad hoc understanding of the relationship between motion and intensity uncertainty models. In this paper, we present a novel backward adaptive approach, named "least-square prediction" (LSP, and demonstrate its potential in video coding. Motivated by the duality between edge contour in images and motion trajectory in video, we propose to derive the best prediction of the current frame from its causal past using least-square method. It is demonstrated that LSP is particularly effective for modeling video material with slow motion and can be extended to handle fast motion by temporal warping and forward adaptation. For typical QCIF test sequences, LSP often achieves smaller MSE than , full-search, quarter-pel block matching algorithm (BMA without the need of transmitting any overhead.

  8. A primer for biomedical scientists on how to execute model II linear regression analysis.

    Science.gov (United States)

    Ludbrook, John

    2012-04-01

    1. There are two very different ways of executing linear regression analysis. One is Model I, when the x-values are fixed by the experimenter. The other is Model II, in which the x-values are free to vary and are subject to error. 2. I have received numerous complaints from biomedical scientists that they have great difficulty in executing Model II linear regression analysis. This may explain the results of a Google Scholar search, which showed that the authors of articles in journals of physiology, pharmacology and biochemistry rarely use Model II regression analysis. 3. I repeat my previous arguments in favour of using least products linear regression analysis for Model II regressions. I review three methods for executing ordinary least products (OLP) and weighted least products (WLP) regression analysis: (i) scientific calculator and/or computer spreadsheet; (ii) specific purpose computer programs; and (iii) general purpose computer programs. 4. Using a scientific calculator and/or computer spreadsheet, it is easy to obtain correct values for OLP slope and intercept, but the corresponding 95% confidence intervals (CI) are inaccurate. 5. Using specific purpose computer programs, the freeware computer program smatr gives the correct OLP regression coefficients and obtains 95% CI by bootstrapping. In addition, smatr can be used to compare the slopes of OLP lines. 6. When using general purpose computer programs, I recommend the commercial programs systat and Statistica for those who regularly undertake linear regression analysis and I give step-by-step instructions in the Supplementary Information as to how to use loss functions. © 2011 The Author. Clinical and Experimental Pharmacology and Physiology. © 2011 Blackwell Publishing Asia Pty Ltd.

  9. Comparison of some biased estimation methods (including ordinary subset regression) in the linear model

    Science.gov (United States)

    Sidik, S. M.

    1975-01-01

    Ridge, Marquardt's generalized inverse, shrunken, and principal components estimators are discussed in terms of the objectives of point estimation of parameters, estimation of the predictive regression function, and hypothesis testing. It is found that as the normal equations approach singularity, more consideration must be given to estimable functions of the parameters as opposed to estimation of the full parameter vector; that biased estimators all introduce constraints on the parameter space; that adoption of mean squared error as a criterion of goodness should be independent of the degree of singularity; and that ordinary least-squares subset regression is the best overall method.

  10. Simplified Least Squares Shadowing sensitivity analysis for chaotic ODEs and PDEs

    Energy Technology Data Exchange (ETDEWEB)

    Chater, Mario, E-mail: chaterm@mit.edu; Ni, Angxiu, E-mail: niangxiu@mit.edu; Wang, Qiqi, E-mail: qiqi@mit.edu

    2017-01-15

    This paper develops a variant of the Least Squares Shadowing (LSS) method, which has successfully computed the derivative for several chaotic ODEs and PDEs. The development in this paper aims to simplify Least Squares Shadowing method by improving how time dilation is treated. Instead of adding an explicit time dilation term as in the original method, the new variant uses windowing, which can be more efficient and simpler to implement, especially for PDEs.

  11. Least-mean-square spatial filter for IR sensors.

    Science.gov (United States)

    Takken, E H; Friedman, D; Milton, A F; Nitzberg, R

    1979-12-15

    A new least-mean-square filter is defined for signal-detection problems. The technique is proposed for scanning IR surveillance systems operating in poorly characterized but primarily low-frequency clutter interference. Near-optimal detection of point-source targets is predicted both for continuous-time and sampled-data systems.

  12. Canards in a minimal piecewise-linear square-wave burster

    Energy Technology Data Exchange (ETDEWEB)

    Desroches, M.; Krupa, M. [Inria Sophia-Antipolis Méditerranée Research Centre, MathNeuro Project-Team 2004 route des Lucioles BP 93, 06902 Valbonne Cedex (France); Fernández-García, S., E-mail: soledad@us.es [Departamento EDAN, University of Seville, Facultad de Matemáticas C/ Tarfia, s/n., 41012 Sevilla (Spain)

    2016-07-15

    We construct a piecewise-linear (PWL) approximation of the Hindmarsh-Rose (HR) neuron model that is minimal, in the sense that the vector field has the least number of linearity zones, in order to reproduce all the dynamics present in the original HR model with classical parameter values. This includes square-wave bursting and also special trajectories called canards, which possess long repelling segments and organise the transitions between stable bursting patterns with n and n + 1 spikes, also referred to as spike-adding canard explosions. We propose a first approximation of the smooth HR model, using a continuous PWL system, and show that its fast subsystem cannot possess a homoclinic bifurcation, which is necessary to obtain proper square-wave bursting. We then relax the assumption of continuity of the vector field across all zones, and we show that we can obtain a homoclinic bifurcation in the fast subsystem. We use the recently developed canard theory for PWL systems in order to reproduce the spike-adding canard explosion feature of the HR model as studied, e.g., in Desroches et al., Chaos 23(4), 046106 (2013).

  13. Least square method of estimation of ecological half-lives of radionuclides in sediments

    International Nuclear Information System (INIS)

    Ranade, A.K.; Pandey, M.; Datta, D.; Ravi, P.M.

    2012-01-01

    Long term behavior of radionuclides in the environment is an important issue for estimating probable radiological consequences and associated risks. It is also useful for evaluating potential use of contaminated areas and the possible effectiveness of remediation activities. The long term behavior is quantified by means of ecological half life, a parameter that aggregates all processes except radioactive decay which causes a decrease of activity in a specific medium. The process involved in ecological half life depends upon the environmental condition of the medium involved. A fitting model based on least square regression approach was used to evaluate the ecological half life. This least square method has to run several times to evaluate the number of ecological half lives present in the medium for the radionuclide. The case study data considered here is for 137 Cs in Mumbai Harbour Bay. The study shows the trend of 137 Cs over the years at a location in Mumbai Harbour Bay. First iteration model illustrate the ecological half life as 4.94 y and subsequently it passes through a number of runs for more number of ecological half-life present by goodness of fit test. The paper presents a methodology for evaluating ecological half life and exemplifies it with a case study of 137 Cs. (author)

  14. Flexible aluminum tubes and a least square multi-objective non-linear optimization scheme

    International Nuclear Information System (INIS)

    Endelt, Benny; Nielsen, Karl Brian; Olsen, Soeren

    2004-01-01

    The automotive industry currently uses rubber hoses as the media carrier between e.g. the radiator and the engine, and the basic idea is to replace the rubber hoses with flexible aluminum tubes.A good quality is defined through several quality measurements, i.e. in the current case the key objective is to produce a flexible convolution through optimization of the tool geometry, but the process should also be stable, and the process stability is evaluated through Forming Limit Diagrams. Typically the defined objectives are conflicting, i.e. the optimized configuration represents therefore a trade-off between the individual objectives, in this case flexibility versus process stability.The optimization problem is solved through iteratively minimizing the object function. A second-order least square scheme is used for the approximation of the quadratic model, and the change in the design parameters is evaluated through the trust region scheme and box constraints are introduced within the trust region framework. Furthermore, the object function is minimized by applying the non-monotone scheme, and the trust region subproblem is solved by applying the Cholesky factorization scheme.An optimal bell shaped geometry is identified and the design is verified experimentally

  15. Least-squares collocation meshless approach for radiative heat transfer in absorbing and scattering media

    Science.gov (United States)

    Liu, L. H.; Tan, J. Y.

    2007-02-01

    A least-squares collocation meshless method is employed for solving the radiative heat transfer in absorbing, emitting and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with the other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate and stable, and can be used for solving the radiative heat transfer in absorbing, emitting and scattering media.

  16. Least-squares collocation meshless approach for radiative heat transfer in absorbing and scattering media

    International Nuclear Information System (INIS)

    Liu, L.H.; Tan, J.Y.

    2007-01-01

    A least-squares collocation meshless method is employed for solving the radiative heat transfer in absorbing, emitting and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with the other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate and stable, and can be used for solving the radiative heat transfer in absorbing, emitting and scattering media

  17. Radioisotopic neutron transmission spectrometry: Quantitative analysis by using partial least-squares method

    International Nuclear Information System (INIS)

    Kim, Jong-Yun; Choi, Yong Suk; Park, Yong Joon; Jung, Sung-Hee

    2009-01-01

    Neutron spectrometry, based on the scattering of high energy fast neutrons from a radioisotope and slowing-down by the light hydrogen atoms, is a useful technique for non-destructive, quantitative measurement of hydrogen content because it has a large measuring volume, and is not affected by temperature, pressure, pH value and color. The most common choice for radioisotope neutron source is 252 Cf or 241 Am-Be. In this study, 252 Cf with a neutron flux of 6.3x10 6 n/s has been used as an attractive neutron source because of its high flux neutron and weak radioactivity. Pulse-height neutron spectra have been obtained by using in-house built radioisotopic neutron spectrometric system equipped with 3 He detector and multi-channel analyzer, including a neutron shield. As a preliminary study, polyethylene block (density of ∼0.947 g/cc and area of 40 cmx25 cm) was used for the determination of hydrogen content by using multivariate calibration models, depending on the thickness of the block. Compared with the results obtained from a simple linear calibration model, partial least-squares regression (PLSR) method offered a better performance in a quantitative data analysis. It also revealed that the PLSR method in a neutron spectrometric system can be promising in the real-time, online monitoring of the powder process to determine the content of any type of molecules containing hydrogen nuclei.

  18. Partial Least Squares Regression for Determining the Control Factors for Runoff and Suspended Sediment Yield during Rainfall Events

    Directory of Open Access Journals (Sweden)

    Nufang Fang

    2015-07-01

    Full Text Available Multivariate statistics are commonly used to identify the factors that control the dynamics of runoff or sediment yields during hydrological processes. However, one issue with the use of conventional statistical methods to address relationships between variables and runoff or sediment yield is multicollinearity. The main objectives of this study were to apply a method for effectively identifying runoff and sediment control factors during hydrological processes and apply that method to a case study. The method combines the clustering approach and partial least squares regression (PLSR models. The case study was conducted in a mountainous watershed in the Three Gorges Area. A total of 29 flood events in three hydrological years in areas with different land uses were obtained. In total, fourteen related variables were separated from hydrographs using the classical hydrograph separation method. Twenty-nine rainfall events were classified into two rainfall regimes (heavy Rainfall Regime I and moderate Rainfall Regime II based on rainfall characteristics and K-means clustering. Four separate PLSR models were constructed to identify the main variables that control runoff and sediment yield for the two rainfall regimes. For Rainfall Regime I, the dominant first-order factors affecting the changes in sediment yield in our study were all of the four rainfall-related variables, flood peak discharge, maximum flood suspended sediment concentration, runoff, and the percentages of forest and farmland. For Rainfall Regime II, antecedent condition-related variables have more effects on both runoff and sediment yield than in Rainfall Regime I. The results suggest that the different control factors of the two rainfall regimes are determined by the rainfall characteristics and thus different runoff mechanisms.

  19. Order-constrained linear optimization.

    Science.gov (United States)

    Tidwell, Joe W; Dougherty, Michael R; Chrabaszcz, Jeffrey S; Thomas, Rick P

    2017-11-01

    Despite the fact that data and theories in the social, behavioural, and health sciences are often represented on an ordinal scale, there has been relatively little emphasis on modelling ordinal properties. The most common analytic framework used in psychological science is the general linear model, whose variants include ANOVA, MANOVA, and ordinary linear regression. While these methods are designed to provide the best fit to the metric properties of the data, they are not designed to maximally model ordinal properties. In this paper, we develop an order-constrained linear least-squares (OCLO) optimization algorithm that maximizes the linear least-squares fit to the data conditional on maximizing the ordinal fit based on Kendall's τ. The algorithm builds on the maximum rank correlation estimator (Han, 1987, Journal of Econometrics, 35, 303) and the general monotone model (Dougherty & Thomas, 2012, Psychological Review, 119, 321). Analyses of simulated data indicate that when modelling data that adhere to the assumptions of ordinary least squares, OCLO shows minimal bias, little increase in variance, and almost no loss in out-of-sample predictive accuracy. In contrast, under conditions in which data include a small number of extreme scores (fat-tailed distributions), OCLO shows less bias and variance, and substantially better out-of-sample predictive accuracy, even when the outliers are removed. We show that the advantages of OCLO over ordinary least squares in predicting new observations hold across a variety of scenarios in which researchers must decide to retain or eliminate extreme scores when fitting data. © 2017 The British Psychological Society.

  20. Least Squares Approach to the Alignment of the Generic High Precision Tracking System

    Science.gov (United States)

    de Renstrom, Pawel Brückman; Haywood, Stephen

    2006-04-01

    A least squares method to solve a generic alignment problem of a high granularity tracking system is presented. The algorithm is based on an analytical linear expansion and allows for multiple nested fits, e.g. imposing a common vertex for groups of particle tracks is of particular interest. We present a consistent and complete recipe to impose constraints on either implicit or explicit parameters. The method has been applied to the full simulation of a subset of the ATLAS silicon tracking system. The ultimate goal is to determine ≈35,000 degrees of freedom (DoF's). We present a limited scale exercise exploring various aspects of the solution.

  1. Applied regression analysis a research tool

    CERN Document Server

    Pantula, Sastry; Dickey, David

    1998-01-01

    Least squares estimation, when used appropriately, is a powerful research tool. A deeper understanding of the regression concepts is essential for achieving optimal benefits from a least squares analysis. This book builds on the fundamentals of statistical methods and provides appropriate concepts that will allow a scientist to use least squares as an effective research tool. Applied Regression Analysis is aimed at the scientist who wishes to gain a working knowledge of regression analysis. The basic purpose of this book is to develop an understanding of least squares and related statistical methods without becoming excessively mathematical. It is the outgrowth of more than 30 years of consulting experience with scientists and many years of teaching an applied regression course to graduate students. Applied Regression Analysis serves as an excellent text for a service course on regression for non-statisticians and as a reference for researchers. It also provides a bridge between a two-semester introduction to...

  2. Forecasting exchange rates: a robust regression approach

    OpenAIRE

    Preminger, Arie; Franck, Raphael

    2005-01-01

    The least squares estimation method as well as other ordinary estimation method for regression models can be severely affected by a small number of outliers, thus providing poor out-of-sample forecasts. This paper suggests a robust regression approach, based on the S-estimation method, to construct forecasting models that are less sensitive to data contamination by outliers. A robust linear autoregressive (RAR) and a robust neural network (RNN) models are estimated to study the predictabil...

  3. Discriminative Elastic-Net Regularized Linear Regression.

    Science.gov (United States)

    Zhang, Zheng; Lai, Zhihui; Xu, Yong; Shao, Ling; Wu, Jian; Xie, Guo-Sen

    2017-03-01

    In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zero-one matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of these methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available data sets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html.

  4. An information geometric approach to least squares minimization

    Science.gov (United States)

    Transtrum, Mark; Machta, Benjamin; Sethna, James

    2009-03-01

    Parameter estimation by nonlinear least squares minimization is a ubiquitous problem that has an elegant geometric interpretation: all possible parameter values induce a manifold embedded within the space of data. The minimization problem is then to find the point on the manifold closest to the origin. The standard algorithm for minimizing sums of squares, the Levenberg-Marquardt algorithm, also has geometric meaning. When the standard algorithm fails to efficiently find accurate fits to the data, geometric considerations suggest improvements. Problems involving large numbers of parameters, such as often arise in biological contexts, are notoriously difficult. We suggest an algorithm based on geodesic motion that may offer improvements over the standard algorithm for a certain class of problems.

  5. Application of sequential and orthogonalised-partial least squares (SO-PLS) regression to predict sensory properties of Cabernet Sauvignon wines from grape chemical composition.

    Science.gov (United States)

    Niimi, Jun; Tomic, Oliver; Næs, Tormod; Jeffery, David W; Bastian, Susan E P; Boss, Paul K

    2018-08-01

    The current study determined the applicability of sequential and orthogonalised-partial least squares (SO-PLS) regression to relate Cabernet Sauvignon grape chemical composition to the sensory perception of the corresponding wines. Grape samples (n = 25) were harvested at a similar maturity and vinified identically in 2013. Twelve measures using various (bio)chemical methods were made on grapes. Wines were evaluated using descriptive analysis with a trained panel (n = 10) for sensory profiling. Data was analysed globally using SO-PLS for the entire sensory profiles (SO-PLS2), as well as for single sensory attributes (SO-PLS1). SO-PLS1 models were superior in validated explained variances than SO-PLS2. SO-PLS provided a structured approach in the selection of predictor chemical data sets that best contributed to the correlation of important sensory attributes. This new approach presents great potential for application in other explorative metabolomics studies of food and beverages to address factors such as quality and regional influences. Copyright © 2018 Elsevier Ltd. All rights reserved.

  6. A step-by-step guide to non-linear regression analysis of experimental data using a Microsoft Excel spreadsheet.

    Science.gov (United States)

    Brown, A M

    2001-06-01

    The objective of this present study was to introduce a simple, easily understood method for carrying out non-linear regression analysis based on user input functions. While it is relatively straightforward to fit data with simple functions such as linear or logarithmic functions, fitting data with more complicated non-linear functions is more difficult. Commercial specialist programmes are available that will carry out this analysis, but these programmes are expensive and are not intuitive to learn. An alternative method described here is to use the SOLVER function of the ubiquitous spreadsheet programme Microsoft Excel, which employs an iterative least squares fitting routine to produce the optimal goodness of fit between data and function. The intent of this paper is to lead the reader through an easily understood step-by-step guide to implementing this method, which can be applied to any function in the form y=f(x), and is well suited to fast, reliable analysis of data in all fields of biology.

  7. Error propagation of partial least squares for parameters optimization in NIR modeling

    Science.gov (United States)

    Du, Chenzhao; Dai, Shengyun; Qiao, Yanjiang; Wu, Zhisheng

    2018-03-01

    A novel methodology is proposed to determine the error propagation of partial least-square (PLS) for parameters optimization in near-infrared (NIR) modeling. The parameters include spectral pretreatment, latent variables and variable selection. In this paper, an open source dataset (corn) and a complicated dataset (Gardenia) were used to establish PLS models under different modeling parameters. And error propagation of modeling parameters for water quantity in corn and geniposide quantity in Gardenia were presented by both type І and type II error. For example, when variable importance in the projection (VIP), interval partial least square (iPLS) and backward interval partial least square (BiPLS) variable selection algorithms were used for geniposide in Gardenia, compared with synergy interval partial least squares (SiPLS), the error weight varied from 5% to 65%, 55% and 15%. The results demonstrated how and what extent the different modeling parameters affect error propagation of PLS for parameters optimization in NIR modeling. The larger the error weight, the worse the model. Finally, our trials finished a powerful process in developing robust PLS models for corn and Gardenia under the optimal modeling parameters. Furthermore, it could provide a significant guidance for the selection of modeling parameters of other multivariate calibration models.

