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,…

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.

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...

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

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…

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

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...

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...

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

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

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.

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.

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.

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…

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.

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

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,…

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.

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.

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

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...

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.

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.

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.

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.

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

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....

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

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.

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.

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.

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.

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.

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.

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

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.

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.

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...

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.

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.

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.

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

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.

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.

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

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.

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

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.

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

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....

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.

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.

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

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

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

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...

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

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.

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.

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

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

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.

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.

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

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.

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

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.

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.

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

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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.

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

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

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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.

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.

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

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.

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)

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...

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

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

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.

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.

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%.

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)

A Least Square-Based Self-Adaptive Localization Method for Wireless Sensor Networks

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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.

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

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.

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.

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.

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

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.

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...

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

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....

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

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

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...

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.

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.

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%

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)

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

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.

And still, a new beginning: the Galerkin least-squares gradient method

International Nuclear Information System (INIS)

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

1988-08-01

A finite element method is proposed to solve a scalar singular diffusion problem. The method is constructed by adding to the standard Galerkin a mesh-dependent term obtained by taking the gradient of the Euler-lagrange equation and multiplying it by its least-squares. For the one-dimensional homogeneous problem the method is designed to develop nodal exact solution. An error estimate shows that the method converges optimaly for any value of the singular parameter. Numerical results demonstrate the good stability and accuracy properties of the method. (author) [pt

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...

A weak Galerkin least-squares finite element method for div-curl systems

Science.gov (United States)

Li, Jichun; Ye, Xiu; Zhang, Shangyou

2018-06-01

In this paper, we introduce a weak Galerkin least-squares method for solving div-curl problem. This finite element method leads to a symmetric positive definite system and has the flexibility to work with general meshes such as hybrid mesh, polytopal mesh and mesh with hanging nodes. Error estimates of the finite element solution are derived. The numerical examples demonstrate the robustness and flexibility of the proposed method.

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.

Joint 2D-DOA and Frequency Estimation for L-Shaped Array Using Iterative Least Squares Method

Directory of Open Access Journals (Sweden)

Ling-yun Xu

2012-01-01

Full Text Available We introduce an iterative least squares method (ILS for estimating the 2D-DOA and frequency based on L-shaped array. The ILS iteratively finds direction matrix and delay matrix, then 2D-DOA and frequency can be obtained by the least squares method. Without spectral peak searching and pairing, this algorithm works well and pairs the parameters automatically. Moreover, our algorithm has better performance than conventional ESPRIT algorithm and propagator method. The useful behavior of the proposed algorithm is verified by simulations.

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.

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

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

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.

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

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...

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

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.

A negative-norm least-squares method for time-harmonic Maxwell equations

KAUST Repository

Copeland, Dylan M.

2012-04-01

This paper presents and analyzes a negative-norm least-squares finite element discretization method for the dimension-reduced time-harmonic Maxwell equations in the case of axial symmetry. The reduced equations are expressed in cylindrical coordinates, and the analysis consequently involves weighted Sobolev spaces based on the degenerate radial weighting. The main theoretical results established in this work include existence and uniqueness of the continuous and discrete formulations and error estimates for simple finite element functions. Numerical experiments confirm the error estimates and efficiency of the method for piecewise constant coefficients. © 2011 Elsevier Inc.

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

Regression modeling methods, theory, and computation with SAS

CERN Document Server

Panik, Michael

2009-01-01

Regression Modeling: Methods, Theory, and Computation with SAS provides an introduction to a diverse assortment of regression techniques using SAS to solve a wide variety of regression problems. The author fully documents the SAS programs and thoroughly explains the output produced by the programs.The text presents the popular ordinary least squares (OLS) approach before introducing many alternative regression methods. It covers nonparametric regression, logistic regression (including Poisson regression), Bayesian regression, robust regression, fuzzy regression, random coefficients regression,

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.

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.

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

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.

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.

Flow Applications of the Least Squares Finite Element Method

Science.gov (United States)

Jiang, Bo-Nan

1998-01-01

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

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.

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.

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.

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.

Ridge regression estimator: combining unbiased and ordinary ridge regression methods of estimation

Directory of Open Access Journals (Sweden)

Sharad Damodar Gore

2009-10-01

Full Text Available Statistical literature has several methods for coping with multicollinearity. This paper introduces a new shrinkage estimator, called modified unbiased ridge (MUR. This estimator is obtained from unbiased ridge regression (URR in the same way that ordinary ridge regression (ORR is obtained from ordinary least squares (OLS. Properties of MUR are derived. Results on its matrix mean squared error (MMSE are obtained. MUR is compared with ORR and URR in terms of MMSE. These results are illustrated with an example based on data generated by Hoerl and Kennard (1975.

Analysis of neutron and x-ray reflectivity data by constrained least-squares methods

DEFF Research Database (Denmark)

Pedersen, J.S.; Hamley, I.W.

1994-01-01

. The coefficients in the series are determined by constrained nonlinear least-squares methods, in which the smoothest solution that agrees with the data is chosen. In the second approach the profile is expressed as a series of sine and cosine terms. A smoothness constraint is used which reduces the coefficients...

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.

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

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

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.

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.

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.

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.