  8. Error propagation of partial least squares for parameters optimization in NIR modeling.

    Science.gov (United States)

    Du, Chenzhao; Dai, Shengyun; Qiao, Yanjiang; Wu, Zhisheng

    2018-03-05

    A novel methodology is proposed to determine the error propagation of partial least-square (PLS) for parameters optimization in near-infrared (NIR) modeling. The parameters include spectral pretreatment, latent variables and variable selection. In this paper, an open source dataset (corn) and a complicated dataset (Gardenia) were used to establish PLS models under different modeling parameters. And error propagation of modeling parameters for water quantity in corn and geniposide quantity in Gardenia were presented by both type І and type II error. For example, when variable importance in the projection (VIP), interval partial least square (iPLS) and backward interval partial least square (BiPLS) variable selection algorithms were used for geniposide in Gardenia, compared with synergy interval partial least squares (SiPLS), the error weight varied from 5% to 65%, 55% and 15%. The results demonstrated how and what extent the different modeling parameters affect error propagation of PLS for parameters optimization in NIR modeling. The larger the error weight, the worse the model. Finally, our trials finished a powerful process in developing robust PLS models for corn and Gardenia under the optimal modeling parameters. Furthermore, it could provide a significant guidance for the selection of modeling parameters of other multivariate calibration models. Copyright © 2017. Published by Elsevier B.V.

  9. Output-only modal parameter estimator of linear time-varying structural systems based on vector TAR model and least squares support vector machine

    Science.gov (United States)

    Zhou, Si-Da; Ma, Yuan-Chen; Liu, Li; Kang, Jie; Ma, Zhi-Sai; Yu, Lei

    2018-01-01

    Identification of time-varying modal parameters contributes to the structural health monitoring, fault detection, vibration control, etc. of the operational time-varying structural systems. However, it is a challenging task because there is not more information for the identification of the time-varying systems than that of the time-invariant systems. This paper presents a vector time-dependent autoregressive model and least squares support vector machine based modal parameter estimator for linear time-varying structural systems in case of output-only measurements. To reduce the computational cost, a Wendland's compactly supported radial basis function is used to achieve the sparsity of the Gram matrix. A Gamma-test-based non-parametric approach of selecting the regularization factor is adapted for the proposed estimator to replace the time-consuming n-fold cross validation. A series of numerical examples have illustrated the advantages of the proposed modal parameter estimator on the suppression of the overestimate and the short data. A laboratory experiment has further validated the proposed estimator.

  10. Application of pulse pile-up correction spectrum to the library least-squares method

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Sang Hoon [Kyungpook National Univ., Daegu (Korea, Republic of)

    2006-12-15

    The Monte Carlo simulation code CEARPPU has been developed and updated to provide pulse pile-up correction spectra for high counting rate cases. For neutron activation analysis, CEARPPU correction spectra were used in library least-squares method to give better isotopic activity results than the convention library least-squares fitting with uncorrected spectra.

  11. An on-line modified least-mean-square algorithm for training neurofuzzy controllers.

    Science.gov (United States)

    Tan, Woei Wan

    2007-04-01

    The problem hindering the use of data-driven modelling methods for training controllers on-line is the lack of control over the amount by which the plant is excited. As the operating schedule determines the information available on-line, the knowledge of the process may degrade if the setpoint remains constant for an extended period. This paper proposes an identification algorithm that alleviates "learning interference" by incorporating fuzzy theory into the normalized least-mean-square update rule. The ability of the proposed methodology to achieve faster learning is examined by employing the algorithm to train a neurofuzzy feedforward controller for controlling a liquid level process. Since the proposed identification strategy has similarities with the normalized least-mean-square update rule and the recursive least-square estimator, the on-line learning rates of these algorithms are also compared.

  12. Performance Evaluation of the Ordinary Least Square (OLS) and ...

    African Journals Online (AJOL)

    Nana Kwasi Peprah

    1Deparment of Geomatic Engineering, University of Mines and Technology, ... precise, accurate and can be used to execute any engineering works due to ..... and Ordinary Least Squares Methods”, Journal of Geomatics and Planning, Vol ... Technology”, Unpublished BSc Project Report, University of Mines and Technology ...

  13. Tensor hypercontraction. II. Least-squares renormalization

    Science.gov (United States)

    Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David

    2012-12-01

    The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

  14. An improved algorithm for the determination of the system paramters of a visual binary by least squares

    Science.gov (United States)

    Xu, Yu-Lin

    The problem of computing the orbit of a visual binary from a set of observed positions is reconsidered. It is a least squares adjustment problem, if the observational errors follow a bias-free multivariate Gaussian distribution and the covariance matrix of the observations is assumed to be known. The condition equations are constructed to satisfy both the conic section equation and the area theorem, which are nonlinear in both the observations and the adjustment parameters. The traditional least squares algorithm, which employs condition equations that are solved with respect to the uncorrelated observations and either linear in the adjustment parameters or linearized by developing them in Taylor series by first-order approximation, is inadequate in our orbit problem. D.C. Brown proposed an algorithm solving a more general least squares adjustment problem in which the scalar residual function, however, is still constructed by first-order approximation. Not long ago, a completely general solution was published by W.H Jefferys, who proposed a rigorous adjustment algorithm for models in which the observations appear nonlinearly in the condition equations and may be correlated, and in which construction of the normal equations and the residual function involves no approximation. This method was successfully applied in our problem. The normal equations were first solved by Newton's scheme. Practical examples show that this converges fast if the observational errors are sufficiently small and the initial approximate solution is sufficiently accurate, and that it fails otherwise. Newton's method was modified to yield a definitive solution in the case the normal approach fails, by combination with the method of steepest descent and other sophisticated algorithms. Practical examples show that the modified Newton scheme can always lead to a final solution. The weighting of observations, the orthogonal parameters and the efficiency of a set of adjustment parameters are also

  15. A FORTRAN program for a least-square fitting

    International Nuclear Information System (INIS)

    Yamazaki, Tetsuo

    1978-01-01

    A practical FORTRAN program for a least-squares fitting is presented. Although the method is quite usual, the program calculates not only the most satisfactory set of values of unknowns but also the plausible errors associated with them. As an example, a measured lateral absorbed-dose distribution in water for a narrow 25-MeV electron beam is fitted to a Gaussian distribution. (auth.)

  16. Least-squares reverse time migration of multiples

    KAUST Repository

    Zhang, Dongliang

    2013-12-06

    The theory of least-squares reverse time migration of multiples (RTMM) is presented. In this method, least squares migration (LSM) is used to image free-surface multiples where the recorded traces are used as the time histories of the virtual sources at the hydrophones and the surface-related multiples are the observed data. For a single source, the entire free-surface becomes an extended virtual source where the downgoing free-surface multiples more fully illuminate the subsurface compared to the primaries. Since each recorded trace is treated as the time history of a virtual source, knowledge of the source wavelet is not required and the ringy time series for each source is automatically deconvolved. If the multiples can be perfectly separated from the primaries, numerical tests on synthetic data for the Sigsbee2B and Marmousi2 models show that least-squares reverse time migration of multiples (LSRTMM) can significantly improve the image quality compared to RTMM or standard reverse time migration (RTM) of primaries. However, if there is imperfect separation and the multiples are strongly interfering with the primaries then LSRTMM images show no significant advantage over the primary migration images. In some cases, they can be of worse quality. Applying LSRTMM to Gulf of Mexico data shows higher signal-to-noise imaging of the salt bottom and top compared to standard RTM images. This is likely attributed to the fact that the target body is just below the sea bed so that the deep water multiples do not have strong interference with the primaries. Migrating a sparsely sampled version of the Marmousi2 ocean bottom seismic data shows that LSM of primaries and LSRTMM provides significantly better imaging than standard RTM. A potential liability of LSRTMM is that multiples require several round trips between the reflector and the free surface, so that high frequencies in the multiples suffer greater attenuation compared to the primary reflections. This can lead to lower

  17. Nonlinear Least Square Based on Control Direction by Dual Method and Its Application

    Directory of Open Access Journals (Sweden)

    Zhengqing Fu

    2016-01-01

    Full Text Available A direction controlled nonlinear least square (NLS estimation algorithm using the primal-dual method is proposed. The least square model is transformed into the primal-dual model; then direction of iteration can be controlled by duality. The iterative algorithm is designed. The Hilbert morbid matrix is processed by the new model and the least square estimate and ridge estimate. The main research method is to combine qualitative analysis and quantitative analysis. The deviation between estimated values and the true value and the estimated residuals fluctuation of different methods are used for qualitative analysis. The root mean square error (RMSE is used for quantitative analysis. The results of experiment show that the model has the smallest residual error and the minimum root mean square error. The new estimate model has effectiveness and high precision. The genuine data of Jining area in unwrapping experiments are used and the comparison with other classical unwrapping algorithms is made, so better results in precision aspects can be achieved through the proposed algorithm.

  18. Application of Fourier transform infrared spectroscopy and orthogonal projections to latent structures/partial least squares regression for estimation of procyanidins average degree of polymerisation.

    Science.gov (United States)

    Passos, Cláudia P; Cardoso, Susana M; Barros, António S; Silva, Carlos M; Coimbra, Manuel A

    2010-02-28

    Fourier transform infrared (FTIR) spectroscopy has being emphasised as a widespread technique in the quick assess of food components. In this work, procyanidins were extracted with methanol and acetone/water from the seeds of white and red grape varieties. A fractionation by graded methanol/chloroform precipitations allowed to obtain 26 samples that were characterised using thiolysis as pre-treatment followed by HPLC-UV and MS detection. The average degree of polymerisation (DPn) of the procyanidins in the samples ranged from 2 to 11 flavan-3-ol residues. FTIR spectroscopy within the wavenumbers region of 1800-700 cm(-1) allowed to build a partial least squares (PLS1) regression model with 8 latent variables (LVs) for the estimation of the DPn, giving a RMSECV of 11.7%, with a R(2) of 0.91 and a RMSEP of 2.58. The application of orthogonal projection to latent structures (O-PLS1) clarifies the interpretation of the regression model vectors. Moreover, the O-PLS procedure has removed 88% of non-correlated variations with the DPn, allowing to relate the increase of the absorbance peaks at 1203 and 1099 cm(-1) with the increase of the DPn due to the higher proportion of substitutions in the aromatic ring of the polymerised procyanidin molecules. Copyright 2009 Elsevier B.V. All rights reserved.

  19. Determination of calibration equations by means of the generalized least squares method

    International Nuclear Information System (INIS)

    Zijp, W.L.

    1984-12-01

    For the determination of two-dimensional calibration curves (e.g. in tank calibration procedures) or of three dimensional calibration equations (e.g. for the calibration of NDA equipment for enrichment measurements) one performs measurements under well chosen conditions, where all observables of interest (inclusive the values of the standard material) are subject to measurement uncertainties. Moreover correlations in several measurements may occur. This document describes the mathematical-statistical approach to determine the values of the model parameters and their covariance matrix, which fit best to the mathematical model for the calibration equation. The formulae are based on the method of generalized least squares where the term generalized implies that non-linear equations in the unknown parameters and also covariance matrices of the measurement data of the calibration can be taken into account. In the general case an iteration procedure is required. No iteration is required when the model is linear in the parameters and the covariance matrices for the measurements of co-ordinates of the calibration points are proportional to each other

  20. Spectral mimetic least-squares method for div-curl systems

    NARCIS (Netherlands)

    Gerritsma, Marc; Palha, Artur; Lirkov, I.; Margenov, S.

    2018-01-01

    In this paper the spectral mimetic least-squares method is applied to a two-dimensional div-curl system. A test problem is solved on orthogonal and curvilinear meshes and both h- and p-convergence results are presented. The resulting solutions will be pointwise divergence-free for these test

  1. Pemodelan Tingkat Penghunian Kamar Hotel di Kendari dengan Transformasi Wavelet Kontinu dan Partial Least Squares

    Directory of Open Access Journals (Sweden)

    Margaretha Ohyver

    2014-12-01

    Full Text Available Multicollinearity and outliers are the common problems when estimating regression model.   Multicollinearitiy occurs when there are high correlations among predictor variables, leading to difficulties in separating the effects of each independent variable on the response variable. While, if outliers are present in the data to be analyzed, then the assumption of normality in the regression will be violated and the results of the analysis may be incorrect or misleading. Both of these cases occurred in the data on room occupancy rate of hotels in Kendari. The purpose of this study is to find a model for the data that is free of multicollinearity and outliers and to determine the factors that affect the level of room occupancy hotels in Kendari. The method used is Continuous Wavelet Transformation and Partial Least Squares. The result of this research is a regression model that is free of multicollinearity and a  pattern of data that resolved the present of outliers.

  2. Non-linear partial least square regression increases the estimation accuracy of grass nitrogen and phosphorus using in situ hyperspectral and environmental data

    CSIR Research Space (South Africa)

    Ramoelo, Abel

    2013-06-01

    Full Text Available in situ hyperspectral and environmental variables yielded the highest grass N and P estimation accuracy (R2 = 0.81, root mean square error (RMSE) = 0.08, and R2 = 0.80, RMSE = 0.03, respectively) as compared to using remote sensing variables only...

  3. Rapid Detection of Pesticide Residues in Chinese Herbal Medicines by Fourier Transform Infrared Spectroscopy Coupled with Partial Least Squares Regression

    Directory of Open Access Journals (Sweden)

    Tianming Yang

    2016-01-01

    Full Text Available This paper reports a simple, rapid, and effective method for simultaneous detection of cartap (Ca, thiocyclam (Th, and tebufenozide (Te in Chinese herbal medicines including Radix Angelicae Dahuricae and Liquorices using Fourier transform infrared spectroscopy (FT-IR coupled with partial least squares regression (PLSR. The proposed method can handle the intrinsic interferences of herbal samples; satisfactory average recoveries attained from near-infrared (NIR and mid-infrared (MIR PLSR models were 99.0±10.8 and 100.2±1.0% for Ca, 100.2±6.9 and 99.7±2.5% for Th, and 99.1±6.3 and 99.6±1.0% for Te, respectively. Furthermore, some statistical parameters and figures of merit are fully investigated to evaluate the performance of the two models. It was found that both models could give accurate results and only the performance of MIR-PLSR was slightly better than that of NIR-PLSR in the cases suffering from herbal matrix interferences. In conclusion, FT-IR spectroscopy in combination with PLSR has been demonstrated for its application in rapid screening and quantitative analysis of multipesticide residues in Chinese herbal medicines without physical or chemical separation pretreatment step and any spectral processing, which also implies other potential applications such as food and drug safety, herbal plants quality, and environmental evaluation, due to its advantages of nontoxic and nondestructive analysis.

  4. Development of a partial least squares-artificial neural network (PLS-ANN) hybrid model for the prediction of consumer liking scores of ready-to-drink green tea beverages.

    Science.gov (United States)

    Yu, Peigen; Low, Mei Yin; Zhou, Weibiao

    2018-01-01

    In order to develop products that would be preferred by consumers, the effects of the chemical compositions of ready-to-drink green tea beverages on consumer liking were studied through regression analyses. Green tea model systems were prepared by dosing solutions of 0.1% green tea extract with differing concentrations of eight flavour keys deemed to be important for green tea aroma and taste, based on a D-optimal experimental design, before undergoing commercial sterilisation. Sensory evaluation of the green tea model system was carried out using an untrained consumer panel to obtain hedonic liking scores of the samples. Regression models were subsequently trained to objectively predict the consumer liking scores of the green tea model systems. A linear partial least squares (PLS) regression model was developed to describe the effects of the eight flavour keys on consumer liking, with a coefficient of determination (R 2 ) of 0.733, and a root-mean-square error (RMSE) of 3.53%. The PLS model was further augmented with an artificial neural network (ANN) to establish a PLS-ANN hybrid model. The established hybrid model was found to give a better prediction of consumer liking scores, based on its R 2 (0.875) and RMSE (2.41%). Copyright © 2017 Elsevier Ltd. All rights reserved.

  5. Nonnegative least-squares image deblurring: improved gradient projection approaches

    Science.gov (United States)

    Benvenuto, F.; Zanella, R.; Zanni, L.; Bertero, M.

    2010-02-01

    The least-squares approach to image deblurring leads to an ill-posed problem. The addition of the nonnegativity constraint, when appropriate, does not provide regularization, even if, as far as we know, a thorough investigation of the ill-posedness of the resulting constrained least-squares problem has still to be done. Iterative methods, converging to nonnegative least-squares solutions, have been proposed. Some of them have the 'semi-convergence' property, i.e. early stopping of the iteration provides 'regularized' solutions. In this paper we consider two of these methods: the projected Landweber (PL) method and the iterative image space reconstruction algorithm (ISRA). Even if they work well in many instances, they are not frequently used in practice because, in general, they require a large number of iterations before providing a sensible solution. Therefore, the main purpose of this paper is to refresh these methods by increasing their efficiency. Starting from the remark that PL and ISRA require only the computation of the gradient of the functional, we propose the application to these algorithms of special acceleration techniques that have been recently developed in the area of the gradient methods. In particular, we propose the application of efficient step-length selection rules and line-search strategies. Moreover, remarking that ISRA is a scaled gradient algorithm, we evaluate its behaviour in comparison with a recent scaled gradient projection (SGP) method for image deblurring. Numerical experiments demonstrate that the accelerated methods still exhibit the semi-convergence property, with a considerable gain both in the number of iterations and in the computational time; in particular, SGP appears definitely the most efficient one.

  6. Two-Stage Method Based on Local Polynomial Fitting for a Linear Heteroscedastic Regression Model and Its Application in Economics

    Directory of Open Access Journals (Sweden)

    Liyun Su

    2012-01-01

    Full Text Available We introduce the extension of local polynomial fitting to the linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to nonparametric technique of local polynomial estimation, we do not need to know the heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we focus on comparison of parameters and reach an optimal fitting. Besides, we verify the asymptotic normality of parameters based on numerical simulations. Finally, this approach is applied to a case of economics, and it indicates that our method is surely effective in finite-sample situations.

  7. Correlation and simple linear regression.

    Science.gov (United States)

    Zou, Kelly H; Tuncali, Kemal; Silverman, Stuart G

    2003-06-01

    In this tutorial article, the concepts of correlation and regression are reviewed and demonstrated. The authors review and compare two correlation coefficients, the Pearson correlation coefficient and the Spearman rho, for measuring linear and nonlinear relationships between two continuous variables. In the case of measuring the linear relationship between a predictor and an outcome variable, simple linear regression analysis is conducted. These statistical concepts are illustrated by using a data set from published literature to assess a computed tomography-guided interventional technique. These statistical methods are important for exploring the relationships between variables and can be applied to many radiologic studies.

  8. Pressurized water reactor monitoring. Study of detection, diagnostic and estimation methods (least error squares and filtering)

    International Nuclear Information System (INIS)

    Gillet, M.

    1986-07-01

    This thesis presents a study for the surveillance of the ''primary coolant circuit inventory monitoring'' of a pressurized water reactor. A reference model is developed in view of an automatic system ensuring detection and diagnostic in real time. The methods used for the present application are statistical tests and a method related to pattern recognition. The estimation of failures detected, difficult owing to the non-linearity of the problem, is treated by the least error squares method of the predictor or corrector type, and by filtering. It is in this frame that a new optimized method with superlinear convergence is developed, and that a segmented linearization of the model is introduced, in view of a multiple filtering [fr

  9. On the calibration process of film dosimetry: OLS inverse regression versus WLS inverse prediction

    International Nuclear Information System (INIS)

    Crop, F; Thierens, H; Rompaye, B Van; Paelinck, L; Vakaet, L; Wagter, C De

    2008-01-01

    The purpose of this study was both putting forward a statistically correct model for film calibration and the optimization of this process. A reliable calibration is needed in order to perform accurate reference dosimetry with radiographic (Gafchromic) film. Sometimes, an ordinary least squares simple linear (in the parameters) regression is applied to the dose-optical-density (OD) curve with the dose as a function of OD (inverse regression) or sometimes OD as a function of dose (inverse prediction). The application of a simple linear regression fit is an invalid method because heteroscedasticity of the data is not taken into account. This could lead to erroneous results originating from the calibration process itself and thus to a lower accuracy. In this work, we compare the ordinary least squares (OLS) inverse regression method with the correct weighted least squares (WLS) inverse prediction method to create calibration curves. We found that the OLS inverse regression method could lead to a prediction bias of up to 7.3 cGy at 300 cGy and total prediction errors of 3% or more for Gafchromic EBT film. Application of the WLS inverse prediction method resulted in a maximum prediction bias of 1.4 cGy and total prediction errors below 2% in a 0-400 cGy range. We developed a Monte-Carlo-based process to optimize calibrations, depending on the needs of the experiment. This type of thorough analysis can lead to a higher accuracy for film dosimetry

  10. Attenuation compensation in least-squares reverse time migration using the visco-acoustic wave equation

    KAUST Repository

    Dutta, Gaurav

    2013-08-20

    Attenuation leads to distortion of amplitude and phase of seismic waves propagating inside the earth. Conventional acoustic and least-squares reverse time migration do not account for this distortion which leads to defocusing of migration images in highly attenuative geological environments. To account for this distortion, we propose to use the visco-acoustic wave equation for least-squares reverse time migration. Numerical tests on synthetic data show that least-squares reverse time migration with the visco-acoustic wave equation corrects for this distortion and produces images with better balanced amplitudes compared to the conventional approach. © 2013 SEG.

  11. Track Circuit Fault Diagnosis Method based on Least Squares Support Vector

    Science.gov (United States)

    Cao, Yan; Sun, Fengru

    2018-01-01

    In order to improve the troubleshooting efficiency and accuracy of the track circuit, track circuit fault diagnosis method was researched. Firstly, the least squares support vector machine was applied to design the multi-fault classifier of the track circuit, and then the measured track data as training samples was used to verify the feasibility of the methods. Finally, the results based on BP neural network fault diagnosis methods and the methods used in this paper were compared. Results shows that the track fault classifier based on least squares support vector machine can effectively achieve the five track circuit fault diagnosis with less computing time.

  12. Improving sensitivity of linear regression-based cell type-specific differential expression deconvolution with per-gene vs. global significance threshold.

    Science.gov (United States)

    Glass, Edmund R; Dozmorov, Mikhail G

    2016-10-06

    The goal of many human disease-oriented studies is to detect molecular mechanisms different between healthy controls and patients. Yet, commonly used gene expression measurements from blood samples suffer from variability of cell composition. This variability hinders the detection of differentially expressed genes and is often ignored. Combined with cell counts, heterogeneous gene expression may provide deeper insights into the gene expression differences on the cell type-specific level. Published computational methods use linear regression to estimate cell type-specific differential expression, and a global cutoff to judge significance, such as False Discovery Rate (FDR). Yet, they do not consider many artifacts hidden in high-dimensional gene expression data that may negatively affect linear regression. In this paper we quantify the parameter space affecting the performance of linear regression (sensitivity of cell type-specific differential expression detection) on a per-gene basis. We evaluated the effect of sample sizes, cell type-specific proportion variability, and mean squared error on sensitivity of cell type-specific differential expression detection using linear regression. Each parameter affected variability of cell type-specific expression estimates and, subsequently, the sensitivity of differential expression detection. We provide the R package, LRCDE, which performs linear regression-based cell type-specific differential expression (deconvolution) detection on a gene-by-gene basis. Accounting for variability around cell type-specific gene expression estimates, it computes per-gene t-statistics of differential detection, p-values, t-statistic-based sensitivity, group-specific mean squared error, and several gene-specific diagnostic metrics. The sensitivity of linear regression-based cell type-specific differential expression detection differed for each gene as a function of mean squared error, per group sample sizes, and variability of the proportions

  13. Evaluation of the prediction precision capability of partial least squares regression approach for analysis of high alloy steel by laser induced breakdown spectroscopy

    Science.gov (United States)

    Sarkar, Arnab; Karki, Vijay; Aggarwal, Suresh K.; Maurya, Gulab S.; Kumar, Rohit; Rai, Awadhesh K.; Mao, Xianglei; Russo, Richard E.

    2015-06-01

    Laser induced breakdown spectroscopy (LIBS) was applied for elemental characterization of high alloy steel using partial least squares regression (PLSR) with an objective to evaluate the analytical performance of this multivariate approach. The optimization of the number of principle components for minimizing error in PLSR algorithm was investigated. The effect of different pre-treatment procedures on the raw spectral data before PLSR analysis was evaluated based on several statistical (standard error of prediction, percentage relative error of prediction etc.) parameters. The pre-treatment with "NORM" parameter gave the optimum statistical results. The analytical performance of PLSR model improved by increasing the number of laser pulses accumulated per spectrum as well as by truncating the spectrum to appropriate wavelength region. It was found that the statistical benefit of truncating the spectrum can also be accomplished by increasing the number of laser pulses per accumulation without spectral truncation. The constituents (Co and Mo) present in hundreds of ppm were determined with relative precision of 4-9% (2σ), whereas the major constituents Cr and Ni (present at a few percent levels) were determined with a relative precision of ~ 2%(2σ).

  14. [Prediction of total nitrogen and alkali hydrolysable nitrogen content in loess using hyperspectral data based on correlation analysis and partial least squares regression].

    Science.gov (United States)

    Liu, Xiu-ying; Wang, Li; Chang, Qing-rui; Wang, Xiao-xing; Shang, Yan

    2015-07-01

    Wuqi County of Shaanxi Province, where the vegetation recovering measures have been carried out for years, was taken as the study area. A total of 100 loess samples from 24 different profiles were collected. Total nitrogen (TN) and alkali hydrolysable nitrogen (AHN) contents of the soil samples were analyzed, and the soil samples were scanned in the visible/near-infrared (VNIR) region of 350-2500 nm in the laboratory. The calibration models were developed between TN and AHN contents and VNIR values based on correlation analysis (CA) and partial least squares regression (PLS). Independent samples validated the calibration models. The results indicated that the optimum model for predicting TN of loess was established by using first derivative of reflectance. The best model for predicting AHN of loess was established by using normal derivative spectra. The optimum TN model could effectively predict TN in loess from 0 to 40 cm, but the optimum AHN model could only roughly predict AHN at the same depth. This study provided a good method for rapidly predicting TN of loess where vegetation recovering measures have been adopted, but prediction of AHN needs to be further studied.

  15. A comparison of two least-squared random coefficient autoregressive models: with and without autocorrelated errors

    OpenAIRE

    Autcha Araveeporn

    2013-01-01

    This paper compares a Least-Squared Random Coefficient Autoregressive (RCA) model with a Least-Squared RCA model based on Autocorrelated Errors (RCA-AR). We looked at only the first order models, denoted RCA(1) and RCA(1)-AR(1). The efficiency of the Least-Squared method was checked by applying the models to Brownian motion and Wiener process, and the efficiency followed closely the asymptotic properties of a normal distribution. In a simulation study, we compared the performance of RCA(1) an...

  16. Application of the Least Squares Method in Axisymmetric Biharmonic Problems

    Directory of Open Access Journals (Sweden)

    Vasyl Chekurin

    2016-01-01

    Full Text Available An approach for solving of the axisymmetric biharmonic boundary value problems for semi-infinite cylindrical domain was developed in the paper. On the lateral surface of the domain homogeneous Neumann boundary conditions are prescribed. On the remaining part of the domain’s boundary four different biharmonic boundary pieces of data are considered. To solve the formulated biharmonic problems the method of least squares on the boundary combined with the method of homogeneous solutions was used. That enabled reducing the problems to infinite systems of linear algebraic equations which can be solved with the use of reduction method. Convergence of the solution obtained with developed approach was studied numerically on some characteristic examples. The developed approach can be used particularly to solve axisymmetric elasticity problems for cylindrical bodies, the heights of which are equal to or exceed their diameters, when on their lateral surface normal and tangential tractions are prescribed and on the cylinder’s end faces various types of boundary conditions in stresses in displacements or mixed ones are given.

  17. Application of the Polynomial-Based Least Squares and Total Least Squares Models for the Attenuated Total Reflection Fourier Transform Infrared Spectra of Binary Mixtures of Hydroxyl Compounds.

    Science.gov (United States)

    Shan, Peng; Peng, Silong; Zhao, Yuhui; Tang, Liang

    2016-03-01

    An analysis of binary mixtures of hydroxyl compound by Attenuated Total Reflection Fourier transform infrared spectroscopy (ATR FT-IR) and classical least squares (CLS) yield large model error due to the presence of unmodeled components such as H-bonded components. To accommodate these spectral variations, polynomial-based least squares (LSP) and polynomial-based total least squares (TLSP) are proposed to capture the nonlinear absorbance-concentration relationship. LSP is based on assuming that only absorbance noise exists; while TLSP takes both absorbance noise and concentration noise into consideration. In addition, based on different solving strategy, two optimization algorithms (limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm and Levenberg-Marquardt (LM) algorithm) are combined with TLSP and then two different TLSP versions (termed as TLSP-LBFGS and TLSP-LM) are formed. The optimum order of each nonlinear model is determined by cross-validation. Comparison and analyses of the four models are made from two aspects: absorbance prediction and concentration prediction. The results for water-ethanol solution and ethanol-ethyl lactate solution show that LSP, TLSP-LBFGS, and TLSP-LM can, for both absorbance prediction and concentration prediction, obtain smaller root mean square error of prediction than CLS. Additionally, they can also greatly enhance the accuracy of estimated pure component spectra. However, from the view of concentration prediction, the Wilcoxon signed rank test shows that there is no statistically significant difference between each nonlinear model and CLS. © The Author(s) 2016.

  18. Pressurized water reactor monitoring. Study of detection, diagnostic and estimation (least squares and filtering) methods

    International Nuclear Information System (INIS)

    Gillet, M.

    1986-07-01

    This thesis presents a study for the surveillance of the Primary circuit water inventory of a pressurized water reactor. A reference model is developed for the development of an automatic system ensuring detection and real-time diagnostic. The methods to our application are statistical tests and adapted a pattern recognition method. The estimation of the detected anomalies is treated by the least square fit method, and by filtering. A new projected optimization method with superlinear convergence is developed in this framework, and a segmented linearization of the model is introduced, in view of a multiple filtering. 46 refs [fr

  19. Fundamental Analysis of the Linear Multiple Regression Technique for Quantification of Water Quality Parameters from Remote Sensing Data. Ph.D. Thesis - Old Dominion Univ.

    Science.gov (United States)

    Whitlock, C. H., III

    1977-01-01

    Constituents with linear radiance gradients with concentration may be quantified from signals which contain nonlinear atmospheric and surface reflection effects for both homogeneous and non-homogeneous water bodies provided accurate data can be obtained and nonlinearities are constant with wavelength. Statistical parameters must be used which give an indication of bias as well as total squared error to insure that an equation with an optimum combination of bands is selected. It is concluded that the effect of error in upwelled radiance measurements is to reduce the accuracy of the least square fitting process and to increase the number of points required to obtain a satisfactory fit. The problem of obtaining a multiple regression equation that is extremely sensitive to error is discussed.

  20. Growth kinetics of borided layers: Artificial neural network and least square approaches

    Science.gov (United States)

    Campos, I.; Islas, M.; Ramírez, G.; VillaVelázquez, C.; Mota, C.

    2007-05-01

    The present study evaluates the growth kinetics of the boride layer Fe 2B in AISI 1045 steel, by means of neural networks and the least square techniques. The Fe 2B phase was formed at the material surface using the paste boriding process. The surface boron potential was modified considering different boron paste thicknesses, with exposure times of 2, 4 and 6 h, and treatment temperatures of 1193, 1223 and 1273 K. The neural network and the least square models were set by the layer thickness of Fe 2B phase, and assuming that the growth of the boride layer follows a parabolic law. The reliability of the techniques used is compared with a set of experiments at a temperature of 1223 K with 5 h of treatment time and boron potentials of 2, 3, 4 and 5 mm. The results of the Fe 2B layer thicknesses show a mean error of 5.31% for the neural network and 3.42% for the least square method.

  1. Unweighted least squares phase unwrapping by means of multigrid techniques

    Science.gov (United States)

    Pritt, Mark D.

    1995-11-01

    We present a multigrid algorithm for unweighted least squares phase unwrapping. This algorithm applies Gauss-Seidel relaxation schemes to solve the Poisson equation on smaller, coarser grids and transfers the intermediate results to the finer grids. This approach forms the basis of our multigrid algorithm for weighted least squares phase unwrapping, which is described in a separate paper. The key idea of our multigrid approach is to maintain the partial derivatives of the phase data in separate arrays and to correct these derivatives at the boundaries of the coarser grids. This maintains the boundary conditions necessary for rapid convergence to the correct solution. Although the multigrid algorithm is an iterative algorithm, we demonstrate that it is nearly as fast as the direct Fourier-based method. We also describe how to parallelize the algorithm for execution on a distributed-memory parallel processor computer or a network-cluster of workstations.

  2. Least Squares Neural Network-Based Wireless E-Nose System Using an SnO₂ Sensor Array.

    Science.gov (United States)

    Shahid, Areej; Choi, Jong-Hyeok; Rana, Abu Ul Hassan Sarwar; Kim, Hyun-Seok

    2018-05-06

    Over the last few decades, the development of the electronic nose (E-nose) for detection and quantification of dangerous and odorless gases, such as methane (CH₄) and carbon monoxide (CO), using an array of SnO₂ gas sensors has attracted considerable attention. This paper addresses sensor cross sensitivity by developing a classifier and estimator using an artificial neural network (ANN) and least squares regression (LSR), respectively. Initially, the ANN was implemented using a feedforward pattern recognition algorithm to learn the collective behavior of an array as the signature of a particular gas. In the second phase, the classified gas was quantified by minimizing the mean square error using LSR. The combined approach produced 98.7% recognition probability, with 95.5 and 94.4% estimated gas concentration accuracies for CH₄ and CO, respectively. The classifier and estimator parameters were deployed in a remote microcontroller for the actualization of a wireless E-nose system.

  3. Dynamic least-squares kernel density modeling of Fokker-Planck equations with application to neural population.

    Science.gov (United States)

    Shotorban, Babak

    2010-04-01

    The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.

  4. A method for nonlinear exponential regression analysis

    Science.gov (United States)

    Junkin, B. G.

    1971-01-01

    A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

  5. A least-squares minimisation approach to depth determination from numerical second horizontal self-potential anomalies

    Science.gov (United States)

    Abdelrahman, El-Sayed Mohamed; Soliman, Khalid; Essa, Khalid Sayed; Abo-Ezz, Eid Ragab; El-Araby, Tarek Mohamed

    2009-06-01

    This paper develops a least-squares minimisation approach to determine the depth of a buried structure from numerical second horizontal derivative anomalies obtained from self-potential (SP) data using filters of successive window lengths. The method is based on using a relationship between the depth and a combination of observations at symmetric points with respect to the coordinate of the projection of the centre of the source in the plane of the measurement points with a free parameter (graticule spacing). The problem of depth determination from second derivative SP anomalies has been transformed into the problem of finding a solution to a non-linear equation of the form f(z)=0. Formulas have been derived for horizontal cylinders, spheres, and vertical cylinders. Procedures are also formulated to determine the electric dipole moment and the polarization angle. The proposed method was tested on synthetic noisy and real SP data. In the case of the synthetic data, the least-squares method determined the correct depths of the sources. In the case of practical data (SP anomalies over a sulfide ore deposit, Sariyer, Turkey and over a Malachite Mine, Jefferson County, Colorado, USA), the estimated depths of the buried structures are in good agreement with the results obtained from drilling and surface geology.

  6. Piecewise linear regression splines with hyperbolic covariates

    International Nuclear Information System (INIS)

    Cologne, John B.; Sposto, Richard

    1992-09-01

    Consider the problem of fitting a curve to data that exhibit a multiphase linear response with smooth transitions between phases. We propose substituting hyperbolas as covariates in piecewise linear regression splines to obtain curves that are smoothly joined. The method provides an intuitive and easy way to extend the two-phase linear hyperbolic response model of Griffiths and Miller and Watts and Bacon to accommodate more than two linear segments. The resulting regression spline with hyperbolic covariates may be fit by nonlinear regression methods to estimate the degree of curvature between adjoining linear segments. The added complexity of fitting nonlinear, as opposed to linear, regression models is not great. The extra effort is particularly worthwhile when investigators are unwilling to assume that the slope of the response changes abruptly at the join points. We can also estimate the join points (the values of the abscissas where the linear segments would intersect if extrapolated) if their number and approximate locations may be presumed known. An example using data on changing age at menarche in a cohort of Japanese women illustrates the use of the method for exploratory data analysis. (author)

  7. Feature extraction through least squares fit to a simple model

    International Nuclear Information System (INIS)

    Demuth, H.B.

    1976-01-01

    The Oak Ridge National Laboratory (ORNL) presented the Los Alamos Scientific Laboratory (LASL) with 18 radiographs of fuel rod test bundles. The problem is to estimate the thickness of the gap between some cylindrical rods and a flat wall surface. The edges of the gaps are poorly defined due to finite source size, x-ray scatter, parallax, film grain noise, and other degrading effects. The radiographs were scanned and the scan-line data were averaged to reduce noise and to convert the problem to one dimension. A model of the ideal gap, convolved with an appropriate point-spread function, was fit to the averaged data with a least squares program; and the gap width was determined from the final fitted-model parameters. The least squares routine did converge and the gaps obtained are of reasonable size. The method is remarkably insensitive to noise. This report describes the problem, the techniques used to solve it, and the results and conclusions. Suggestions for future work are also given

  8. A deterministic iterative least-squares algorithm for beam weight optimization in conformal radiotherapy

    International Nuclear Information System (INIS)

    Chen Yan; Michalski, Darek; Houser, Christopher; Galvin, James M.

    2002-01-01

    Currently, inverse treatment planning in conformal radiotherapy is, in part, a trial-and-error process due to the interplay of many competing criteria for obtaining a clinically acceptable dose distribution. A new method is developed for beam weight optimization that incorporates clinically relevant nonlinear and linear constraints. The process is driven by a nonlinear, quasi-quadratic objective function and the solution space is defined by a set of linear constraints. At each step of iteration, the optimization problem is linearized by a self-consistent approximation that is local to the existing dose distribution. The dose distribution is then improved by solving a series of constrained least-squares problems using an established method until all prescribed constraints are satisfied. This differs from the current approaches in that it does not rely on the search for the global minimum of a specific objective function. Essentially, our proposed objective function can be construed as a functional that comprises a class of dose-based quadratic objective functions. Empirical adjustment for appropriate model parameters in the construction of objective function is minimized, since these parameters are in effect adaptively adjusted during optimization. The method is robust in solving difficult clinical cases using either aperture or pencil beam based planning techniques for intensity-modulated radiation therapy. (author)

  9. Constrained Balancing of Two Industrial Rotor Systems: Least Squares and Min-Max Approaches

    Directory of Open Access Journals (Sweden)

    Bin Huang

    2009-01-01

    Full Text Available Rotor vibrations caused by rotor mass unbalance distributions are a major source of maintenance problems in high-speed rotating machinery. Minimizing this vibration by balancing under practical constraints is quite important to industry. This paper considers balancing of two large industrial rotor systems by constrained least squares and min-max balancing methods. In current industrial practice, the weighted least squares method has been utilized to minimize rotor vibrations for many years. One of its disadvantages is that it cannot guarantee that the maximum value of vibration is below a specified value. To achieve better balancing performance, the min-max balancing method utilizing the Second Order Cone Programming (SOCP with the maximum correction weight constraint, the maximum residual response constraint as well as the weight splitting constraint has been utilized for effective balancing. The min-max balancing method can guarantee a maximum residual vibration value below an optimum value and is shown by simulation to significantly outperform the weighted least squares method.

  10. Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations

    KAUST Repository

    Cao, Jiguo; Huang, Jianhua Z.; Wu, Hulin

    2012-01-01

    Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online.

  11. DEM4-26, Least Square Fit for IBM PC by Deming Method

    International Nuclear Information System (INIS)

    Rinard, P.M.; Bosler, G.E.