New model for prediction binary mixture of antihistamine decongestant using artificial neural networks and least squares support vector machine by spectrophotometry method

Science.gov (United States)

Mofavvaz, Shirin; Sohrabi, Mahmoud Reza; Nezamzadeh-Ejhieh, Alireza

2017-07-01

In the present study, artificial neural networks (ANNs) and least squares support vector machines (LS-SVM) as intelligent methods based on absorption spectra in the range of 230-300 nm have been used for determination of antihistamine decongestant contents. In the first step, one type of network (feed-forward back-propagation) from the artificial neural network with two different training algorithms, Levenberg-Marquardt (LM) and gradient descent with momentum and adaptive learning rate back-propagation (GDX) algorithm, were employed and their performance was evaluated. The performance of the LM algorithm was better than the GDX algorithm. In the second one, the radial basis network was utilized and results compared with the previous network. In the last one, the other intelligent method named least squares support vector machine was proposed to construct the antihistamine decongestant prediction model and the results were compared with two of the aforementioned networks. The values of the statistical parameters mean square error (MSE), Regression coefficient (R2), correlation coefficient (r) and also mean recovery (%), relative standard deviation (RSD) used for selecting the best model between these methods. Moreover, the proposed methods were compared to the high- performance liquid chromatography (HPLC) as a reference method. One way analysis of variance (ANOVA) test at the 95% confidence level applied to the comparison results of suggested and reference methods that there were no significant differences between them.

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.

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.

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.

A Bayesian least-squares support vector machine method for predicting the remaining useful life of a microwave component

Directory of Open Access Journals (Sweden)

Fuqiang Sun

2017-01-01

Full Text Available Rapid and accurate lifetime prediction of critical components in a system is important to maintaining the system’s reliable operation. To this end, many lifetime prediction methods have been developed to handle various failure-related data collected in different situations. Among these methods, machine learning and Bayesian updating are the most popular ones. In this article, a Bayesian least-squares support vector machine method that combines least-squares support vector machine with Bayesian inference is developed for predicting the remaining useful life of a microwave component. A degradation model describing the change in the component’s power gain over time is developed, and the point and interval remaining useful life estimates are obtained considering a predefined failure threshold. In our case study, the radial basis function neural network approach is also implemented for comparison purposes. The results indicate that the Bayesian least-squares support vector machine method is more precise and stable in predicting the remaining useful life of this type of components.

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.

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.

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...

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.

Gravity Search Algorithm hybridized Recursive Least Square method for power system harmonic estimation

Directory of Open Access Journals (Sweden)

Santosh Kumar Singh

2017-06-01

Full Text Available This paper presents a new hybrid method based on Gravity Search Algorithm (GSA and Recursive Least Square (RLS, known as GSA-RLS, to solve the harmonic estimation problems in the case of time varying power signals in presence of different noises. GSA is based on the Newton’s law of gravity and mass interactions. In the proposed method, the searcher agents are a collection of masses that interact with each other using Newton’s laws of gravity and motion. The basic GSA algorithm strategy is combined with RLS algorithm sequentially in an adaptive way to update the unknown parameters (weights of the harmonic signal. Simulation and practical validation are made with the experimentation of the proposed algorithm with real time data obtained from a heavy paper industry. A comparative performance of the proposed algorithm is evaluated with other recently reported algorithms like, Differential Evolution (DE, Particle Swarm Optimization (PSO, Bacteria Foraging Optimization (BFO, Fuzzy-BFO (F-BFO hybridized with Least Square (LS and BFO hybridized with RLS algorithm, which reveals that the proposed GSA-RLS algorithm is the best in terms of accuracy, convergence and computational time.

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...

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

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

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

A least squares principle unifying finite element, finite difference and nodal methods for diffusion theory

International Nuclear Information System (INIS)

Ackroyd, R.T.

1987-01-01

A least squares principle is described which uses a penalty function treatment of boundary and interface conditions. Appropriate choices of the trial functions and vectors employed in a dual representation of an approximate solution established complementary principles for the diffusion equation. A geometrical interpretation of the principles provides weighted residual methods for diffusion theory, thus establishing a unification of least squares, variational and weighted residual methods. The complementary principles are used with either a trial function for the flux or a trial vector for the current to establish for regular meshes a connection between finite element, finite difference and nodal methods, which can be exact if the mesh pitches are chosen appropriately. Whereas the coefficients in the usual nodal equations have to be determined iteratively, those derived via the complementary principles are given explicitly in terms of the data. For the further development of the connection between finite element, finite difference and nodal methods, some hybrid variational methods are described which employ both a trial function and a trial vector. (author)

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.

Cognitive assessment in mathematics with the least squares distance method.

Science.gov (United States)

Ma, Lin; Çetin, Emre; Green, Kathy E

2012-01-01

This study investigated the validation of comprehensive cognitive attributes of an eighth-grade mathematics test using the least squares distance method and compared performance on attributes by gender and region. A sample of 5,000 students was randomly selected from the data of the 2005 Turkish national mathematics assessment of eighth-grade students. Twenty-five math items were assessed for presence or absence of 20 cognitive attributes (content, cognitive processes, and skill). Four attributes were found to be misspecified or nonpredictive. However, results demonstrated the validity of cognitive attributes in terms of the revised set of 17 attributes. The girls had similar performance on the attributes as the boys. The students from the two eastern regions significantly underperformed on the most attributes.

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.

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.

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

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).

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

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

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.

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.

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

Least square methods and covariance matrix applied to the relative efficiency calibration of a Ge(Li) detector

International Nuclear Information System (INIS)

Geraldo, L.P.; Smith, D.L.