    1989-01-01

    1 - Description of program or function: DEM4-26 is a generalized least square fitting program based on Deming's method. Functions built into the program for fitting include linear, quadratic, cubic, power, Howard's, exponential, and Gaussian; others can easily be added. The program has the following capabilities: (1) entry, editing, and saving of data; (2) fitting of any of the built-in functions or of a user-supplied function; (3) plotting the data and fitted function on the display screen, with error limits if requested, and with the option of copying the plot to the printer; (4) interpolation of x or y values from the fitted curve with error estimates based on error limits selected by the user; and (5) plotting the residuals between the y data values and the fitted curve, with the option copying the plot to the printer. 2 - Method of solution: Deming's method

  12. Analysis of a plane stress wave by the moving least squares method

    Directory of Open Access Journals (Sweden)

    Wojciech Dornowski

    2014-08-01

    Full Text Available A meshless method based on the moving least squares approximation is applied to stress wave propagation analysis. Two kinds of node meshes, the randomly generated mesh and the regular mesh are used. The nearest neighbours’ problem is developed from a triangulation that satisfies minimum edges length conditions. It is found that this method of neighbours’ choice significantly improves the solution accuracy. The reflection of stress waves from the free edge is modelled using fictitious nodes (outside the plate. The comparison with the finite difference results also demonstrated the accuracy of the proposed approach.[b]Keywords[/b]: civil engineering, meshless method, moving least squares method, elastic waves

  13. Regularized plane-wave least-squares Kirchhoff migration

    KAUST Repository

    Wang, Xin

    2013-09-22

    A Kirchhoff least-squares migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images. A regularization term is included that accounts for mispositioning of reflectors due to errors in the velocity model. Both synthetic and field results show that: 1) LSM with a reflectivity model common for all the plane-wave gathers provides the best image when the migration velocity model is accurate, but it is more sensitive to the velocity errors, 2) the regularized plane-wave LSM is more robust in the presence of velocity errors, and 3) LSM achieves both computational and IO saving by plane-wave encoding compared to shot-domain LSM for the models tested.

  14. Multiples least-squares reverse time migration

    KAUST Repository

    Zhang, Dongliang

    2013-01-01

    To enhance the image quality, we propose multiples least-squares reverse time migration (MLSRTM) that transforms each hydrophone into a virtual point source with a time history equal to that of the recorded data. Since each recorded trace is treated as a virtual source, knowledge of the source wavelet is not required. Numerical tests on synthetic data for the Sigsbee2B model and field data from Gulf of Mexico show that MLSRTM can improve the image quality by removing artifacts, balancing amplitudes, and suppressing crosstalk compared to standard migration of the free-surface multiples. The potential liability of this method is that multiples require several roundtrips between the reflector and the free surface, so that high frequencies in the multiples are attenuated compared to the primary reflections. This can lead to lower resolution in the migration image compared to that computed from primaries.

  15. An improved algorithm for the determination of the system parameters of a visual binary by least squares

    International Nuclear Information System (INIS)

    Xu, Yu-Lin.

    1988-01-01

    The problem of computing the orbit of a visual binary from a set of observed positions is reconsidered. It is a least squares adjustment problem, if the observational errors follow a bias-free multivariate Gaussian distribution and the covariance matrix of the observations is assumed to be known. The condition equations are constructed to satisfy both the conic section equation and the area theorem, which are nonlinear in both the observations and the adjustment parameters. The traditional least squares algorithm, which employs condition equations that are solved with respect to the uncorrelated observations and either linear in the adjustment parameters or linearized by developing them in Taylor series by first-order approximation, is inadequate in the orbit problem. Not long ago, a completely general solution was published by W. H. Jefferys, who proposed a rigorous adjustment algorithm for models in which the observations appear nonlinearly in the condition equations and may be correlated, and in which construction of the normal equations and the residual function involves no approximation. This method was successfully applied in this problem. The normal equations were first solved by Newton's scheme. Newton's method was modified to yield a definitive solution in the case the normal approach fails, by combination with the method of steepest descent and other sophisticated algorithms. Practical examples show that the modified Newton scheme can always lead to a final solution. The weighting of observations, the orthogonal parameters and the efficiency of a set of adjustment parameters are also considered

  16. Least squares shadowing sensitivity analysis of a modified Kuramoto–Sivashinsky equation

    International Nuclear Information System (INIS)

    Blonigan, Patrick J.; Wang, Qiqi

    2014-01-01

    Highlights: •Modifying the Kuramoto–Sivashinsky equation and changing its boundary conditions make it an ergodic dynamical system. •The modified Kuramoto–Sivashinsky equation exhibits distinct dynamics for three different ranges of system parameters. •Least squares shadowing sensitivity analysis computes accurate gradients for a wide range of system parameters. - Abstract: Computational methods for sensitivity analysis are invaluable tools for scientists and engineers investigating a wide range of physical phenomena. However, many of these methods fail when applied to chaotic systems, such as the Kuramoto–Sivashinsky (K–S) equation, which models a number of different chaotic systems found in nature. The following paper discusses the application of a new sensitivity analysis method developed by the authors to a modified K–S equation. We find that least squares shadowing sensitivity analysis computes accurate gradients for solutions corresponding to a wide range of system parameters

  17. Applying the methodology of Design of Experiments to stability studies: a Partial Least Squares approach for evaluation of drug stability.

    Science.gov (United States)

    Jordan, Nika; Zakrajšek, Jure; Bohanec, Simona; Roškar, Robert; Grabnar, Iztok

    2018-05-01

    The aim of the present research is to show that the methodology of Design of Experiments can be applied to stability data evaluation, as they can be seen as multi-factor and multi-level experimental designs. Linear regression analysis is usually an approach for analyzing stability data, but multivariate statistical methods could also be used to assess drug stability during the development phase. Data from a stability study for a pharmaceutical product with hydrochlorothiazide (HCTZ) as an unstable drug substance was used as a case example in this paper. The design space of the stability study was modeled using Umetrics MODDE 10.1 software. We showed that a Partial Least Squares model could be used for a multi-dimensional presentation of all data generated in a stability study and for determination of the relationship among factors that influence drug stability. It might also be used for stability predictions and potentially for the optimization of the extent of stability testing needed to determine shelf life and storage conditions, which would be time and cost-effective for the pharmaceutical industry.

  18. First-order system least-squares for second-order elliptic problems with discontinuous coefficients: Further results

    Energy Technology Data Exchange (ETDEWEB)

    Bloechle, B.; Manteuffel, T.; McCormick, S.; Starke, G.

    1996-12-31

    Many physical phenomena are modeled as scalar second-order elliptic boundary value problems with discontinuous coefficients. The first-order system least-squares (FOSLS) methodology is an alternative to standard mixed finite element methods for such problems. The occurrence of singularities at interface corners and cross-points requires that care be taken when implementing the least-squares finite element method in the FOSLS context. We introduce two methods of handling the challenges resulting from singularities. The first method is based on a weighted least-squares functional and results in non-conforming finite elements. The second method is based on the use of singular basis functions and results in conforming finite elements. We also share numerical results comparing the two approaches.

  19. Non-stationary least-squares complex decomposition for microseismic noise attenuation

    Science.gov (United States)

    Chen, Yangkang

    2018-06-01

    Microseismic data processing and imaging are crucial for subsurface real-time monitoring during hydraulic fracturing process. Unlike the active-source seismic events or large-scale earthquake events, the microseismic event is usually of very small magnitude, which makes its detection challenging. The biggest trouble of microseismic data is the low signal-to-noise ratio issue. Because of the small energy difference between effective microseismic signal and ambient noise, the effective signals are usually buried in strong random noise. I propose a useful microseismic denoising algorithm that is based on decomposing a microseismic trace into an ensemble of components using least-squares inversion. Based on the predictive property of useful microseismic event along the time direction, the random noise can be filtered out via least-squares fitting of multiple damping exponential components. The method is flexible and almost automated since the only parameter needed to be defined is a decomposition number. I use some synthetic and real data examples to demonstrate the potential of the algorithm in processing complicated microseismic data sets.

  20. Non-linear calibration models for near infrared spectroscopy

    DEFF Research Database (Denmark)

    Ni, Wangdong; Nørgaard, Lars; Mørup, Morten

    2014-01-01

    by ridge regression (RR). The performance of the different methods is demonstrated by their practical applications using three real-life near infrared (NIR) data sets. Different aspects of the various approaches including computational time, model interpretability, potential over-fitting using the non-linear...... models on linear problems, robustness to small or medium sample sets, and robustness to pre-processing, are discussed. The results suggest that GPR and BANN are powerful and promising methods for handling linear as well as nonlinear systems, even when the data sets are moderately small. The LS......-SVM), relevance vector machines (RVM), Gaussian process regression (GPR), artificial neural network (ANN), and Bayesian ANN (BANN). In this comparison, partial least squares (PLS) regression is used as a linear benchmark, while the relationship of the methods is considered in terms of traditional calibration...

  1. Modeling and control of PEMFC based on least squares support vector machines

    International Nuclear Information System (INIS)

    Li Xi; Cao Guangyi; Zhu Xinjian

    2006-01-01

    The proton exchange membrane fuel cell (PEMFC) is one of the most important power supplies. The operating temperature of the stack is an important controlled variable, which impacts the performance of the PEMFC. In order to improve the generating performance of the PEMFC, prolong its life and guarantee safety, credibility and low cost of the PEMFC system, it must be controlled efficiently. A nonlinear predictive control algorithm based on a least squares support vector machine (LS-SVM) model is presented for a family of complex systems with severe nonlinearity, such as the PEMFC, in this paper. The nonlinear off line model of the PEMFC is built by a LS-SVM model with radial basis function (RBF) kernel so as to implement nonlinear predictive control of the plant. During PEMFC operation, the off line model is linearized at each sampling instant, and the generalized predictive control (GPC) algorithm is applied to the predictive control of the plant. Experimental results demonstrate the effectiveness and advantages of this approach

  2. Distributed weighted least-squares estimation with fast convergence for large-scale systems☆

    Science.gov (United States)

    Marelli, Damián Edgardo; Fu, Minyue

    2015-01-01

    In this paper we study a distributed weighted least-squares estimation problem for a large-scale system consisting of a network of interconnected sub-systems. Each sub-system is concerned with a subset of the unknown parameters and has a measurement linear in the unknown parameters with additive noise. The distributed estimation task is for each sub-system to compute the globally optimal estimate of its own parameters using its own measurement and information shared with the network through neighborhood communication. We first provide a fully distributed iterative algorithm to asymptotically compute the global optimal estimate. The convergence rate of the algorithm will be maximized using a scaling parameter and a preconditioning method. This algorithm works for a general network. For a network without loops, we also provide a different iterative algorithm to compute the global optimal estimate which converges in a finite number of steps. We include numerical experiments to illustrate the performances of the proposed methods. PMID:25641976

  3. Distributed weighted least-squares estimation with fast convergence for large-scale systems.

    Science.gov (United States)

    Marelli, Damián Edgardo; Fu, Minyue

    2015-01-01

    In this paper we study a distributed weighted least-squares estimation problem for a large-scale system consisting of a network of interconnected sub-systems. Each sub-system is concerned with a subset of the unknown parameters and has a measurement linear in the unknown parameters with additive noise. The distributed estimation task is for each sub-system to compute the globally optimal estimate of its own parameters using its own measurement and information shared with the network through neighborhood communication. We first provide a fully distributed iterative algorithm to asymptotically compute the global optimal estimate. The convergence rate of the algorithm will be maximized using a scaling parameter and a preconditioning method. This algorithm works for a general network. For a network without loops, we also provide a different iterative algorithm to compute the global optimal estimate which converges in a finite number of steps. We include numerical experiments to illustrate the performances of the proposed methods.

  4. A cross-correlation objective function for least-squares migration and visco-acoustic imaging

    KAUST Repository

    Dutta, Gaurav

    2014-08-05

    Conventional acoustic least-squares migration inverts for a reflectivity image that best matches the amplitudes of the observed data. However, for field data applications, it is not easy to match the recorded amplitudes because of the visco-elastic nature of the earth and inaccuracies in the estimation of source signature and strength at different shot locations. To relax the requirement for strong amplitude matching of least-squares migration, we use a normalized cross-correlation objective function that is only sensitive to the similarity between the predicted and the observed data. Such a normalized cross-correlation objective function is also equivalent to a time-domain phase inversion method where the main emphasis is only on matching the phase of the data rather than the amplitude. Numerical tests on synthetic and field data show that such an objective function can be used as an alternative to visco-acoustic least-squares reverse time migration (Qp-LSRTM) when there is strong attenuation in the subsurface and the estimation of the attenuation parameter Qp is insufficiently accurate.

  5. A cross-correlation objective function for least-squares migration and visco-acoustic imaging

    KAUST Repository

    Dutta, Gaurav; Sinha, Mrinal; Schuster, Gerard T.

    2014-01-01

    Conventional acoustic least-squares migration inverts for a reflectivity image that best matches the amplitudes of the observed data. However, for field data applications, it is not easy to match the recorded amplitudes because of the visco-elastic nature of the earth and inaccuracies in the estimation of source signature and strength at different shot locations. To relax the requirement for strong amplitude matching of least-squares migration, we use a normalized cross-correlation objective function that is only sensitive to the similarity between the predicted and the observed data. Such a normalized cross-correlation objective function is also equivalent to a time-domain phase inversion method where the main emphasis is only on matching the phase of the data rather than the amplitude. Numerical tests on synthetic and field data show that such an objective function can be used as an alternative to visco-acoustic least-squares reverse time migration (Qp-LSRTM) when there is strong attenuation in the subsurface and the estimation of the attenuation parameter Qp is insufficiently accurate.

  6. Skeletonized Least Squares Wave Equation Migration

    KAUST Repository

    Zhan, Ge

    2010-10-17

    The theory for skeletonized least squares wave equation migration (LSM) is presented. The key idea is, for an assumed velocity model, the source‐side Green\\'s function and the geophone‐side Green\\'s function are computed by a numerical solution of the wave equation. Only the early‐arrivals of these Green\\'s functions are saved and skeletonized to form the migration Green\\'s function (MGF) by convolution. Then the migration image is obtained by a dot product between the recorded shot gathers and the MGF for every trial image point. The key to an efficient implementation of iterative LSM is that at each conjugate gradient iteration, the MGF is reused and no new finitedifference (FD) simulations are needed to get the updated migration image. It is believed that this procedure combined with phase‐encoded multi‐source technology will allow for the efficient computation of wave equation LSM images in less time than that of conventional reverse time migration (RTM).

  7. A Monte Carlo Library Least Square approach in the Neutron Inelastic-scattering and Thermal-capture Analysis (NISTA) process in bulk coal samples

    Science.gov (United States)

    Reyhancan, Iskender Atilla; Ebrahimi, Alborz; Çolak, Üner; Erduran, M. Nizamettin; Angin, Nergis

    2017-01-01

    A new Monte-Carlo Library Least Square (MCLLS) approach for treating non-linear radiation analysis problem in Neutron Inelastic-scattering and Thermal-capture Analysis (NISTA) was developed. 14 MeV neutrons were produced by a neutron generator via the 3H (2H , n) 4He reaction. The prompt gamma ray spectra from bulk samples of seven different materials were measured by a Bismuth Germanate (BGO) gamma detection system. Polyethylene was used as neutron moderator along with iron and lead as neutron and gamma ray shielding, respectively. The gamma detection system was equipped with a list mode data acquisition system which streams spectroscopy data directly to the computer, event-by-event. A GEANT4 simulation toolkit was used for generating the single-element libraries of all the elements of interest. These libraries were then used in a Linear Library Least Square (LLLS) approach with an unknown experimental sample spectrum to fit it with the calculated elemental libraries. GEANT4 simulation results were also used for the selection of the neutron shielding material.

  8. Simultaneous spectrophotometric determination of crystal violet and malachite green in water samples using partial least squares regression and central composite design after preconcentration by dispersive solid-phase extraction.

    Science.gov (United States)

    Razi-Asrami, Mahboobeh; Ghasemi, Jahan B; Amiri, Nayereh; Sadeghi, Seyed Jamal

    2017-04-01

    In this paper, a simple, fast, and inexpensive method is introduced for the simultaneous spectrophotometric determination of crystal violet (CV) and malachite green (MG) contents in aquatic samples using partial least squares regression (PLS) as a multivariate calibration technique after preconcentration by graphene oxide (GO). The method was based on the sorption and desorption of analytes onto GO and direct determination by ultraviolet-visible spectrophotometric techniques. GO was synthesized according to Hummers method. To characterize the shape and structure of GO, FT-IR, SEM, and XRD were used. The effective factors on the extraction efficiency such as pH, extraction time, and the amount of adsorbent were optimized using central composite design. The optimum values of these factors were 6, 15 min, and 12 mg, respectively. The maximum capacity of GO for the adsorption of CV and MG was 63.17 and 77.02 mg g -1 , respectively. Preconcentration factors and extraction recoveries were obtained and were 19.6, 98% for CV and 20, 100% for MG, respectively. LOD and linear dynamic ranges for CV and MG were 0.009, 0.03-0.3, 0.015, and 0.05-0.5 (μg mL -1 ), respectively. The intra-day and inter-day relative standard deviations were 1.99 and 0.58 for CV and 1.69 and 3.13 for MG at the concentration level of 50 ng mL -1 , respectively. Finally, the proposed DSPE/PLS method was successfully applied for the simultaneous determination of the trace amount of CV and MG in the real water samples.

  9. Attenuation compensation for least-squares reverse time migration using the viscoacoustic-wave equation

    KAUST Repository

    Dutta, Gaurav

    2014-10-01

    Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. Conventional acoustic reverse time migration (RTM) and least-squares reverse time migration (LSRTM) do not account for this distortion, which can lead to defocusing of migration images in highly attenuative geologic environments. To correct for this distortion, we used a linearized inversion method, denoted as Qp-LSRTM. During the leastsquares iterations, we used a linearized viscoacoustic modeling operator for forward modeling. The adjoint equations were derived using the adjoint-state method for back propagating the residual wavefields. The merit of this approach compared with conventional RTM and LSRTM was that Qp-LSRTM compensated for the amplitude loss due to attenuation and could produce images with better balanced amplitudes and more resolution below highly attenuative layers. Numerical tests on synthetic and field data illustrated the advantages of Qp-LSRTM over RTM and LSRTM when the recorded data had strong attenuation effects. Similar to standard LSRTM, the sensitivity tests for background velocity and Qp errors revealed that the liability of this method is the requirement for smooth and accurate migration velocity and attenuation models.

  10. Attenuation compensation for least-squares reverse time migration using the viscoacoustic-wave equation

    KAUST Repository

    Dutta, Gaurav; Schuster, Gerard T.

    2014-01-01

    Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. Conventional acoustic reverse time migration (RTM) and least-squares reverse time migration (LSRTM) do not account for this distortion, which can lead to defocusing of migration images in highly attenuative geologic environments. To correct for this distortion, we used a linearized inversion method, denoted as Qp-LSRTM. During the leastsquares iterations, we used a linearized viscoacoustic modeling operator for forward modeling. The adjoint equations were derived using the adjoint-state method for back propagating the residual wavefields. The merit of this approach compared with conventional RTM and LSRTM was that Qp-LSRTM compensated for the amplitude loss due to attenuation and could produce images with better balanced amplitudes and more resolution below highly attenuative layers. Numerical tests on synthetic and field data illustrated the advantages of Qp-LSRTM over RTM and LSRTM when the recorded data had strong attenuation effects. Similar to standard LSRTM, the sensitivity tests for background velocity and Qp errors revealed that the liability of this method is the requirement for smooth and accurate migration velocity and attenuation models.

  11. Validating the Galerkin least-squares finite element methods in predicting mixing flows in stirred tank reactors

    International Nuclear Information System (INIS)

    Johnson, K.; Bittorf, K.J.

    2002-01-01

    A novel approach for computer aided modeling and optimizing mixing process has been developed using Galerkin least-squares finite element technology. Computer aided mixing modeling and analysis involves Lagrangian and Eulerian analysis for relative fluid stretching, and energy dissipation concepts for laminar and turbulent flows. High quality, conservative, accurate, fluid velocity, and continuity solutions are required for determining mixing quality. The ORCA Computational Fluid Dynamics (CFD) package, based on a finite element formulation, solves the incompressible Reynolds Averaged Navier Stokes (RANS) equations. Although finite element technology has been well used in areas of heat transfer, solid mechanics, and aerodynamics for years, it has only recently been applied to the area of fluid mixing. ORCA, developed using the Galerkin Least-Squares (GLS) finite element technology, provides another formulation for numerically solving the RANS based and LES based fluid mechanics equations. The ORCA CFD package is validated against two case studies. The first, a free round jet, demonstrates that the CFD code predicts the theoretical velocity decay rate, linear expansion rate, and similarity profile. From proper prediction of fundamental free jet characteristics, confidence can be derived when predicting flows in a stirred tank, as a stirred tank reactor can be considered a series of free jets and wall jets. (author)

  12. Analysis of total least squares in estimating the parameters of a mortar trajectory

    Energy Technology Data Exchange (ETDEWEB)

    Lau, D.L.; Ng, L.C.

    1994-12-01

    Least Squares (LS) is a method of curve fitting used with the assumption that error exists in the observation vector. The method of Total Least Squares (TLS) is more useful in cases where there is error in the data matrix as well as the observation vector. This paper describes work done in comparing the LS and TLS results for parameter estimation of a mortar trajectory based on a time series of angular observations. To improve the results, we investigated several derivations of the LS and TLS methods, and early findings show TLS provided slightly, 10%, improved results over the LS method.

  13. Time-Series INSAR: An Integer Least-Squares Approach For Distributed Scatterers

    Science.gov (United States)

    Samiei-Esfahany, Sami; Hanssen, Ramon F.

    2012-01-01

    The objective of this research is to extend the geode- tic mathematical model which was developed for persistent scatterers to a model which can exploit distributed scatterers (DS). The main focus is on the integer least- squares framework, and the main challenge is to include the decorrelation effect in the mathematical model. In order to adapt the integer least-squares mathematical model for DS we altered the model from a single master to a multi-master configuration and introduced the decorrelation effect stochastically. This effect is described in our model by a full covariance matrix. We propose to de- rive this covariance matrix by numerical integration of the (joint) probability distribution function (PDF) of interferometric phases. This PDF is a function of coherence values and can be directly computed from radar data. We show that the use of this model can improve the performance of temporal phase unwrapping of distributed scatterers.

  14. Robust design optimization using the price of robustness, robust least squares and regularization methods

    Science.gov (United States)

    Bukhari, Hassan J.

    2017-12-01

    In this paper a framework for robust optimization of mechanical design problems and process systems that have parametric uncertainty is presented using three different approaches. Robust optimization problems are formulated so that the optimal solution is robust which means it is minimally sensitive to any perturbations in parameters. The first method uses the price of robustness approach which assumes the uncertain parameters to be symmetric and bounded. The robustness for the design can be controlled by limiting the parameters that can perturb.The second method uses the robust least squares method to determine the optimal parameters when data itself is subjected to perturbations instead of the parameters. The last method manages uncertainty by restricting the perturbation on parameters to improve sensitivity similar to Tikhonov regularization. The methods are implemented on two sets of problems; one linear and the other non-linear. This methodology will be compared with a prior method using multiple Monte Carlo simulation runs which shows that the approach being presented in this paper results in better performance.

  15. Adaptive Noise Canceling Menggunakan Algoritma Least Mean Square (Lms)

    OpenAIRE

    Nardiana, Anita; Sumaryono, Sari Sujoko

    2011-01-01

    Noise is inevitable in communication system. In some cases, noise can disturb signal. It is veryannoying as the received signal is jumbled with the noise itself. To reduce or remove noise, filter lowpass,highpass or bandpass can solve the problems, but this method cannot reach a maximum standard. One ofthe alternatives to solve the problem is by using adaptive filter. Adaptive algorithm frequently used is LeastMean Square (LMS) Algorithm which is compatible to Finite Impulse Response (FIR). T...

  16. Determination of Ethanol in Blood Samples Using Partial Least Square Regression Applied to Surface Enhanced Raman Spectroscopy.

    Science.gov (United States)

    Açikgöz, Güneş; Hamamci, Berna; Yildiz, Abdulkadir

    2018-04-01

    Alcohol consumption triggers toxic effect to organs and tissues in the human body. The risks are essentially thought to be related to ethanol content in alcoholic beverages. The identification of ethanol in blood samples requires rapid, minimal sample handling, and non-destructive analysis, such as Raman Spectroscopy. This study aims to apply Raman Spectroscopy for identification of ethanol in blood samples. Silver nanoparticles were synthesized to obtain Surface Enhanced Raman Spectroscopy (SERS) spectra of blood samples. The SERS spectra were used for Partial Least Square (PLS) for determining ethanol quantitatively. To apply PLS method, 920~820 cm -1 band interval was chosen and the spectral changes of the observed concentrations statistically associated with each other. The blood samples were examined according to this model and the quantity of ethanol was determined as that: first a calibration method was established. A strong relationship was observed between known concentration values and the values obtained by PLS method (R 2 = 1). Second instead of then, quantities of ethanol in 40 blood samples were predicted according to the calibration method. Quantitative analysis of the ethanol in the blood was done by analyzing the data obtained by Raman spectroscopy and the PLS method.

  17. Spatial Estimation of Losses Attributable to Meteorological Disasters in a Specific Area (105.0°E–115.0°E, 25°N–35°N Using Bayesian Maximum Entropy and Partial Least Squares Regression

    Directory of Open Access Journals (Sweden)

    F. S. Zhang

    2016-01-01

    Full Text Available The spatial mapping of losses attributable to such disasters is now well established as a means of describing the spatial patterns of disaster risk, and it has been shown to be suitable for many types of major meteorological disasters. However, few studies have been carried out by developing a regression model to estimate the effects of the spatial distribution of meteorological factors on losses associated with meteorological disasters. In this study, the proposed approach is capable of the following: (a estimating the spatial distributions of seven meteorological factors using Bayesian maximum entropy, (b identifying the four mapping methods used in this research with the best performance based on the cross validation, and (c establishing a fitted model between the PLS components and disaster losses information using partial least squares regression within a specific research area. The results showed the following: (a best mapping results were produced by multivariate Bayesian maximum entropy with probabilistic soft data; (b the regression model using three PLS components, extracted from seven meteorological factors by PLS method, was the most predictive by means of PRESS/SS test; (c northern Hunan Province sustains the most damage, and southeastern Gansu Province and western Guizhou Province sustained the least.

  18. Learning a Nonnegative Sparse Graph for Linear Regression.

    Science.gov (United States)

    Fang, Xiaozhao; Xu, Yong; Li, Xuelong; Lai, Zhihui; Wong, Wai Keung

    2015-09-01

    Previous graph-based semisupervised learning (G-SSL) methods have the following drawbacks: 1) they usually predefine the graph structure and then use it to perform label prediction, which cannot guarantee an overall optimum and 2) they only focus on the label prediction or the graph structure construction but are not competent in handling new samples. To this end, a novel nonnegative sparse graph (NNSG) learning method was first proposed. Then, both the label prediction and projection learning were integrated into linear regression. Finally, the linear regression and graph structure learning were unified within the same framework to overcome these two drawbacks. Therefore, a novel method, named learning a NNSG for linear regression was presented, in which the linear regression and graph learning were simultaneously performed to guarantee an overall optimum. In the learning process, the label information can be accurately propagated via the graph structure so that the linear regression can learn a discriminative projection to better fit sample labels and accurately classify new samples. An effective algorithm was designed to solve the corresponding optimization problem with fast convergence. Furthermore, NNSG provides a unified perceptiveness for a number of graph-based learning methods and linear regression methods. The experimental results showed that NNSG can obtain very high classification accuracy and greatly outperforms conventional G-SSL methods, especially some conventional graph construction methods.

  19. Comparison of two-concentration with multi-concentration linear regressions: Retrospective data analysis of multiple regulated LC-MS bioanalytical projects.

    Science.gov (United States)

    Musuku, Adrien; Tan, Aimin; Awaiye, Kayode; Trabelsi, Fethi

    2013-09-01

    Linear calibration is usually performed using eight to ten calibration concentration levels in regulated LC-MS bioanalysis because a minimum of six are specified in regulatory guidelines. However, we have previously reported that two-concentration linear calibration is as reliable as or even better than using multiple concentrations. The purpose of this research is to compare two-concentration with multiple-concentration linear calibration through retrospective data analysis of multiple bioanalytical projects that were conducted in an independent regulated bioanalytical laboratory. A total of 12 bioanalytical projects were randomly selected: two validations and two studies for each of the three most commonly used types of sample extraction methods (protein precipitation, liquid-liquid extraction, solid-phase extraction). When the existing data were retrospectively linearly regressed using only the lowest and the highest concentration levels, no extra batch failure/QC rejection was observed and the differences in accuracy and precision between the original multi-concentration regression and the new two-concentration linear regression are negligible. Specifically, the differences in overall mean apparent bias (square root of mean individual bias squares) are within the ranges of -0.3% to 0.7% and 0.1-0.7% for the validations and studies, respectively. The differences in mean QC concentrations are within the ranges of -0.6% to 1.8% and -0.8% to 2.5% for the validations and studies, respectively. The differences in %CV are within the ranges of -0.7% to 0.9% and -0.3% to 0.6% for the validations and studies, respectively. The average differences in study sample concentrations are within the range of -0.8% to 2.3%. With two-concentration linear regression, an average of 13% of time and cost could have been saved for each batch together with 53% of saving in the lead-in for each project (the preparation of working standard solutions, spiking, and aliquoting). Furthermore

  20. Online Identification of Multivariable Discrete Time Delay Systems Using a Recursive Least Square Algorithm

    Directory of Open Access Journals (Sweden)

    Saïda Bedoui

    2013-01-01

    Full Text Available This paper addresses the problem of simultaneous identification of linear discrete time delay multivariable systems. This problem involves both the estimation of the time delays and the dynamic parameters matrices. In fact, we suggest a new formulation of this problem allowing defining the time delay and the dynamic parameters in the same estimated vector and building the corresponding observation vector. Then, we use this formulation to propose a new method to identify the time delays and the parameters of these systems using the least square approach. Convergence conditions and statistics properties of the proposed method are also developed. Simulation results are presented to illustrate the performance of the proposed method. An application of the developed approach to compact disc player arm is also suggested in order to validate simulation results.

  1. Removing Malmquist bias from linear regressions

    Science.gov (United States)

    Verter, Frances

    1993-01-01

    Malmquist bias is present in all astronomical surveys where sources are observed above an apparent brightness threshold. Those sources which can be detected at progressively larger distances are progressively more limited to the intrinsically luminous portion of the true distribution. This bias does not distort any of the measurements, but distorts the sample composition. We have developed the first treatment to correct for Malmquist bias in linear regressions of astronomical data. A demonstration of the corrected linear regression that is computed in four steps is presented.

  2. Multi-frequency Phase Unwrap from Noisy Data: Adaptive Least Squares Approach

    Science.gov (United States)

    Katkovnik, Vladimir; Bioucas-Dias, José

    2010-04-01

    Multiple frequency interferometry is, basically, a phase acquisition strategy aimed at reducing or eliminating the ambiguity of the wrapped phase observations or, equivalently, reducing or eliminating the fringe ambiguity order. In multiple frequency interferometry, the phase measurements are acquired at different frequencies (or wavelengths) and recorded using the corresponding sensors (measurement channels). Assuming that the absolute phase to be reconstructed is piece-wise smooth, we use a nonparametric regression technique for the phase reconstruction. The nonparametric estimates are derived from a local least squares criterion, which, when applied to the multifrequency data, yields denoised (filtered) phase estimates with extended ambiguity (periodized), compared with the phase ambiguities inherent to each measurement frequency. The filtering algorithm is based on local polynomial (LPA) approximation for design of nonlinear filters (estimators) and adaptation of these filters to unknown smoothness of the spatially varying absolute phase [9]. For phase unwrapping, from filtered periodized data, we apply the recently introduced robust (in the sense of discontinuity preserving) PUMA unwrapping algorithm [1]. Simulations give evidence that the proposed algorithm yields state-of-the-art performance for continuous as well as for discontinues phase surfaces, enabling phase unwrapping in extraordinary difficult situations when all other algorithms fail.

  3. Q-Least Squares Reverse Time Migration with Viscoacoustic Deblurring Filters

    KAUST Repository

    Chen, Yuqing; Dutta, Gaurav; Dai, Wei; Schuster, Gerard T.

    2017-01-01

    Viscoacoustic least-squares reverse time migration (Q-LSRTM) linearly inverts for the subsurface reflectivity model from lossy data. Compared to the conventional migration methods, it can compensate for the amplitude loss in the migrated images because of the strong subsurface attenuation and can produce reflectors that are accurately positioned in depth. However, the adjoint Q propagators used for backward propagating the residual data are also attenuative. Thus, the inverted images from Q-LSRTM are often observed to have lower resolution when compared to the benchmark acoustic LSRTM images from acoustic data. To increase the resolution and accelerate the convergence of Q-LSRTM, we propose using viscoacoustic deblurring filters as a preconditioner for Q-LSRTM. These filters can be estimated by matching a simulated migration image to its reference reflectivity model. Numerical tests on synthetic and field data demonstrate that Q-LSRTM combined with viscoacoustic deblurring filters can produce images with higher resolution and more balanced amplitudes than images from acoustic RTM, acoustic LSRTM and Q-LSRTM when there is strong attenuation in the background medium. The proposed preconditioning method is also shown to improve the convergence rate of Q-LSRTM by more than 30 percent in some cases and significantly compensate for the lossy artifacts in RTM images.

  4. Q-Least Squares Reverse Time Migration with Viscoacoustic Deblurring Filters

    KAUST Repository

    Chen, Yuqing

    2017-08-02

    Viscoacoustic least-squares reverse time migration (Q-LSRTM) linearly inverts for the subsurface reflectivity model from lossy data. Compared to the conventional migration methods, it can compensate for the amplitude loss in the migrated images because of the strong subsurface attenuation and can produce reflectors that are accurately positioned in depth. However, the adjoint Q propagators used for backward propagating the residual data are also attenuative. Thus, the inverted images from Q-LSRTM are often observed to have lower resolution when compared to the benchmark acoustic LSRTM images from acoustic data. To increase the resolution and accelerate the convergence of Q-LSRTM, we propose using viscoacoustic deblurring filters as a preconditioner for Q-LSRTM. These filters can be estimated by matching a simulated migration image to its reference reflectivity model. Numerical tests on synthetic and field data demonstrate that Q-LSRTM combined with viscoacoustic deblurring filters can produce images with higher resolution and more balanced amplitudes than images from acoustic RTM, acoustic LSRTM and Q-LSRTM when there is strong attenuation in the background medium. The proposed preconditioning method is also shown to improve the convergence rate of Q-LSRTM by more than 30 percent in some cases and significantly compensate for the lossy artifacts in RTM images.

  5. An Inverse Function Least Square Fitting Approach of the Buildup Factor for Radiation Shielding Analysis

    Energy Technology Data Exchange (ETDEWEB)

    Park, Chang Je [Sejong Univ., Seoul (Korea, Republic of); Alkhatee, Sari; Roh, Gyuhong; Lee, Byungchul [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

    2014-05-15

    Dose absorption and energy absorption buildup factors are widely used in the shielding analysis. The dose rate of the medium is main concern in the dose buildup factor, however energy absorption is an important parameter in the energy buildup factors. ANSI/ANS-6.4.3-1991 standard data is widely used based on interpolation and extrapolation by means of an approximation method. Recently, Yoshida's geometric progression (GP) formulae are also popular and it is already implemented in QAD code. In the QAD code, two buildup factors are notated as DOSE for standard air exposure response and ENG for the response of the energy absorbed in the material itself. In this paper, a new least square fitting method is suggested to obtain a reliable buildup factors proposed since 1991. Total 4 datasets of air exposure buildup factors are used for evaluation including ANSI/ANS-6.4.3-1991, Taylor, Berger, and GP data. The standard deviation of the fitted data are analyzed based on the results. A new reverse least square fitting method is proposed in this study in order to reduce the fitting uncertainties. It adapts an inverse function rather than the original function by the distribution slope of dataset. Some quantitative comparisons are provided for concrete and lead in this paper, too. This study is focused on the least square fitting of existing buildup factors to be utilized in the point-kernel code for radiation shielding analysis. The inverse least square fitting method is suggested to obtain more reliable results of concave shaped dataset such as concrete. In the concrete case, the variance and residue are decreased significantly, too. However, the convex shaped case of lead can be applied to the usual least square fitting method. In the future, more datasets will be tested by using the least square fitting. And the fitted data could be implemented to the existing point-kernel codes.

  6. Quantification of endocrine disruptors and pesticides in water by gas chromatography-tandem mass spectrometry. Method validation using weighted linear regression schemes.

    Science.gov (United States)

    Mansilha, C; Melo, A; Rebelo, H; Ferreira, I M P L V O; Pinho, O; Domingues, V; Pinho, C; Gameiro, P

    2010-10-22

    A multi-residue methodology based on a solid phase extraction followed by gas chromatography-tandem mass spectrometry was developed for trace analysis of 32 compounds in water matrices, including estrogens and several pesticides from different chemical families, some of them with endocrine disrupting properties. Matrix standard calibration solutions were prepared by adding known amounts of the analytes to a residue-free sample to compensate matrix-induced chromatographic response enhancement observed for certain pesticides. Validation was done mainly according to the International Conference on Harmonisation recommendations, as well as some European and American validation guidelines with specifications for pesticides analysis and/or GC-MS methodology. As the assumption of homoscedasticity was not met for analytical data, weighted least squares linear regression procedure was applied as a simple and effective way to counteract the greater influence of the greater concentrations on the fitted regression line, improving accuracy at the lower end of the calibration curve. The method was considered validated for 31 compounds after consistent evaluation of the key analytical parameters: specificity, linearity, limit of detection and quantification, range, precision, accuracy, extraction efficiency, stability and robustness. Copyright © 2010 Elsevier B.V. All rights reserved.

  7. Sub-Model Partial Least Squares for Improved Accuracy in Quantitative Laser Induced Breakdown Spectroscopy

    Science.gov (United States)

    Anderson, R. B.; Clegg, S. M.; Frydenvang, J.

    2015-12-01

    One of the primary challenges faced by the ChemCam instrument on the Curiosity Mars rover is developing a regression model that can accurately predict the composition of the wide range of target types encountered (basalts, calcium sulfate, feldspar, oxides, etc.). The original calibration used 69 rock standards to train a partial least squares (PLS) model for each major element. By expanding the suite of calibration samples to >400 targets spanning a wider range of compositions, the accuracy of the model was improved, but some targets with "extreme" compositions (e.g. pure minerals) were still poorly predicted. We have therefore developed a simple method, referred to as "submodel PLS", to improve the performance of PLS across a wide range of target compositions. In addition to generating a "full" (0-100 wt.%) PLS model for the element of interest, we also generate several overlapping submodels (e.g. for SiO2, we generate "low" (0-50 wt.%), "mid" (30-70 wt.%), and "high" (60-100 wt.%) models). The submodels are generally more accurate than the "full" model for samples within their range because they are able to adjust for matrix effects that are specific to that range. To predict the composition of an unknown target, we first predict the composition with the submodels and the "full" model. Then, based on the predicted composition from the "full" model, the appropriate submodel prediction can be used (e.g. if the full model predicts a low composition, use the "low" model result, which is likely to be more accurate). For samples with "full" predictions that occur in a region of overlap between submodels, the submodel predictions are "blended" using a simple linear weighted sum. The submodel PLS method shows improvements in most of the major elements predicted by ChemCam and reduces the occurrence of negative predictions for low wt.% targets. Submodel PLS is currently being used in conjunction with ICA regression for the major element compositions of ChemCam data.