1989-01-01

The methodology of covariance matrix and square methods have been applied in the relative efficiency calibration for a Ge(Li) detector apllied in the relative efficiency calibration for a Ge(Li) detector. Procedures employed to generate, manipulate and test covariance matrices which serve to properly represent uncertainties of experimental data are discussed. Calibration data fitting using least square methods has been performed for a particular experimental data set. (author) [pt

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.

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.

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

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.

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.

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

A Collocation Method by Moving Least Squares Applicable to European Option Pricing

Directory of Open Access Journals (Sweden)

M. Amirfakhrian

2016-05-01

Full Text Available The subject matter of the present inquiry is the pricing of European options in the actual form of numbers. To assess the numerical prices of European options, a scheme independent of any kind of mesh but rather powered by moving least squares (MLS estimation is made. In practical terms, first the discretion of time variable is implemented and then, an MLS-powered method is applied for spatial approximation. As, unlike other methods, these courses of action mentioned here don't rely on a mesh, one can firmly claim they are to be categorized under mesh-less methods. And, of course, at the end of the paper, various experiments are offered to prove how efficient and how powerful the introduced approach is.

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.

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

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.

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.

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 ...

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

Obtention of the parameters of the Voigt function using the least square fit method

International Nuclear Information System (INIS)

Flores Ll, H.; Cabral P, A.; Jimenez D, H.

1990-01-01

The fundamental parameters of the Voigt function are determined: lorentzian wide (Γ L ) and gaussian wide (Γ G ) with an error for almost all the cases inferior to 1% in the intervals 0.01 ≤ Γ L / Γ G ≤1 and 0.3 ≤ Γ G / Γ L ≤1. This is achieved using the least square fit method with an algebraic function, being obtained a simple method to obtain the fundamental parameters of the Voigt function used in many spectroscopies. (Author)

Kennard-Stone combined with least square support vector machine method for noncontact discriminating human blood species

Science.gov (United States)

Zhang, Linna; Li, Gang; Sun, Meixiu; Li, Hongxiao; Wang, Zhennan; Li, Yingxin; Lin, Ling

2017-11-01

Identifying whole bloods to be either human or nonhuman is an important responsibility for import-export ports and inspection and quarantine departments. Analytical methods and DNA testing methods are usually destructive. Previous studies demonstrated that visible diffuse reflectance spectroscopy method can realize noncontact human and nonhuman blood discrimination. An appropriate method for calibration set selection was very important for a robust quantitative model. In this paper, Random Selection (RS) method and Kennard-Stone (KS) method was applied in selecting samples for calibration set. Moreover, proper stoichiometry method can be greatly beneficial for improving the performance of classification model or quantification model. Partial Least Square Discrimination Analysis (PLSDA) method was commonly used in identification of blood species with spectroscopy methods. Least Square Support Vector Machine (LSSVM) was proved to be perfect for discrimination analysis. In this research, PLSDA method and LSSVM method was used for human blood discrimination. Compared with the results of PLSDA method, this method could enhance the performance of identified models. The overall results convinced that LSSVM method was more feasible for identifying human and animal blood species, and sufficiently demonstrated LSSVM method was a reliable and robust method for human blood identification, and can be more effective and accurate.

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.

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

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.

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

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

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?

Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

Science.gov (United States)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

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.

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.

A method based on moving least squares for XRII image distortion correction

International Nuclear Information System (INIS)

Yan Shiju; Wang Chengtao; Ye Ming

2007-01-01

This paper presents a novel integrated method to correct geometric distortions of XRII (x-ray image intensifier) images. The method has been compared, in terms of mean-squared residual error measured at control and intermediate points, with two traditional local methods and a traditional global methods. The proposed method is based on the methods of moving least squares (MLS) and polynomial fitting. Extensive experiments were performed on simulated and real XRII images. In simulation, the effect of pincushion distortion, sigmoidal distortion, local distortion, noise, and the number of control points was tested. The traditional local methods were sensitive to pincushion and sigmoidal distortion. The traditional global method was only sensitive to sigmoidal distortion. The proposed method was found neither sensitive to pincushion distortion nor sensitive to sigmoidal distortion. The sensitivity of the proposed method to local distortion was lower than or comparable with that of the traditional global method. The sensitivity of the proposed method to noise was higher than that of all three traditional methods. Nevertheless, provided the standard deviation of noise was not greater than 0.1 pixels, accuracy of the proposed method is still higher than the traditional methods. The sensitivity of the proposed method to the number of control points was greatly lower than that of the traditional methods. Provided that a proper cutoff radius is chosen, accuracy of the proposed method is higher than that of the traditional methods. Experiments on real images, carried out by using a 9 in. XRII, showed that residual error of the proposed method (0.2544±0.2479 pixels) is lower than that of the traditional global method (0.4223±0.3879 pixels) and local methods (0.4555±0.3518 pixels and 0.3696±0.4019 pixels, respectively)

Decentralized Gauss-Newton method for nonlinear least squares on wide area network

Science.gov (United States)

Liu, Lanchao; Ling, Qing; Han, Zhu

2014-10-01

This paper presents a decentralized approach of Gauss-Newton (GN) method for nonlinear least squares (NLLS) on wide area network (WAN). In a multi-agent system, a centralized GN for NLLS requires the global GN Hessian matrix available at a central computing unit, which may incur large communication overhead. In the proposed decentralized alternative, each agent only needs local GN Hessian matrix to update iterates with the cooperation of neighbors. The detail formulation of decentralized NLLS on WAN is given, and the iteration at each agent is defined. The convergence property of the decentralized approach is analyzed, and numerical results validate the effectiveness of the proposed algorithm.