  8. Seismic time-lapse imaging using Interferometric least-squares migration

    KAUST Repository

    Sinha, Mrinal

    2016-09-06

    One of the problems with 4D surveys is that the environmental conditions change over time so that the experiment is insufficiently repeatable. To mitigate this problem, we propose the use of interferometric least-squares migration (ILSM) to estimate the migration image for the baseline and monitor surveys. Here, a known reflector is used as the reference reflector for ILSM. Results with synthetic and field data show that ILSM can eliminate artifacts caused by non-repeatability in time-lapse surveys.

  9. Seismic time-lapse imaging using Interferometric least-squares migration

    KAUST Repository

    Sinha, Mrinal; Schuster, Gerard T.

    2016-01-01

    One of the problems with 4D surveys is that the environmental conditions change over time so that the experiment is insufficiently repeatable. To mitigate this problem, we propose the use of interferometric least-squares migration (ILSM) to estimate the migration image for the baseline and monitor surveys. Here, a known reflector is used as the reference reflector for ILSM. Results with synthetic and field data show that ILSM can eliminate artifacts caused by non-repeatability in time-lapse surveys.

  10. Partial least squares path modeling basic concepts, methodological issues and applications

    CERN Document Server

    Noonan, Richard

    2017-01-01

    This edited book presents the recent developments in partial least squares-path modeling (PLS-PM) and provides a comprehensive overview of the current state of the most advanced research related to PLS-PM. The first section of this book emphasizes the basic concepts and extensions of the PLS-PM method. The second section discusses the methodological issues that are the focus of the recent development of the PLS-PM method. The third part discusses the real world application of the PLS-PM method in various disciplines. The contributions from expert authors in the field of PLS focus on topics such as the factor-based PLS-PM, the perfect match between a model and a mode, quantile composite-based path modeling (QC-PM), ordinal consistent partial least squares (OrdPLSc), non-symmetrical composite-based path modeling (NSCPM), modern view for mediation analysis in PLS-PM, a multi-method approach for identifying and treating unobserved heterogeneity, multigroup analysis (PLS-MGA), the assessment of the common method b...

  11. Block Least Mean Squares Algorithm over Distributed Wireless Sensor Network

    Directory of Open Access Journals (Sweden)

    T. Panigrahi

    2012-01-01

    Full Text Available In a distributed parameter estimation problem, during each sampling instant, a typical sensor node communicates its estimate either by the diffusion algorithm or by the incremental algorithm. Both these conventional distributed algorithms involve significant communication overheads and, consequently, defeat the basic purpose of wireless sensor networks. In the present paper, we therefore propose two new distributed algorithms, namely, block diffusion least mean square (BDLMS and block incremental least mean square (BILMS by extending the concept of block adaptive filtering techniques to the distributed adaptation scenario. The performance analysis of the proposed BDLMS and BILMS algorithms has been carried out and found to have similar performances to those offered by conventional diffusion LMS and incremental LMS algorithms, respectively. The convergence analyses of the proposed algorithms obtained from the simulation study are also found to be in agreement with the theoretical analysis. The remarkable and interesting aspect of the proposed block-based algorithms is that their communication overheads per node and latencies are less than those of the conventional algorithms by a factor as high as the block size used in the algorithms.

  12. Least squares methodology applied to LWR-PV damage dosimetry, experience and expectations

    International Nuclear Information System (INIS)

    Wagschal, J.J.; Broadhead, B.L.; Maerker, R.E.

    1979-01-01

    The development of an advanced methodology for Light Water Reactors (LWR) Pressure Vessel (PV) damage dosimetry applications is the subject of an ongoing EPRI-sponsored research project at ORNL. This methodology includes a generalized least squares approach to a combination of data. The data include measured foil activations, evaluated cross sections and calculated fluxes. The uncertainties associated with the data as well as with the calculational methods are an essential component of this methodology. Activation measurements in two NBS benchmark neutron fields ( 252 Cf ISNF) and in a prototypic reactor field (Oak Ridge Pool Critical Assembly - PCA) are being analyzed using a generalized least squares method. The sensitivity of the results to the representation of the uncertainties (covariances) was carefully checked. Cross element covariances were found to be of utmost importance

  13. Positive Scattering Cross Sections using Constrained Least Squares

    International Nuclear Information System (INIS)

    Dahl, J.A.; Ganapol, B.D.; Morel, J.E.

    1999-01-01

    A method which creates a positive Legendre expansion from truncated Legendre cross section libraries is presented. The cross section moments of order two and greater are modified by a constrained least squares algorithm, subject to the constraints that the zeroth and first moments remain constant, and that the standard discrete ordinate scattering matrix is positive. A method using the maximum entropy representation of the cross section which reduces the error of these modified moments is also presented. These methods are implemented in PARTISN, and numerical results from a transport calculation using highly anisotropic scattering cross sections with the exponential discontinuous spatial scheme is presented

  14. Modified multiblock partial least squares path modeling algorithm with backpropagation neural networks approach

    Science.gov (United States)

    Yuniarto, Budi; Kurniawan, Robert

    2017-03-01

    PLS Path Modeling (PLS-PM) is different from covariance based SEM, where PLS-PM use an approach based on variance or component, therefore, PLS-PM is also known as a component based SEM. Multiblock Partial Least Squares (MBPLS) is a method in PLS regression which can be used in PLS Path Modeling which known as Multiblock PLS Path Modeling (MBPLS-PM). This method uses an iterative procedure in its algorithm. This research aims to modify MBPLS-PM with Back Propagation Neural Network approach. The result is MBPLS-PM algorithm can be modified using the Back Propagation Neural Network approach to replace the iterative process in backward and forward step to get the matrix t and the matrix u in the algorithm. By modifying the MBPLS-PM algorithm using Back Propagation Neural Network approach, the model parameters obtained are relatively not significantly different compared to model parameters obtained by original MBPLS-PM algorithm.

  15. Least-squares reverse time migration of marine data with frequency-selection encoding

    KAUST Repository

    Dai, Wei; Huang, Yunsong; Schuster, Gerard T.

    2013-01-01

    The phase-encoding technique can sometimes increase the efficiency of the least-squares reverse time migration (LSRTM) by more than one order of magnitude. However, traditional random encoding functions require all the encoded shots to share

  16. On the use of a penalized least squares method to process kinematic full-field measurements

    International Nuclear Information System (INIS)

    Moulart, Raphaël; Rotinat, René

    2014-01-01

    This work is aimed at exploring the performances of an alternative procedure to smooth and differentiate full-field displacement measurements. After recalling the strategies currently used by the experimental mechanics community, a short overview of the available smoothing algorithms is drawn up and the requirements that such an algorithm has to fulfil to be applicable to process kinematic measurements are listed. A comparative study of the chosen algorithm is performed including the 2D penalized least squares method and two other commonly implemented strategies. The results obtained by penalized least squares are comparable in terms of quality to those produced by the two other algorithms, while the penalized least squares method appears to be the fastest and the most flexible. Unlike both the other considered methods, it is possible with penalized least squares to automatically choose the parameter governing the amount of smoothing to apply. Unfortunately, it appears that this automation is not suitable for the proposed application since it does not lead to optimal strain maps. Finally, it is possible with this technique to perform the derivation to obtain strain maps before smoothing them (while the smoothing is normally applied to displacement maps before the differentiation), which can lead in some cases to a more effective reconstruction of the strain fields. (paper)

  17. Partial Least Square with Savitzky Golay Derivative in Predicting Blood Hemoglobin Using Near Infrared Spectrum

    Directory of Open Access Journals (Sweden)

    Mohd Idrus Mohd Nazrul Effendy

    2018-01-01

    Full Text Available Near infrared spectroscopy (NIRS is a reliable technique that widely used in medical fields. Partial least square was developed to predict blood hemoglobin concentration using NIRS. The aims of this paper are (i to develop predictive model for near infrared spectroscopic analysis in blood hemoglobin prediction, (ii to establish relationship between blood hemoglobin and near infrared spectrum using a predictive model, (iii to evaluate the predictive accuracy of a predictive model based on root mean squared error (RMSE and coefficient of determination rp2. Partial least square with first order Savitzky Golay (SG derivative preprocessing (PLS-SGd1 showed the higher performance of predictions with RMSE = 0.7965 and rp2= 0.9206 in K-fold cross validation. Optimum number of latent variable (LV and frame length (f were 32 and 27 nm, respectively. These findings suggest that the relationship between blood hemoglobin and near infrared spectrum is strong, and the partial least square with first order SG derivative is able to predict the blood hemoglobin using near infrared spectral data.

  18. Enhanced least squares Monte Carlo method for real-time decision optimizations for evolving natural hazards

    DEFF Research Database (Denmark)

    Anders, Annett; Nishijima, Kazuyoshi

    The present paper aims at enhancing a solution approach proposed by Anders & Nishijima (2011) to real-time decision problems in civil engineering. The approach takes basis in the Least Squares Monte Carlo method (LSM) originally proposed by Longstaff & Schwartz (2001) for computing American option...... prices. In Anders & Nishijima (2011) the LSM is adapted for a real-time operational decision problem; however it is found that further improvement is required in regard to the computational efficiency, in order to facilitate it for practice. This is the focus in the present paper. The idea behind...... the improvement of the computational efficiency is to “best utilize” the least squares method; i.e. least squares method is applied for estimating the expected utility for terminal decisions, conditional on realizations of underlying random phenomena at respective times in a parametric way. The implementation...

  19. A least squares calculational method: application to e±-H elastic scattering

    International Nuclear Information System (INIS)

    Das, J.N.; Chakraborty, S.

    1989-01-01

    The least squares calcualtional method proposed by Das has been applied for the e ± -H elastic scattering problems for intermediate energies. Some important conclusions are made on the basis of the calculation. (author). 7 refs ., 2 tabs

  20. Statistical methods in regression and calibration analysis of chromosome aberration data

    International Nuclear Information System (INIS)

    Merkle, W.

    1983-01-01

    The method of iteratively reweighted least squares for the regression analysis of Poisson distributed chromosome aberration data is reviewed in the context of other fit procedures used in the cytogenetic literature. As an application of the resulting regression curves methods for calculating confidence intervals on dose from aberration yield are described and compared, and, for the linear quadratic model a confidence interval is given. Emphasis is placed on the rational interpretation and the limitations of various methods from a statistical point of view. (orig./MG)

  1. Non-linear least squares curve fitting of a simple theoretical model to radioimmunoassay dose-response data using a mini-computer

    International Nuclear Information System (INIS)

    Wilkins, T.A.; Chadney, D.C.; Bryant, J.; Palmstroem, S.H.; Winder, R.L.

    1977-01-01

    Using the simple univalent antigen univalent-antibody equilibrium model the dose-response curve of a radioimmunoassay (RIA) may be expressed as a function of Y, X and the four physical parameters of the idealised system. A compact but powerful mini-computer program has been written in BASIC for rapid iterative non-linear least squares curve fitting and dose interpolation with this function. In its simplest form the program can be operated in an 8K byte mini-computer. The program has been extensively tested with data from 10 different assay systems (RIA and CPBA) for measurement of drugs and hormones ranging in molecular size from thyroxine to insulin. For each assay system the results have been analysed in terms of (a) curve fitting biases and (b) direct comparison with manual fitting. In all cases the quality of fitting was remarkably good in spite of the fact that the chemistry of each system departed significantly from one or more of the assumptions implicit in the model used. A mathematical analysis of departures from the model's principal assumption has provided an explanation for this somewhat unexpected observation. The essential features of this analysis are presented in this paper together with the statistical analyses of the performance of the program. From these and the results obtained to date in the routine quality control of these 10 assays, it is concluded that the method of curve fitting and dose interpolation presented in this paper is likely to be of general applicability. (orig.) [de

  2. Regularized Partial Least Squares with an Application to NMR Spectroscopy

    OpenAIRE

    Allen, Genevera I.; Peterson, Christine; Vannucci, Marina; Maletic-Savatic, Mirjana

    2012-01-01

    High-dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension reduction techniques in the context of supervised data analysis. We introduce a framework for Regularized PLS by solving a relaxation of the SIMPLS optimization problem with penalties on the PLS loadings vectors. Our approach enjoys many advantages including flexi...

  3. Multisource Least-squares Reverse Time Migration

    KAUST Repository

    Dai, Wei

    2012-12-01

    Least-squares migration has been shown to be able to produce high quality migration images, but its computational cost is considered to be too high for practical imaging. In this dissertation, a multisource least-squares reverse time migration algorithm (LSRTM) is proposed to increase by up to 10 times the computational efficiency by utilizing the blended sources processing technique. There are three main chapters in this dissertation. In Chapter 2, the multisource LSRTM algorithm is implemented with random time-shift and random source polarity encoding functions. Numerical tests on the 2D HESS VTI data show that the multisource LSRTM algorithm suppresses migration artifacts, balances the amplitudes, improves image resolution, and reduces crosstalk noise associated with the blended shot gathers. For this example, multisource LSRTM is about three times faster than the conventional RTM method. For the 3D example of the SEG/EAGE salt model, with comparable computational cost, multisource LSRTM produces images with more accurate amplitudes, better spatial resolution, and fewer migration artifacts compared to conventional RTM. The empirical results suggest that the multisource LSRTM can produce more accurate reflectivity images than conventional RTM does with similar or less computational cost. The caveat is that LSRTM image is sensitive to large errors in the migration velocity model. In Chapter 3, the multisource LSRTM algorithm is implemented with frequency selection encoding strategy and applied to marine streamer data, for which traditional random encoding functions are not applicable. The frequency-selection encoding functions are delta functions in the frequency domain, so that all the encoded shots have unique non-overlapping frequency content. Therefore, the receivers can distinguish the wavefield from each shot according to the frequencies. With the frequency-selection encoding method, the computational efficiency of LSRTM is increased so that its cost is

  4. A new finite element formulation for CFD:VIII. The Galerkin/least-squares method for advective-diffusive equations

    International Nuclear Information System (INIS)

    Hughes, T.J.R.; Hulbert, G.M.; Franca, L.P.

    1988-10-01

    Galerkin/least-squares finite element methods are presented for advective-diffusive equations. Galerkin/least-squares represents a conceptual simplification of SUPG, and is in fact applicable to a wide variety of other problem types. A convergence analysis and error estimates are presented. (author) [pt

  5. A ¤nonparametric dynamic additive regression model for longitudinal data

    DEFF Research Database (Denmark)

    Martinussen, T.; Scheike, T. H.

    2000-01-01

    dynamic linear models, estimating equations, least squares, longitudinal data, nonparametric methods, partly conditional mean models, time-varying-coefficient models......dynamic linear models, estimating equations, least squares, longitudinal data, nonparametric methods, partly conditional mean models, time-varying-coefficient models...

  6. The comparison between several robust ridge regression estimators in the presence of multicollinearity and multiple outliers

    Science.gov (United States)

    Zahari, Siti Meriam; Ramli, Norazan Mohamed; Moktar, Balkiah; Zainol, Mohammad Said

    2014-09-01

    In the presence of multicollinearity and multiple outliers, statistical inference of linear regression model using ordinary least squares (OLS) estimators would be severely affected and produces misleading results. To overcome this, many approaches have been investigated. These include robust methods which were reported to be less sensitive to the presence of outliers. In addition, ridge regression technique was employed to tackle multicollinearity problem. In order to mitigate both problems, a combination of ridge regression and robust methods was discussed in this study. The superiority of this approach was examined when simultaneous presence of multicollinearity and multiple outliers occurred in multiple linear regression. This study aimed to look at the performance of several well-known robust estimators; M, MM, RIDGE and robust ridge regression estimators, namely Weighted Ridge M-estimator (WRM), Weighted Ridge MM (WRMM), Ridge MM (RMM), in such a situation. Results of the study showed that in the presence of simultaneous multicollinearity and multiple outliers (in both x and y-direction), the RMM and RIDGE are more or less similar in terms of superiority over the other estimators, regardless of the number of observation, level of collinearity and percentage of outliers used. However, when outliers occurred in only single direction (y-direction), the WRMM estimator is the most superior among the robust ridge regression estimators, by producing the least variance. In conclusion, the robust ridge regression is the best alternative as compared to robust and conventional least squares estimators when dealing with simultaneous presence of multicollinearity and outliers.

  7. A Monte Carlo Investigation of the Box-Cox Model and a Nonlinear Least Squares Alternative.

    OpenAIRE

    Showalter, Mark H

    1994-01-01

    This paper reports a Monte Carlo study of the Box-Cox model and a nonlinear least squares alternative. Key results include the following: the transformation parameter in the Box-Cox model appears to be inconsistently estimated in the presence of conditional heteroskedasticity; the constant term in both the Box-Cox and the nonlinear least squares models is poorly estimated in small samples; conditional mean forecasts tend to underestimate their true value in the Box-Cox model when the transfor...

  8. Multispectral colormapping using penalized least square regression

    DEFF Research Database (Denmark)

    Dissing, Bjørn Skovlund; Carstensen, Jens Michael; Larsen, Rasmus

    2010-01-01

    The authors propose a novel method to map a multispectral image into the device independent color space CIE-XYZ. This method provides a way to visualize multispectral images by predicting colorvalues from spectral values while maintaining interpretability and is tested on a light emitting diode...... that the interpretability improves significantly but comes at the cost of slightly worse predictability....

  9. A rigid-body least-squares program with angular and translation scan facilities

    CERN Document Server

    Kutschabsky, L

    1981-01-01

    The described computer program, written in CERN Fortran, is designed to enlarge the convergence radius of the rigid-body least-squares method by allowing a stepwise change of the angular and/or translational parameters within a chosen range. (6 refs).

  10. Harmonic tidal analysis at a few stations using the least squares method

    Digital Repository Service at National Institute of Oceanography (India)

    Fernandes, A.A.; Das, V.K.; Bahulayan, N.

    Using the least squares method, harmonic analysis has been performed on hourly water level records of 29 days at several stations depicting different types of non-tidal noise. For a tidal record at Mormugao, which was free from storm surges (low...

  11. Tip-tilt disturbance model identification based on non-linear least squares fitting for Linear Quadratic Gaussian control

    Science.gov (United States)

    Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing

    2018-05-01

    We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.

  12. Conjugate gradient and cross-correlation based least-square reverse time migration and its application

    Science.gov (United States)

    Sun, Xiao-Dong; Ge, Zhong-Hui; Li, Zhen-Chun

    2017-09-01

    Although conventional reverse time migration can be perfectly applied to structural imaging it lacks the capability of enabling detailed delineation of a lithological reservoir due to irregular illumination. To obtain reliable reflectivity of the subsurface it is necessary to solve the imaging problem using inversion. The least-square reverse time migration (LSRTM) (also known as linearized reflectivity inversion) aims to obtain relatively high-resolution amplitude preserving imaging by including the inverse of the Hessian matrix. In practice, the conjugate gradient algorithm is proven to be an efficient iterative method for enabling use of LSRTM. The velocity gradient can be derived from a cross-correlation between observed data and simulated data, making LSRTM independent of wavelet signature and thus more robust in practice. Tests on synthetic and marine data show that LSRTM has good potential for use in reservoir description and four-dimensional (4D) seismic images compared to traditional RTM and Fourier finite difference (FFD) migration. This paper investigates the first order approximation of LSRTM, which is also known as the linear Born approximation. However, for more complex geological structures a higher order approximation should be considered to improve imaging quality.