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.

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.

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...

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

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.

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.

Comparison of ERBS orbit determination accuracy using batch least-squares and sequential methods

Science.gov (United States)

Oza, D. H.; Jones, T. L.; Fabien, S. M.; Mistretta, G. D.; Hart, R. C.; Doll, C. E.

1991-10-01

The Flight Dynamics Div. (FDD) at NASA-Goddard commissioned a study to develop the Real Time Orbit Determination/Enhanced (RTOD/E) system as a prototype system for sequential orbit determination of spacecraft on a DOS based personal computer (PC). An overview is presented of RTOD/E capabilities and the results are presented of a study to compare the orbit determination accuracy for a Tracking and Data Relay Satellite System (TDRSS) user spacecraft obtained using RTOS/E on a PC with the accuracy of an established batch least squares system, the Goddard Trajectory Determination System (GTDS), operating on a mainframe computer. RTOD/E was used to perform sequential orbit determination for the Earth Radiation Budget Satellite (ERBS), and the Goddard Trajectory Determination System (GTDS) was used to perform the batch least squares orbit determination. The estimated ERBS ephemerides were obtained for the Aug. 16 to 22, 1989, timeframe, during which intensive TDRSS tracking data for ERBS were available. Independent assessments were made to examine the consistencies of results obtained by the batch and sequential methods. Comparisons were made between the forward filtered RTOD/E orbit solutions and definitive GTDS orbit solutions for ERBS; the solution differences were less than 40 meters after the filter had reached steady state.

Comparison of ERBS orbit determination accuracy using batch least-squares and sequential methods

Science.gov (United States)

Oza, D. H.; Jones, T. L.; Fabien, S. M.; Mistretta, G. D.; Hart, R. C.; Doll, C. E.

1991-01-01

The Flight Dynamics Div. (FDD) at NASA-Goddard commissioned a study to develop the Real Time Orbit Determination/Enhanced (RTOD/E) system as a prototype system for sequential orbit determination of spacecraft on a DOS based personal computer (PC). An overview is presented of RTOD/E capabilities and the results are presented of a study to compare the orbit determination accuracy for a Tracking and Data Relay Satellite System (TDRSS) user spacecraft obtained using RTOS/E on a PC with the accuracy of an established batch least squares system, the Goddard Trajectory Determination System (GTDS), operating on a mainframe computer. RTOD/E was used to perform sequential orbit determination for the Earth Radiation Budget Satellite (ERBS), and the Goddard Trajectory Determination System (GTDS) was used to perform the batch least squares orbit determination. The estimated ERBS ephemerides were obtained for the Aug. 16 to 22, 1989, timeframe, during which intensive TDRSS tracking data for ERBS were available. Independent assessments were made to examine the consistencies of results obtained by the batch and sequential methods. Comparisons were made between the forward filtered RTOD/E orbit solutions and definitive GTDS orbit solutions for ERBS; the solution differences were less than 40 meters after the filter had reached steady state.

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...

Resolution of the neutron transport equation by a three-dimensional least square method

International Nuclear Information System (INIS)

Varin, Elisabeth

2001-01-01

The knowledge of space and time distribution of neutrons with a certain energy or speed allows the exploitation and control of a nuclear reactor and the assessment of the irradiation dose about an irradiated nuclear fuel storage site. The neutron density is described by a transport equation. The objective of this research thesis is to develop a software for the resolution of this stationary equation in a three-dimensional Cartesian domain by means of a deterministic method. After a presentation of the transport equation, the author gives an overview of the different deterministic resolution approaches, identifies their benefits and drawbacks, and discusses the choice of the Ressel method. The least square method is precisely described and then applied. Numerical benchmarks are reported for validation purposes

A task specific uncertainty analysis method for least-squares-based form characterization of ultra-precision freeform surfaces

International Nuclear Information System (INIS)

Ren, M J; Cheung, C F; Kong, L B

2012-01-01

In the measurement of ultra-precision freeform surfaces, least-squares-based form characterization methods are widely used to evaluate the form error of the measured surfaces. Although many methodologies have been proposed in recent years to improve the efficiency of the characterization process, relatively little research has been conducted on the analysis of associated uncertainty in the characterization results which may result from those characterization methods being used. As a result, this paper presents a task specific uncertainty analysis method with application in the least-squares-based form characterization of ultra-precision freeform surfaces. That is, the associated uncertainty in the form characterization results is estimated when the measured data are extracted from a specific surface with specific sampling strategy. Three factors are considered in this study which include measurement error, surface form error and sample size. The task specific uncertainty analysis method has been evaluated through a series of experiments. The results show that the task specific uncertainty analysis method can effectively estimate the uncertainty of the form characterization results for a specific freeform surface measurement

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

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.

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

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.

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.

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.

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.

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

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

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

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.

Combining Partial Least Squares and the Gradient-Boosting Method for Soil Property Retrieval Using Visible Near-Infrared Shortwave Infrared Spectra

Directory of Open Access Journals (Sweden)

Lanfa Liu

2017-12-01

Full Text Available Soil spectroscopy has experienced a tremendous increase in soil property characterisation, and can be used not only in the laboratory but also from the space (imaging spectroscopy. Partial least squares (PLS regression is one of the most common approaches for the calibration of soil properties using soil spectra. Besides functioning as a calibration method, PLS can also be used as a dimension reduction tool, which has scarcely been studied in soil spectroscopy. PLS components retained from high-dimensional spectral data can further be explored with the gradient-boosted decision tree (GBDT method. Three soil sample categories were extracted from the Land Use/Land Cover Area Frame Survey (LUCAS soil library according to the type of land cover (woodland, grassland, and cropland. First, PLS regression and GBDT were separately applied to build the spectroscopic models for soil organic carbon (OC, total nitrogen content (N, and clay for each soil category. Then, PLS-derived components were used as input variables for the GBDT model. The results demonstrate that the combined PLS-GBDT approach has better performance than PLS or GBDT alone. The relative important variables for soil property estimation revealed by the proposed method demonstrated that the PLS method is a useful dimension reduction tool for soil spectra to retain target-related information.

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...

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.)

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)).

Concerning an application of the method of least squares with a variable weight matrix

Science.gov (United States)

Sukhanov, A. A.

1979-01-01

An estimate of a state vector for a physical system when the weight matrix in the method of least squares is a function of this vector is considered. An iterative procedure is proposed for calculating the desired estimate. Conditions for the existence and uniqueness of the limit of this procedure are obtained, and a domain is found which contains the limit estimate. A second method for calculating the desired estimate which reduces to the solution of a system of algebraic equations is proposed. The question of applying Newton's method of tangents to solving the given system of algebraic equations is considered and conditions for the convergence of the modified Newton's method are obtained. Certain properties of the estimate obtained are presented together with an example.

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.

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.

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...

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.

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

Petroleomics by electrospray ionization FT-ICR mass spectrometry coupled to partial least squares with variable selection methods: prediction of the total acid number of crude oils.

Science.gov (United States)

Terra, Luciana A; Filgueiras, Paulo R; Tose, Lílian V; Romão, Wanderson; de Souza, Douglas D; de Castro, Eustáquio V R; de Oliveira, Mirela S L; Dias, Júlio C M; Poppi, Ronei J

2014-10-07

Negative-ion mode electrospray ionization, ESI(-), with Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) was coupled to a Partial Least Squares (PLS) regression and variable selection methods to estimate the total acid number (TAN) of Brazilian crude oil samples. Generally, ESI(-)-FT-ICR mass spectra present a power of resolution of ca. 500,000 and a mass accuracy less than 1 ppm, producing a data matrix containing over 5700 variables per sample. These variables correspond to heteroatom-containing species detected as deprotonated molecules, [M - H](-) ions, which are identified primarily as naphthenic acids, phenols and carbazole analog species. The TAN values for all samples ranged from 0.06 to 3.61 mg of KOH g(-1). To facilitate the spectral interpretation, three methods of variable selection were studied: variable importance in the projection (VIP), interval partial least squares (iPLS) and elimination of uninformative variables (UVE). The UVE method seems to be more appropriate for selecting important variables, reducing the dimension of the variables to 183 and producing a root mean square error of prediction of 0.32 mg of KOH g(-1). By reducing the size of the data, it was possible to relate the selected variables with their corresponding molecular formulas, thus identifying the main chemical species responsible for the TAN values.

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.

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.

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.

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.

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

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)

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.

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...

Reconstruction method for fluorescent X-ray computed tomography by least-squares method using singular value decomposition

Science.gov (United States)

Yuasa, T.; Akiba, M.; Takeda, T.; Kazama, M.; Hoshino, A.; Watanabe, Y.; Hyodo, K.; Dilmanian, F. A.; Akatsuka, T.; Itai, Y.

1997-02-01

We describe a new attenuation correction method for fluorescent X-ray computed tomography (FXCT) applied to image nonradioactive contrast materials in vivo. The principle of the FXCT imaging is that of computed tomography of the first generation. Using monochromatized synchrotron radiation from the BLNE-5A bending-magnet beam line of Tristan Accumulation Ring in KEK, Japan, we studied phantoms with the FXCT method, and we succeeded in delineating a 4-mm-diameter channel filled with a 500 /spl mu/g I/ml iodine solution in a 20-mm-diameter acrylic cylindrical phantom. However, to detect smaller iodine concentrations, attenuation correction is needed. We present a correction method based on the equation representing the measurement process. The discretized equation system is solved by the least-squares method using the singular value decomposition. The attenuation correction method is applied to the projections by the Monte Carlo simulation and the experiment to confirm its effectiveness.

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.

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...

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.

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 ...

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.

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

A Least Squares Collocation Method for Accuracy Improvement of Mobile LiDAR Systems

Directory of Open Access Journals (Sweden)

Qingzhou Mao

2015-06-01

Full Text Available In environments that are hostile to Global Navigation Satellites Systems (GNSS, the precision achieved by a mobile light detection and ranging (LiDAR system (MLS can deteriorate into the sub-meter or even the meter range due to errors in the positioning and orientation system (POS. This paper proposes a novel least squares collocation (LSC-based method to improve the accuracy of the MLS in these hostile environments. Through a thorough consideration of the characteristics of POS errors, the proposed LSC-based method effectively corrects these errors using LiDAR control points, thereby improving the accuracy of the MLS. This method is also applied to the calibration of misalignment between the laser scanner and the POS. Several datasets from different scenarios have been adopted in order to evaluate the effectiveness of the proposed method. The results from experiments indicate that this method would represent a significant improvement in terms of the accuracy of the MLS in environments that are essentially hostile to GNSS and is also effective regarding the calibration of misalignment.