  13. Improving imaging quality using least-squares reverse time migration: application to data from Bohai basin

    KAUST Repository

    Zhang, Hao; Liu, Qiancheng; Wu, Jizhong

    2017-01-01

    Least-squares reverse time migration (LSRTM) is a seismic imaging technique based on linear inversion, which usually aims to improve the quality of seismic image through removing the acquisition footprint, suppressing migration artifacts, and enhancing resolution. LSRTM has been shown to produce migration images with better quality than those computed by conventional migration. In this paper, our derivation of LSRTM approximates the near-incident reflection coefficient with the normal-incident reflection coefficient, which shows that the reflectivity term defined is related to the normal-incident reflection coefficient and the background velocity. With reflected data, LSRTM is mainly sensitive to impedance perturbations. According to an approximate relationship between them, we reformulate the perturbation related system into a reflection-coefficient related one. Then, we seek the inverted image through linearized iteration. In the proposed algorithm, we only need the migration velocity for LSRTM considering that the density changes gently when compared with migration velocity. To validate our algorithms, we first apply it to a synthetic case and then a field data set. Both applications illustrate that our imaging results are of good quality.

  14. Improving imaging quality using least-squares reverse time migration: application to data from Bohai basin

    KAUST Repository

    Zhang, Hao

    2017-07-07

    Least-squares reverse time migration (LSRTM) is a seismic imaging technique based on linear inversion, which usually aims to improve the quality of seismic image through removing the acquisition footprint, suppressing migration artifacts, and enhancing resolution. LSRTM has been shown to produce migration images with better quality than those computed by conventional migration. In this paper, our derivation of LSRTM approximates the near-incident reflection coefficient with the normal-incident reflection coefficient, which shows that the reflectivity term defined is related to the normal-incident reflection coefficient and the background velocity. With reflected data, LSRTM is mainly sensitive to impedance perturbations. According to an approximate relationship between them, we reformulate the perturbation related system into a reflection-coefficient related one. Then, we seek the inverted image through linearized iteration. In the proposed algorithm, we only need the migration velocity for LSRTM considering that the density changes gently when compared with migration velocity. To validate our algorithms, we first apply it to a synthetic case and then a field data set. Both applications illustrate that our imaging results are of good quality.

  15. A Hybrid Least Square Support Vector Machine Model with Parameters Optimization for Stock Forecasting

    Directory of Open Access Journals (Sweden)

    Jian Chai

    2015-01-01

    Full Text Available This paper proposes an EMD-LSSVM (empirical mode decomposition least squares support vector machine model to analyze the CSI 300 index. A WD-LSSVM (wavelet denoising least squares support machine is also proposed as a benchmark to compare with the performance of EMD-LSSVM. Since parameters selection is vital to the performance of the model, different optimization methods are used, including simplex, GS (grid search, PSO (particle swarm optimization, and GA (genetic algorithm. Experimental results show that the EMD-LSSVM model with GS algorithm outperforms other methods in predicting stock market movement direction.

  16. Comparison of Classical and Robust Estimates of Threshold Auto-regression Parameters

    Directory of Open Access Journals (Sweden)

    V. B. Goryainov

    2017-01-01

    Full Text Available The study object is the first-order threshold auto-regression model with a single zero-located threshold. The model describes a stochastic temporal series with discrete time by means of a piecewise linear equation consisting of two linear classical first-order autoregressive equations. One of these equations is used to calculate a running value of the temporal series. A control variable that determines the choice between these two equations is the sign of the previous value of the same series.The first-order threshold autoregressive model with a single threshold depends on two real parameters that coincide with the coefficients of the piecewise linear threshold equation. These parameters are assumed to be unknown. The paper studies an estimate of the least squares, an estimate the least modules, and the M-estimates of these parameters. The aim of the paper is a comparative study of the accuracy of these estimates for the main probabilistic distributions of the updating process of the threshold autoregressive equation. These probability distributions were normal, contaminated normal, logistic, double-exponential distributions, a Student's distribution with different number of degrees of freedom, and a Cauchy distribution.As a measure of the accuracy of each estimate, was chosen its variance to measure the scattering of the estimate around the estimated parameter. An estimate with smaller variance made from the two estimates was considered to be the best. The variance was estimated by computer simulation. To estimate the smallest modules an iterative weighted least-squares method was used and the M-estimates were done by the method of a deformable polyhedron (the Nelder-Mead method. To calculate the least squares estimate, an explicit analytic expression was used.It turned out that the estimation of least squares is best only with the normal distribution of the updating process. For the logistic distribution and the Student's distribution with the

  17. SOCP relaxation bounds for the optimal subset selection problem applied to robust linear regression

    OpenAIRE

    Flores, Salvador

    2015-01-01

    This paper deals with the problem of finding the globally optimal subset of h elements from a larger set of n elements in d space dimensions so as to minimize a quadratic criterion, with an special emphasis on applications to computing the Least Trimmed Squares Estimator (LTSE) for robust regression. The computation of the LTSE is a challenging subset selection problem involving a nonlinear program with continuous and binary variables, linked in a highly nonlinear fashion. The selection of a ...

  18. A hybrid partial least squares and random forest approach to ...

    African Journals Online (AJOL)

    Nicole Reddy

    GLCM describes the texture features by the stochastic ... The linear regression model is then fit to the latent variables known as the PLS factors in an .... The hyper-parameter optimization results for all the E. grandis and E.dunnii models ...

  19. Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems

    Czech Academy of Sciences Publication Activity Database

    Morikuni, Keiichi; Hayami, K.

    2015-01-01

    Roč. 36, č. 1 (2015), s. 225-250 ISSN 0895-4798 Institutional support: RVO:67985807 Keywords : least squares problem * iterative methods * preconditioner * inner-outer iteration * GMRES method * stationary iterative method * rank-deficient problem Subject RIV: BA - General Mathematics Impact factor: 1.883, year: 2015

  20. Least-squares approximation of an improper correlation matrix by a proper one

    NARCIS (Netherlands)

    Knol, Dirk L.; ten Berge, Jos M.F.

    1989-01-01

    An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based upon a solution for Mosier's oblique Procrustes rotation problem offered by ten Berge and Nevels. A necessary and

  1. PRIM: An Efficient Preconditioning Iterative Reweighted Least Squares Method for Parallel Brain MRI Reconstruction.

    Science.gov (United States)

    Xu, Zheng; Wang, Sheng; Li, Yeqing; Zhu, Feiyun; Huang, Junzhou

    2018-02-08

    The most recent history of parallel Magnetic Resonance Imaging (pMRI) has in large part been devoted to finding ways to reduce acquisition time. While joint total variation (JTV) regularized model has been demonstrated as a powerful tool in increasing sampling speed for pMRI, however, the major bottleneck is the inefficiency of the optimization method. While all present state-of-the-art optimizations for the JTV model could only reach a sublinear convergence rate, in this paper, we squeeze the performance by proposing a linear-convergent optimization method for the JTV model. The proposed method is based on the Iterative Reweighted Least Squares algorithm. Due to the complexity of the tangled JTV objective, we design a novel preconditioner to further accelerate the proposed method. Extensive experiments demonstrate the superior performance of the proposed algorithm for pMRI regarding both accuracy and efficiency compared with state-of-the-art methods.

  2. Use of probabilistic weights to enhance linear regression myoelectric control.

    Science.gov (United States)

    Smith, Lauren H; Kuiken, Todd A; Hargrove, Levi J

    2015-12-01

    Clinically available prostheses for transradial amputees do not allow simultaneous myoelectric control of degrees of freedom (DOFs). Linear regression methods can provide simultaneous myoelectric control, but frequently also result in difficulty with isolating individual DOFs when desired. This study evaluated the potential of using probabilistic estimates of categories of gross prosthesis movement, which are commonly used in classification-based myoelectric control, to enhance linear regression myoelectric control. Gaussian models were fit to electromyogram (EMG) feature distributions for three movement classes at each DOF (no movement, or movement in either direction) and used to weight the output of linear regression models by the probability that the user intended the movement. Eight able-bodied and two transradial amputee subjects worked in a virtual Fitts' law task to evaluate differences in controllability between linear regression and probability-weighted regression for an intramuscular EMG-based three-DOF wrist and hand system. Real-time and offline analyses in able-bodied subjects demonstrated that probability weighting improved performance during single-DOF tasks (p linear regression control. Use of probability weights can improve the ability to isolate individual during linear regression myoelectric control, while maintaining the ability to simultaneously control multiple DOFs.

  3. Implementation of the Least-Squares Lattice with Order and Forgetting Factor Estimation for FPGA

    Czech Academy of Sciences Publication Activity Database

    Pohl, Zdeněk; Tichý, Milan; Kadlec, Jiří

    2008-01-01

    Roč. 2008, č. 2008 (2008), s. 1-11 ISSN 1687-6172 R&D Projects: GA MŠk(CZ) 1M0567 EU Projects: European Commission(XE) 027611 - AETHER Program:FP6 Institutional research plan: CEZ:AV0Z10750506 Keywords : DSP * Least-squares lattice * order estimation * exponential forgetting factor estimation * FPGA implementation * scheduling * dynamic reconfiguration * microblaze Subject RIV: IN - Informatics, Computer Science Impact factor: 1.055, year: 2008 http://library.utia.cas.cz/separaty/2008/ZS/pohl-tichy-kadlec-implementation%20of%20the%20least-squares%20lattice%20with%20order%20and%20forgetting%20factor%20estimation%20for%20fpga.pdf

  4. Linear regression crash prediction models : issues and proposed solutions.

    Science.gov (United States)

    2010-05-01

    The paper develops a linear regression model approach that can be applied to : crash data to predict vehicle crashes. The proposed approach involves novice data aggregation : to satisfy linear regression assumptions; namely error structure normality ...

  5. A Least Square-Based Self-Adaptive Localization Method for Wireless Sensor Networks

    Directory of Open Access Journals (Sweden)

    Baoguo Yu

    2016-01-01

    Full Text Available In the wireless sensor network (WSN localization methods based on Received Signal Strength Indicator (RSSI, it is usually required to determine the parameters of the radio signal propagation model before estimating the distance between the anchor node and an unknown node with reference to their communication RSSI value. And finally we use a localization algorithm to estimate the location of the unknown node. However, this localization method, though high in localization accuracy, has weaknesses such as complex working procedure and poor system versatility. Concerning these defects, a self-adaptive WSN localization method based on least square is proposed, which uses the least square criterion to estimate the parameters of radio signal propagation model, which positively reduces the computation amount in the estimation process. The experimental results show that the proposed self-adaptive localization method outputs a high processing efficiency while satisfying the high localization accuracy requirement. Conclusively, the proposed method is of definite practical value.

  6. Method for exploiting bias in factor analysis using constrained alternating least squares algorithms

    Science.gov (United States)

    Keenan, Michael R.

    2008-12-30

    Bias plays an important role in factor analysis and is often implicitly made use of, for example, to constrain solutions to factors that conform to physical reality. However, when components are collinear, a large range of solutions may exist that satisfy the basic constraints and fit the data equally well. In such cases, the introduction of mathematical bias through the application of constraints may select solutions that are less than optimal. The biased alternating least squares algorithm of the present invention can offset mathematical bias introduced by constraints in the standard alternating least squares analysis to achieve factor solutions that are most consistent with physical reality. In addition, these methods can be used to explicitly exploit bias to provide alternative views and provide additional insights into spectral data sets.

  7. Least-squares migration of multisource data with a deblurring filter

    KAUST Repository

    Dai, Wei; Wang, Xin; Schuster, Gerard T.

    2011-01-01

    Least-squares migration (LSM) has been shown to be able to produce high-quality migration images, but its computational cost is considered to be too high for practical imaging. We have developed a multisource least-squares migration algorithm (MLSM) to increase the computational efficiency by using the blended sources processing technique. To expedite convergence, a multisource deblurring filter is used as a preconditioner to reduce the data residual. This MLSM algorithm is applicable with Kirchhoff migration, wave-equation migration, or reverse time migration, and the gain in computational efficiency depends on the choice of migration method. Numerical results with Kirchhoff LSM on the 2D SEG/EAGE salt model show that an accurate image is obtained by migrating a supergather of 320 phase-encoded shots. When the encoding functions are the same for every iteration, the input/output cost of MLSM is reduced by 320 times. Empirical results show that the crosstalk noise introduced by blended sources is more effectively reduced when the encoding functions are changed at every iteration. The analysis of signal-to-noise ratio (S/N) suggests that not too many iterations are needed to enhance the S/N to an acceptable level. Therefore, when implemented with wave-equation migration or reverse time migration methods, the MLSM algorithm can be more efficient than the conventional migration method. © 2011 Society of Exploration Geophysicists.

  8. Least-squares migration of multisource data with a deblurring filter

    KAUST Repository

    Dai, Wei

    2011-09-01

    Least-squares migration (LSM) has been shown to be able to produce high-quality migration images, but its computational cost is considered to be too high for practical imaging. We have developed a multisource least-squares migration algorithm (MLSM) to increase the computational efficiency by using the blended sources processing technique. To expedite convergence, a multisource deblurring filter is used as a preconditioner to reduce the data residual. This MLSM algorithm is applicable with Kirchhoff migration, wave-equation migration, or reverse time migration, and the gain in computational efficiency depends on the choice of migration method. Numerical results with Kirchhoff LSM on the 2D SEG/EAGE salt model show that an accurate image is obtained by migrating a supergather of 320 phase-encoded shots. When the encoding functions are the same for every iteration, the input/output cost of MLSM is reduced by 320 times. Empirical results show that the crosstalk noise introduced by blended sources is more effectively reduced when the encoding functions are changed at every iteration. The analysis of signal-to-noise ratio (S/N) suggests that not too many iterations are needed to enhance the S/N to an acceptable level. Therefore, when implemented with wave-equation migration or reverse time migration methods, the MLSM algorithm can be more efficient than the conventional migration method. © 2011 Society of Exploration Geophysicists.

  9. Applying ISO 11929:2010 Standard to detection limit calculation in least-squares based multi-nuclide gamma-ray spectrum evaluation

    Energy Technology Data Exchange (ETDEWEB)

    Kanisch, G., E-mail: guenter.kanisch@hanse.net

    2017-05-21

    The concepts of ISO 11929 (2010) are applied to evaluation of radionuclide activities from more complex multi-nuclide gamma-ray spectra. From net peak areas estimated by peak fitting, activities and their standard uncertainties are calculated by weighted linear least-squares method with an additional step, where uncertainties of the design matrix elements are taken into account. A numerical treatment of the standard's uncertainty function, based on ISO 11929 Annex C.5, leads to a procedure for deriving decision threshold and detection limit values. The methods shown allow resolving interferences between radionuclide activities also in case of calculating detection limits where they can improve the latter by including more than one gamma line per radionuclide. The co'mmon single nuclide weighted mean is extended to an interference-corrected (generalized) weighted mean, which, combined with the least-squares method, allows faster detection limit calculations. In addition, a new grouped uncertainty budget was inferred, which for each radionuclide gives uncertainty budgets from seven main variables, such as net count rates, peak efficiencies, gamma emission intensities and others; grouping refers to summation over lists of peaks per radionuclide.

  10. Variable forgetting factor mechanisms for diffusion recursive least squares algorithm in sensor networks

    Science.gov (United States)

    Zhang, Ling; Cai, Yunlong; Li, Chunguang; de Lamare, Rodrigo C.

    2017-12-01

    In this work, we present low-complexity variable forgetting factor (VFF) techniques for diffusion recursive least squares (DRLS) algorithms. Particularly, we propose low-complexity VFF-DRLS algorithms for distributed parameter and spectrum estimation in sensor networks. For the proposed algorithms, they can adjust the forgetting factor automatically according to the posteriori error signal. We develop detailed analyses in terms of mean and mean square performance for the proposed algorithms and derive mathematical expressions for the mean square deviation (MSD) and the excess mean square error (EMSE). The simulation results show that the proposed low-complexity VFF-DRLS algorithms achieve superior performance to the existing DRLS algorithm with fixed forgetting factor when applied to scenarios of distributed parameter and spectrum estimation. Besides, the simulation results also demonstrate a good match for our proposed analytical expressions.

  11. Mitigation of defocusing by statics and near-surface velocity errors by interferometric least-squares migration

    KAUST Repository

    Sinha, Mrinal

    2015-08-19

    We propose an interferometric least-squares migration method that can significantly reduce migration artifacts due to statics and errors in the near-surface velocity model. We first choose a reference reflector whose topography is well known from the, e.g., well logs. Reflections from this reference layer are correlated with the traces associated with reflections from deeper interfaces to get crosscorrelograms. These crosscorrelograms are then migrated using interferometric least-squares migration (ILSM). In this way statics and velocity errors at the near surface are largely eliminated for the examples in our paper.

  12. Linear regression and the normality assumption.

    Science.gov (United States)

    Schmidt, Amand F; Finan, Chris

    2017-12-16

    Researchers often perform arbitrary outcome transformations to fulfill the normality assumption of a linear regression model. This commentary explains and illustrates that in large data settings, such transformations are often unnecessary, and worse may bias model estimates. Linear regression assumptions are illustrated using simulated data and an empirical example on the relation between time since type 2 diabetes diagnosis and glycated hemoglobin levels. Simulation results were evaluated on coverage; i.e., the number of times the 95% confidence interval included the true slope coefficient. Although outcome transformations bias point estimates, violations of the normality assumption in linear regression analyses do not. The normality assumption is necessary to unbiasedly estimate standard errors, and hence confidence intervals and P-values. However, in large sample sizes (e.g., where the number of observations per variable is >10) violations of this normality assumption often do not noticeably impact results. Contrary to this, assumptions on, the parametric model, absence of extreme observations, homoscedasticity, and independency of the errors, remain influential even in large sample size settings. Given that modern healthcare research typically includes thousands of subjects focusing on the normality assumption is often unnecessary, does not guarantee valid results, and worse may bias estimates due to the practice of outcome transformations. Copyright © 2017 Elsevier Inc. All rights reserved.

  13. 'AJUSTAR' a interactive processor for to Fit, by means of least squares, one variable polinomials (arbitrary degree) at experimental points

    International Nuclear Information System (INIS)

    Sanchez Miro, J.J.; Pena, J.

    1991-01-01

    In this repport is offered, to scientist and technical people, a numeric tool consisting in a FORTRAN program, of interactive use, with destination to make lineal 'least squares', fittings on any set of empirical observations. The method based in the orthogonal functions (for discrete case), instead of direct solving the equations system, is used. The procedure includes also the optionally facilities of: variable change, direct interpolation, correlation non linear factor, 'weights' of the points, confidence intervals (Scheffe, Miller, Student), and plotting results. (Author). 10 refs

  14. Least-Squares Approximation of an Improper Correlation Matrix by a Proper One.

    Science.gov (United States)

    Knol, Dirk L.; ten Berge, Jos M. F.

    1989-01-01

    An algorithm, based on a solution for C. I. Mosier's oblique Procrustes rotation problem, is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. Results are of interest for missing value and tetrachoric correlation, indefinite matrix correlation, and constrained…

  15. Application of the tuning algorithm with the least squares approximation to the suboptimal control algorithm for integrating objects

    Science.gov (United States)

    Kuzishchin, V. F.; Merzlikina, E. I.; Van Va, Hoang

    2017-11-01

    The problem of PID and PI-algorithms tuning by means of the approximation by the least square method of the frequency response of a linear algorithm to the sub-optimal algorithm is considered. The advantage of the method is that the parameter values are obtained through one cycle of calculation. Recommendations how to choose the parameters of the least square method taking into consideration the plant dynamics are given. The parameters mentioned are the time constant of the filter, the approximation frequency range and the correction coefficient for the time delay parameter. The problem is considered for integrating plants for some practical cases (the level control system in a boiler drum). The transfer function of the suboptimal algorithm is determined relating to the disturbance that acts in the point of the control impact input, it is typical for thermal plants. In the recommendations it is taken into consideration that the overregulation for the transient process when the setpoint is changed is also limited. In order to compare the results the systems under consideration are also calculated by the classical method with the limited frequency oscillation index. The results given in the paper can be used by specialists dealing with tuning systems with the integrating plants.