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.

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

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

Least-squares finite-element method for shallow-water equations with source terms

Institute of Scientific and Technical Information of China (English)

Shin-Jye Liang; Tai-Wen Hsu

2009-01-01

Numerical solution of shallow-water equations (SWE) has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include: the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.

Artificial neural network and classical least-squares methods for neurotransmitter mixture analysis.

Science.gov (United States)

Schulze, H G; Greek, L S; Gorzalka, B B; Bree, A V; Blades, M W; Turner, R F

1995-02-01

Identification of individual components in biological mixtures can be a difficult problem regardless of the analytical method employed. In this work, Raman spectroscopy was chosen as a prototype analytical method due to its inherent versatility and applicability to aqueous media, making it useful for the study of biological samples. Artificial neural networks (ANNs) and the classical least-squares (CLS) method were used to identify and quantify the Raman spectra of the small-molecule neurotransmitters and mixtures of such molecules. The transfer functions used by a network, as well as the architecture of a network, played an important role in the ability of the network to identify the Raman spectra of individual neurotransmitters and the Raman spectra of neurotransmitter mixtures. Specifically, networks using sigmoid and hyperbolic tangent transfer functions generalized better from the mixtures in the training data set to those in the testing data sets than networks using sine functions. Networks with connections that permit the local processing of inputs generally performed better than other networks on all the testing data sets. and better than the CLS method of curve fitting, on novel spectra of some neurotransmitters. The CLS method was found to perform well on noisy, shifted, and difference spectra.

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.

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.

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.

Calculation of Credit Valuation Adjustment Based on Least Square Monte Carlo Methods

Directory of Open Access Journals (Sweden)

Qian Liu

2015-01-01

Full Text Available Counterparty credit risk has become one of the highest-profile risks facing participants in the financial markets. Despite this, relatively little is known about how counterparty credit risk is actually priced mathematically. We examine this issue using interest rate swaps. This largely traded financial product allows us to well identify the risk profiles of both institutions and their counterparties. Concretely, Hull-White model for rate and mean-reverting model for default intensity have proven to be in correspondence with the reality and to be well suited for financial institutions. Besides, we find that least square Monte Carlo method is quite efficient in the calculation of credit valuation adjustment (CVA, for short as it avoids the redundant step to generate inner scenarios. As a result, it accelerates the convergence speed of the CVA estimators. In the second part, we propose a new method to calculate bilateral CVA to avoid double counting in the existing bibliographies, where several copula functions are adopted to describe the dependence of two first to default times.

Amplitude differences least squares method applied to temporal cardiac beat alignment

International Nuclear Information System (INIS)

Correa, R O; Laciar, E; Valentinuzzi, M E

2007-01-01

High resolution averaged ECG is an important diagnostic technique in post-infarcted and/or chagasic patients with high risk of ventricular tachycardia (VT). It calls for precise determination of the synchronism point (fiducial point) in each beat to be averaged. Cross-correlation (CC) between each detected beat and a reference beat is, by and large, the standard alignment procedure. However, the fiducial point determination is not precise in records contaminated with high levels of noise. Herein, we propose an alignment procedure based on the least squares calculation of the amplitude differences (LSAD) between the ECG samples and a reference or template beat. Both techniques, CC and LSAD, were tested in high resolution ECG's corrupted with white noise and 50 Hz line interference of varying amplitudes (RMS range: 0-100μV). Results point out that LSDA produced a lower alignment error in all contaminated records while in those blurred by power line interference better results were found only within the 0-40 μV range. It is concluded that the proposed method represents a valid alignment alternative

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.

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.

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)

Uncertainty evaluation for ordinary least-square fitting with arbitrary order polynomial in joule balance method

International Nuclear Information System (INIS)

You, Qiang; Xu, JinXin; Wang, Gang; Zhang, Zhonghua

2016-01-01

The ordinary least-square fitting with polynomial is used in both the dynamic phase of the watt balance method and the weighting phase of joule balance method but few researches have been conducted to evaluate the uncertainty of the fitting data in the electrical balance methods. In this paper, a matrix-calculation method for evaluating the uncertainty of the polynomial fitting data is derived and the properties of this method are studied by simulation. Based on this, another two derived methods are proposed. One is used to find the optimal fitting order for the watt or joule balance methods. Accuracy and effective factors of this method are experimented with simulations. The other is used to evaluate the uncertainty of the integral of the fitting data for joule balance, which is demonstrated with an experiment from the NIM-1 joule balance. (paper)

Bayesian inference for data assimilation using Least-Squares Finite Element methods

International Nuclear Information System (INIS)

Dwight, Richard P

2010-01-01

It has recently been observed that Least-Squares Finite Element methods (LS-FEMs) can be used to assimilate experimental data into approximations of PDEs in a natural way, as shown by Heyes et al. in the case of incompressible Navier-Stokes flow. The approach was shown to be effective without regularization terms, and can handle substantial noise in the experimental data without filtering. Of great practical importance is that - unlike other data assimilation techniques - it is not significantly more expensive than a single physical simulation. However the method as presented so far in the literature is not set in the context of an inverse problem framework, so that for example the meaning of the final result is unclear. In this paper it is shown that the method can be interpreted as finding a maximum a posteriori (MAP) estimator in a Bayesian approach to data assimilation, with normally distributed observational noise, and a Bayesian prior based on an appropriate norm of the governing equations. In this setting the method may be seen to have several desirable properties: most importantly discretization and modelling error in the simulation code does not affect the solution in limit of complete experimental information, so these errors do not have to be modelled statistically. Also the Bayesian interpretation better justifies the choice of the method, and some useful generalizations become apparent. The technique is applied to incompressible Navier-Stokes flow in a pipe with added velocity data, where its effectiveness, robustness to noise, and application to inverse problems is demonstrated.

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....

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

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.

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

A Novel Method for Lithium-Ion Battery Online Parameter Identification Based on Variable Forgetting Factor Recursive Least Squares

Directory of Open Access Journals (Sweden)

Zizhou Lao

2018-05-01

Full Text Available For model-based state of charge (SOC estimation methods, the battery model parameters change with temperature, SOC, and so forth, causing the estimation error to increase. Constantly updating model parameters during battery operation, also known as online parameter identification, can effectively solve this problem. In this paper, a lithium-ion battery is modeled using the Thevenin model. A variable forgetting factor (VFF strategy is introduced to improve forgetting factor recursive least squares (FFRLS to variable forgetting factor recursive least squares (VFF-RLS. A novel method based on VFF-RLS for the online identification of the Thevenin model is proposed. Experiments verified that VFF-RLS gives more stable online parameter identification results than FFRLS. Combined with an unscented Kalman filter (UKF algorithm, a joint algorithm named VFF-RLS-UKF is proposed for SOC estimation. In a variable-temperature environment, a battery SOC estimation experiment was performed using the joint algorithm. The average error of the SOC estimation was as low as 0.595% in some experiments. Experiments showed that VFF-RLS can effectively track the changes in model parameters. The joint algorithm improved the SOC estimation accuracy compared to the method with the fixed forgetting factor.

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

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.

[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.

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

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.

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.

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.

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.

A scaled Lagrangian method for performing a least squares fit of a model to plant data

International Nuclear Information System (INIS)

Crisp, K.E.

1988-01-01

Due to measurement errors, even a perfect mathematical model will not be able to match all the corresponding plant measurements simultaneously. A further discrepancy may be introduced if an un-modelled change in conditions occurs within the plant which should have required a corresponding change in model parameters - e.g. a gradual deterioration in the performance of some component(s). Taking both these factors into account, what is required is that the overall discrepancy between the model predictions and the plant data is kept to a minimum. This process is known as 'model fitting', A method is presented for minimising any function which consists of the sum of squared terms, subject to any constraints. Its most obvious application is in the process of model fitting, where a weighted sum of squares of the differences between model predictions and plant data is the function to be minimised. When implemented within existing Central Electricity Generating Board computer models, it will perform a least squares fit of a model to plant data within a single job submission. (author)

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.

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.

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

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.

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...

Window least squares method applied to statistical noise smoothing of positron annihilation data

International Nuclear Information System (INIS)

Adam, G.; Adam, S.; Barbiellini, B.; Hoffmann, L.; Manuel, A.A.; Peter, M.

1993-06-01

The paper deals with the off-line processing of experimental data obtained by two-dimensional angular correlation of the electron-positron annihilation radiation (2D-ACAR) technique on high-temperature superconductors. A piecewise continuous window least squares (WLS) method devoted to the statistical noise smoothing of 2D-ACAR data, under close control of the crystal reciprocal lattice periodicity, is derived. Reliability evaluation of the constant local weight WLS smoothing formula (CW-WLSF) shows that consistent processing 2D-ACAR data by CW-WLSF is possible. CW-WLSF analysis of 2D-ACAR data collected on untwinned Y Ba 2 Cu 3 O 7-δ single crystals yields significantly improved signature of the Fermi surface ridge at second Umklapp processes and resolves, for the first time, the ridge signature at third Umklapp processes. (author). 24 refs, 9 figs

A comparative analysis of the EEDF obtained by Regularization and by Least square fit methods

International Nuclear Information System (INIS)

Gutierrez T, C.; Flores Ll, H.

2004-01-01

The second derived of the characteristic curve current-voltage (I - V) of a Langmuir probe (I - V) is numerically calculated using the Tikhonov method for to determine the distribution function of the electrons energy (EEDF). One comparison of the obtained EEDF and a fit by least square are discussed (LS). The I - V experimental curve is obtained in a plasma source in the electron cyclotron resonance (ECR) using a cylindrical probe. The parameters of plasma are determined of the EEDF by means of the Laframboise theory. For the case of the LS fit, the obtained results are similar to those obtained by the Tikhonov method, but in the first case the procedure is slow to achieve the best fit. (Author)

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

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.

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.

A least squares method for a longitudinal fin with temperature dependent internal heat generation and thermal conductivity

International Nuclear Information System (INIS)

Aziz, A.; Bouaziz, M.N.