  16. Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator

    DEFF Research Database (Denmark)

    Johansen, Søren; Nielsen, Bent

    2013-01-01

    In regression we can delete outliers based upon a preliminary estimator and reestimate the parameters by least squares based upon the retained observations. We study the properties of an iteratively defined sequence of estimators based on this idea. We relate the sequence to the Huber-skip estima......In regression we can delete outliers based upon a preliminary estimator and reestimate the parameters by least squares based upon the retained observations. We study the properties of an iteratively defined sequence of estimators based on this idea. We relate the sequence to the Huber...... that the normalized estimation errors are tight and are close to a linear function of the kernel, thus providing a stochastic expansion of the estimators, which is the same as for the Huber-skip. This implies that the iterated estimator is a close approximation of the Huber-skip...

  17. Return-Volatility Relationship: Insights from Linear and Non-Linear Quantile Regression

    NARCIS (Netherlands)

    D.E. Allen (David); A.K. Singh (Abhay); R.J. Powell (Robert); M.J. McAleer (Michael); J. Taylor (James); L. Thomas (Lyn)

    2013-01-01

    textabstractThe purpose of this paper is to examine the asymmetric relationship between price and implied volatility and the associated extreme quantile dependence using linear and non linear quantile regression approach. Our goal in this paper is to demonstrate that the relationship between the

  18. Moving Least Squares Method for a One-Dimensional Parabolic Inverse Problem

    Directory of Open Access Journals (Sweden)

    Baiyu Wang

    2014-01-01

    Full Text Available This paper investigates the numerical solution of a class of one-dimensional inverse parabolic problems using the moving least squares approximation; the inverse problem is the determination of an unknown source term depending on time. The collocation method is used for solving the equation; some numerical experiments are presented and discussed to illustrate the stability and high efficiency of the method.

  19. Applying Least Absolute Shrinkage Selection Operator and Akaike Information Criterion Analysis to Find the Best Multiple Linear Regression Models between Climate Indices and Components of Cow's Milk.

    Science.gov (United States)

    Marami Milani, Mohammad Reza; Hense, Andreas; Rahmani, Elham; Ploeger, Angelika

    2016-07-23

    This study focuses on multiple linear regression models relating six climate indices (temperature humidity THI, environmental stress ESI, equivalent temperature index ETI, heat load HLI, modified HLI (HLI new ), and respiratory rate predictor RRP) with three main components of cow's milk (yield, fat, and protein) for cows in Iran. The least absolute shrinkage selection operator (LASSO) and the Akaike information criterion (AIC) techniques are applied to select the best model for milk predictands with the smallest number of climate predictors. Uncertainty estimation is employed by applying bootstrapping through resampling. Cross validation is used to avoid over-fitting. Climatic parameters are calculated from the NASA-MERRA global atmospheric reanalysis. Milk data for the months from April to September, 2002 to 2010 are used. The best linear regression models are found in spring between milk yield as the predictand and THI, ESI, ETI, HLI, and RRP as predictors with p -value < 0.001 and R ² (0.50, 0.49) respectively. In summer, milk yield with independent variables of THI, ETI, and ESI show the highest relation ( p -value < 0.001) with R ² (0.69). For fat and protein the results are only marginal. This method is suggested for the impact studies of climate variability/change on agriculture and food science fields when short-time series or data with large uncertainty are available.

  20. Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

    KAUST Repository

    Chkifa, Abdellah

    2015-04-08

    Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that in the univariate case, the least-squares method is quasi-optimal in expectation in [A. Cohen, M A. Davenport and D. Leviatan. Found. Comput. Math. 13 (2013) 819–834] and in probability in [G. Migliorati, F. Nobile, E. von Schwerin, R. Tempone, Found. Comput. Math. 14 (2014) 419–456], under suitable conditions that relate the number of samples with respect to the dimension of the polynomial space. Here “quasi-optimal” means that the accuracy of the least-squares approximation is comparable with that of the best approximation in the given polynomial space. In this paper, we discuss the quasi-optimality of the polynomial least-squares method in arbitrary dimension. Our analysis applies to any arbitrary multivariate polynomial space (including tensor product, total degree or hyperbolic crosses), under the minimal requirement that its associated index set is downward closed. The optimality criterion only involves the relation between the number of samples and the dimension of the polynomial space, independently of the anisotropic shape and of the number of variables. We extend our results to the approximation of Hilbert space-valued functions in order to apply them to the approximation of parametric and stochastic elliptic PDEs. As a particular case, we discuss “inclusion type” elliptic PDE models, and derive an exponential convergence estimate for the least-squares method. Numerical results confirm our estimate, yet pointing out a gap between the condition necessary to achieve optimality in the theory, and the condition that in practice yields the optimal convergence rate.

  1. Incoherent dictionary learning for reducing crosstalk noise in least-squares reverse time migration

    Science.gov (United States)

    Wu, Juan; Bai, Min

    2018-05-01

    We propose to apply a novel incoherent dictionary learning (IDL) algorithm for regularizing the least-squares inversion in seismic imaging. The IDL is proposed to overcome the drawback of traditional dictionary learning algorithm in losing partial texture information. Firstly, the noisy image is divided into overlapped image patches, and some random patches are extracted for dictionary learning. Then, we apply the IDL technology to minimize the coherency between atoms during dictionary learning. Finally, the sparse representation problem is solved by a sparse coding algorithm, and image is restored by those sparse coefficients. By reducing the correlation among atoms, it is possible to preserve most of the small-scale features in the image while removing much of the long-wavelength noise. The application of the IDL method to regularization of seismic images from least-squares reverse time migration shows successful performance.

  2. Small-kernel, constrained least-squares restoration of sampled image data

    Science.gov (United States)

    Hazra, Rajeeb; Park, Stephen K.

    1992-01-01

    Following the work of Park (1989), who extended a derivation of the Wiener filter based on the incomplete discrete/discrete model to a more comprehensive end-to-end continuous/discrete/continuous model, it is shown that a derivation of the constrained least-squares (CLS) filter based on the discrete/discrete model can also be extended to this more comprehensive continuous/discrete/continuous model. This results in an improved CLS restoration filter, which can be efficiently implemented as a small-kernel convolution in the spatial domain.

  3. Classification and quantitation of milk powder by near-infrared spectroscopy and mutual information-based variable selection and partial least squares

    Science.gov (United States)

    Chen, Hui; Tan, Chao; Lin, Zan; Wu, Tong

    2018-01-01

    Milk is among the most popular nutrient source worldwide, which is of great interest due to its beneficial medicinal properties. The feasibility of the classification of milk powder samples with respect to their brands and the determination of protein concentration is investigated by NIR spectroscopy along with chemometrics. Two datasets were prepared for experiment. One contains 179 samples of four brands for classification and the other contains 30 samples for quantitative analysis. Principal component analysis (PCA) was used for exploratory analysis. Based on an effective model-independent variable selection method, i.e., minimal-redundancy maximal-relevance (MRMR), only 18 variables were selected to construct a partial least-square discriminant analysis (PLS-DA) model. On the test set, the PLS-DA model based on the selected variable set was compared with the full-spectrum PLS-DA model, both of which achieved 100% accuracy. In quantitative analysis, the partial least-square regression (PLSR) model constructed by the selected subset of 260 variables outperforms significantly the full-spectrum model. It seems that the combination of NIR spectroscopy, MRMR and PLS-DA or PLSR is a powerful tool for classifying different brands of milk and determining the protein content.

  4. Error analysis of some Galerkin - least squares methods for the elasticity equations

    International Nuclear Information System (INIS)

    Franca, L.P.; Stenberg, R.

    1989-05-01

    We consider the recent technique of stabilizing mixed finite element methods by augmenting the Galerkin formulation with least squares terms calculated separately on each element. The error analysis is performed in a unified manner yielding improved results for some methods introduced earlier. In addition, a new formulation is introduced and analyzed [pt

  5. Robust Regression and its Application in Financial Data Analysis

    OpenAIRE

    Mansoor Momeni; Mahmoud Dehghan Nayeri; Ali Faal Ghayoumi; Hoda Ghorbani

    2010-01-01

    This research is aimed to describe the application of robust regression and its advantages over the least square regression method in analyzing financial data. To do this, relationship between earning per share, book value of equity per share and share price as price model and earning per share, annual change of earning per share and return of stock as return model is discussed using both robust and least square regressions, and finally the outcomes are compared. Comparing the results from th...

  6. Robust Bayesian linear regression with application to an analysis of the CODATA values for the Planck constant

    Science.gov (United States)

    Wübbeler, Gerd; Bodnar, Olha; Elster, Clemens

    2018-02-01

    Weighted least-squares estimation is commonly applied in metrology to fit models to measurements that are accompanied with quoted uncertainties. The weights are chosen in dependence on the quoted uncertainties. However, when data and model are inconsistent in view of the quoted uncertainties, this procedure does not yield adequate results. When it can be assumed that all uncertainties ought to be rescaled by a common factor, weighted least-squares estimation may still be used, provided that a simple correction of the uncertainty obtained for the estimated model is applied. We show that these uncertainties and credible intervals are robust, as they do not rely on the assumption of a Gaussian distribution of the data. Hence, common software for weighted least-squares estimation may still safely be employed in such a case, followed by a simple modification of the uncertainties obtained by that software. We also provide means of checking the assumptions of such an approach. The Bayesian regression procedure is applied to analyze the CODATA values for the Planck constant published over the past decades in terms of three different models: a constant model, a straight line model and a spline model. Our results indicate that the CODATA values may not have yet stabilized.

  7. Determination of regression laws: Linear and nonlinear

    International Nuclear Information System (INIS)

    Onishchenko, A.M.

    1994-01-01

    A detailed mathematical determination of regression laws is presented in the article. Particular emphasis is place on determining the laws of X j on X l to account for source nuclei decay and detector errors in nuclear physics instrumentation. Both linear and nonlinear relations are presented. Linearization of 19 functions is tabulated, including graph, relation, variable substitution, obtained linear function, and remarks. 6 refs., 1 tab

  8. A gentle introduction to quantile regression for ecologists

    Science.gov (United States)

    Cade, B.S.; Noon, B.R.

    2003-01-01

    Quantile regression is a way to estimate the conditional quantiles of a response variable distribution in the linear model that provides a more complete view of possible causal relationships between variables in ecological processes. Typically, all the factors that affect ecological processes are not measured and included in the statistical models used to investigate relationships between variables associated with those processes. As a consequence, there may be a weak or no predictive relationship between the mean of the response variable (y) distribution and the measured predictive factors (X). Yet there may be stronger, useful predictive relationships with other parts of the response variable distribution. This primer relates quantile regression estimates to prediction intervals in parametric error distribution regression models (eg least squares), and discusses the ordering characteristics, interval nature, sampling variation, weighting, and interpretation of the estimates for homogeneous and heterogeneous regression models.

  9. The detection of influential subsets in linear regression using an influence matrix

    OpenAIRE

    Peña, Daniel; Yohai, Víctor J.

    1991-01-01

    This paper presents a new method to identify influential subsets in linear regression problems. The procedure uses the eigenstructure of an influence matrix which is defined as the matrix of uncentered covariance of the effect on the whole data set of deleting each observation, normalized to include the univariate Cook's statistics in the diagonal. It is shown that points in an influential subset will appear with large weight in at least one of the eigenvector linked to the largest eigenvalue...

  10. Introductory Linear Regression Programs in Undergraduate Chemistry.

    Science.gov (United States)

    Gale, Robert J.

    1982-01-01

    Presented are simple programs in BASIC and FORTRAN to apply the method of least squares. They calculate gradients and intercepts and express errors as standard deviations. An introduction of undergraduate students to such programs in a chemistry class is reviewed, and issues instructors should be aware of are noted. (MP)

  11. Optimization of sequential decisions by least squares Monte Carlo method

    DEFF Research Database (Denmark)

    Nishijima, Kazuyoshi; Anders, Annett

    change adaptation measures, and evacuation of people and assets in the face of an emerging natural hazard event. Focusing on the last example, an efficient solution scheme is proposed by Anders and Nishijima (2011). The proposed solution scheme takes basis in the least squares Monte Carlo method, which...... is proposed by Longstaff and Schwartz (2001) for pricing of American options. The present paper formulates the decision problem in a more general manner and explains how the solution scheme proposed by Anders and Nishijima (2011) is implemented for the optimization of the formulated decision problem...

  12. Least-squares resolution of gamma-ray spectra in environmental samples

    International Nuclear Information System (INIS)

    Kanipe, L.G.; Seale, S.K.; Liggett, W.S.

    1977-08-01

    The use of ALPHA-M, a least squares computer program for analyzing NaI (Tl) gamma spectra of environmental samples, is evaluated. Included is a comprehensive set of program instructions, listings, and flowcharts. Two other programs, GEN4 and SIMSPEC, are also described. GEN4 is used to create standard libraries for ALPHA-M, and SIMSPEC is used to simulate spectra for ALPHA-M analysis. Tests to evaluate the standard libraries selected for use in analyzing environmental samples are provided. An evaluation of the results of sample analyses is discussed

  13. Evaluation of Linear Regression Simultaneous Myoelectric Control Using Intramuscular EMG.

    Science.gov (United States)

    Smith, Lauren H; Kuiken, Todd A; Hargrove, Levi J

    2016-04-01

    The objective of this study was to evaluate the ability of linear regression models to decode patterns of muscle coactivation from intramuscular electromyogram (EMG) and provide simultaneous myoelectric control of a virtual 3-DOF wrist/hand system. Performance was compared to the simultaneous control of conventional myoelectric prosthesis methods using intramuscular EMG (parallel dual-site control)-an approach that requires users to independently modulate individual muscles in the residual limb, which can be challenging for amputees. Linear regression control was evaluated in eight able-bodied subjects during a virtual Fitts' law task and was compared to performance of eight subjects using parallel dual-site control. An offline analysis also evaluated how different types of training data affected prediction accuracy of linear regression control. The two control systems demonstrated similar overall performance; however, the linear regression method demonstrated improved performance for targets requiring use of all three DOFs, whereas parallel dual-site control demonstrated improved performance for targets that required use of only one DOF. Subjects using linear regression control could more easily activate multiple DOFs simultaneously, but often experienced unintended movements when trying to isolate individual DOFs. Offline analyses also suggested that the method used to train linear regression systems may influence controllability. Linear regression myoelectric control using intramuscular EMG provided an alternative to parallel dual-site control for 3-DOF simultaneous control at the wrist and hand. The two methods demonstrated different strengths in controllability, highlighting the tradeoff between providing simultaneous control and the ability to isolate individual DOFs when desired.

  14. Canonical Least-Squares Monte Carlo Valuation of American Options: Convergence and Empirical Pricing Analysis

    Directory of Open Access Journals (Sweden)

    Xisheng Yu

    2014-01-01

    Full Text Available The paper by Liu (2010 introduces a method termed the canonical least-squares Monte Carlo (CLM which combines a martingale-constrained entropy model and a least-squares Monte Carlo algorithm to price American options. In this paper, we first provide the convergence results of CLM and numerically examine the convergence properties. Then, the comparative analysis is empirically conducted using a large sample of the S&P 100 Index (OEX puts and IBM puts. The results on the convergence show that choosing the shifted Legendre polynomials with four regressors is more appropriate considering the pricing accuracy and the computational cost. With this choice, CLM method is empirically demonstrated to be superior to the benchmark methods of binominal tree and finite difference with historical volatilities.

  15. Real time flaw detection and characterization in tube through partial least squares and SVR: Application to eddy current testing

    Science.gov (United States)

    Ahmed, Shamim; Miorelli, Roberto; Calmon, Pierre; Anselmi, Nicola; Salucci, Marco

    2018-04-01

    This paper describes Learning-By-Examples (LBE) technique for performing quasi real time flaw localization and characterization within a conductive tube based on Eddy Current Testing (ECT) signals. Within the framework of LBE, the combination of full-factorial (i.e., GRID) sampling and Partial Least Squares (PLS) feature extraction (i.e., GRID-PLS) techniques are applied for generating a suitable training set in offine phase. Support Vector Regression (SVR) is utilized for model development and inversion during offine and online phases, respectively. The performance and robustness of the proposed GIRD-PLS/SVR strategy on noisy test set is evaluated and compared with standard GRID/SVR approach.

  16. Weighted least-square approach for simultaneous measurement of multiple reflective surfaces

    Science.gov (United States)

    Tang, Shouhong; Bills, Richard E.; Freischlad, Klaus

    2007-09-01

    Phase shifting interferometry (PSI) is a highly accurate method for measuring the nanometer-scale relative surface height of a semi-reflective test surface. PSI is effectively used in conjunction with Fizeau interferometers for optical testing, hard disk inspection, and semiconductor wafer flatness. However, commonly-used PSI algorithms are unable to produce an accurate phase measurement if more than one reflective surface is present in the Fizeau interferometer test cavity. Examples of test parts that fall into this category include lithography mask blanks and their protective pellicles, and plane parallel optical beam splitters. The plane parallel surfaces of these parts generate multiple interferograms that are superimposed in the recording plane of the Fizeau interferometer. When using wavelength shifting in PSI the phase shifting speed of each interferogram is proportional to the optical path difference (OPD) between the two reflective surfaces. The proposed method is able to differentiate each underlying interferogram from each other in an optimal manner. In this paper, we present a method for simultaneously measuring the multiple test surfaces of all underlying interferograms from these superimposed interferograms through the use of a weighted least-square fitting technique. The theoretical analysis of weighted least-square technique and the measurement results will be described in this paper.

  17. Influence of the least-squares phase on optical vortices in strongly scintillated beams

    CSIR Research Space (South Africa)

    Chen, M

    2009-06-01

    Full Text Available , the average total number of vortices is reduced further. However, the reduction becomes smaller for each succes- sive step. This indicates that the ability of getting rid of optical vortices by removing the least-squares phase becomes progressively less...

  18. Expectile smoothing: new perspectives on asymmetric least squares. An application to life expectancy

    NARCIS (Netherlands)

    Schnabel, S.K.

    2011-01-01

    While initially motivated from a demographic application, this thesis develops methodology for expectile estimation. To this end first the basic model for expectile curves using least asymmetrically weighted squares (LAWS) was introduced as well as methods for smoothing in this context. The simple

  19. Doppler-shift estimation of flat underwater channel using data-aided least-square approach

    Directory of Open Access Journals (Sweden)

    Weiqiang Pan

    2015-03-01

    Full Text Available In this paper we proposed a dada-aided Doppler estimation method for underwater acoustic communication. The training sequence is non-dedicate, hence it can be designed for Doppler estimation as well as channel equalization. We assume the channel has been equalized and consider only flat-fading channel. First, based on the training symbols the theoretical received sequence is composed. Next the least square principle is applied to build the objective function, which minimizes the error between the composed and the actual received signal. Then an iterative approach is applied to solve the least square problem. The proposed approach involves an outer loop and inner loop, which resolve the channel gain and Doppler coefficient, respectively. The theoretical performance bound, i.e. the Cramer-Rao Lower Bound (CRLB of estimation is also derived. Computer simulations results show that the proposed algorithm achieves the CRLB in medium to high SNR cases.

  20. Doppler-shift estimation of flat underwater channel using data-aided least-square approach

    Science.gov (United States)

    Pan, Weiqiang; Liu, Ping; Chen, Fangjiong; Ji, Fei; Feng, Jing

    2015-06-01

    In this paper we proposed a dada-aided Doppler estimation method for underwater acoustic communication. The training sequence is non-dedicate, hence it can be designed for Doppler estimation as well as channel equalization. We assume the channel has been equalized and consider only flat-fading channel. First, based on the training symbols the theoretical received sequence is composed. Next the least square principle is applied to build the objective function, which minimizes the error between the composed and the actual received signal. Then an iterative approach is applied to solve the least square problem. The proposed approach involves an outer loop and inner loop, which resolve the channel gain and Doppler coefficient, respectively. The theoretical performance bound, i.e. the Cramer-Rao Lower Bound (CRLB) of estimation is also derived. Computer simulations results show that the proposed algorithm achieves the CRLB in medium to high SNR cases.