2011-01-01

Highlights: → Analytical solutions for a rectangular fin with temperature dependent heat generation and thermal conductivity. → Graphs give temperature distributions and fin efficiency. → Comparison of analytical and numerical solutions. → Method of least squares used for the analytical solutions. - Abstract: Approximate but highly accurate solutions for the temperature distribution, fin efficiency, and optimum fin parameter for a constant area longitudinal fin with temperature dependent internal heat generation and thermal conductivity are derived analytically. The method of least squares recently used by the authors is applied to treat the two nonlinearities, one associated with the temperature dependent internal heat generation and the other due to temperature dependent thermal conductivity. The solution is built from the classical solution for a fin with uniform internal heat generation and constant thermal conductivity. The results are presented graphically and compared with the direct numerical solutions. The analytical solutions retain their accuracy (within 1% of the numerical solution) even when there is a 60% increase in thermal conductivity and internal heat generation at the base temperature from their corresponding values at the sink temperature. The present solution is simple (involves hyperbolic functions only) compared with the fairly complex approximate solutions based on the homotopy perturbation method, variational iteration method, and the double series regular perturbation method and offers high accuracy. The simple analytical expressions for the temperature distribution, the fin efficiency and the optimum fin parameter are convenient for use by engineers dealing with the design and analysis of heat generating fins operating with a large temperature difference between the base and the environment.

A novel approach to the experimental study on methane/steam reforming kinetics using the Orthogonal Least Squares method

Science.gov (United States)

Sciazko, Anna; Komatsu, Yosuke; Brus, Grzegorz; Kimijima, Shinji; Szmyd, Janusz S.

2014-09-01

For a mathematical model based on the result of physical measurements, it becomes possible to determine their influence on the final solution and its accuracy. However, in classical approaches, the influence of different model simplifications on the reliability of the obtained results are usually not comprehensively discussed. This paper presents a novel approach to the study of methane/steam reforming kinetics based on an advanced methodology called the Orthogonal Least Squares method. The kinetics of the reforming process published earlier are divergent among themselves. To obtain the most probable values of kinetic parameters and enable direct and objective model verification, an appropriate calculation procedure needs to be proposed. The applied Generalized Least Squares (GLS) method includes all the experimental results into the mathematical model which becomes internally contradicted, as the number of equations is greater than number of unknown variables. The GLS method is adopted to select the most probable values of results and simultaneously determine the uncertainty coupled with all the variables in the system. In this paper, the evaluation of the reaction rate after the pre-determination of the reaction rate, which was made by preliminary calculation based on the obtained experimental results over a Nickel/Yttria-stabilized Zirconia catalyst, was performed.

Least median of squares filtering of locally optimal point matches for compressible flow image registration

International Nuclear Information System (INIS)

Castillo, Edward; Guerrero, Thomas; Castillo, Richard; White, Benjamin; Rojo, Javier

2012-01-01

Compressible flow based image registration operates under the assumption that the mass of the imaged material is conserved from one image to the next. Depending on how the mass conservation assumption is modeled, the performance of existing compressible flow methods is limited by factors such as image quality, noise, large magnitude voxel displacements, and computational requirements. The Least Median of Squares Filtered Compressible Flow (LFC) method introduced here is based on a localized, nonlinear least squares, compressible flow model that describes the displacement of a single voxel that lends itself to a simple grid search (block matching) optimization strategy. Spatially inaccurate grid search point matches, corresponding to erroneous local minimizers of the nonlinear compressible flow model, are removed by a novel filtering approach based on least median of squares fitting and the forward search outlier detection method. The spatial accuracy of the method is measured using ten thoracic CT image sets and large samples of expert determined landmarks (available at www.dir-lab.com). The LFC method produces an average error within the intra-observer error on eight of the ten cases, indicating that the method is capable of achieving a high spatial accuracy for thoracic CT registration. (paper)

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.

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.

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.

Single Directional SMO Algorithm for Least Squares Support Vector Machines

Directory of Open Access Journals (Sweden)

Xigao Shao

2013-01-01

Full Text Available Working set selection is a major step in decomposition methods for training least squares support vector machines (LS-SVMs. In this paper, a new technique for the selection of working set in sequential minimal optimization- (SMO- type decomposition methods is proposed. By the new method, we can select a single direction to achieve the convergence of the optimality condition. A simple asymptotic convergence proof for the new algorithm is given. Experimental comparisons demonstrate that the classification accuracy of the new method is not largely different from the existing methods, but the training speed is faster than existing ones.

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).

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.

A New Global Regression Analysis Method for the Prediction of Wind Tunnel Model Weight Corrections

Science.gov (United States)

Ulbrich, Norbert Manfred; Bridge, Thomas M.; Amaya, Max A.

2014-01-01

A new global regression analysis method is discussed that predicts wind tunnel model weight corrections for strain-gage balance loads during a wind tunnel test. The method determines corrections by combining "wind-on" model attitude measurements with least squares estimates of the model weight and center of gravity coordinates that are obtained from "wind-off" data points. The method treats the least squares fit of the model weight separate from the fit of the center of gravity coordinates. Therefore, it performs two fits of "wind- off" data points and uses the least squares estimator of the model weight as an input for the fit of the center of gravity coordinates. Explicit equations for the least squares estimators of the weight and center of gravity coordinates are derived that simplify the implementation of the method in the data system software of a wind tunnel. In addition, recommendations for sets of "wind-off" data points are made that take typical model support system constraints into account. Explicit equations of the confidence intervals on the model weight and center of gravity coordinates and two different error analyses of the model weight prediction are also discussed in the appendices of the paper.

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.

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.

Dissemination of the National Standard of Mass from INACAL using the gauss Markov method by generalized least squares

OpenAIRE

Taipe, Donny

2017-01-01

This article sustains the transfer of the national standard of mass (KP1) of INACAL to two reference standards ‘Weight 1’, ‘Weight 2’ and also KP2 (as witnessed mass standard and with known error). The dissemination was done using the Gauss Markov method by Generalized Least Squares. The uncertainty calculation was performed using Univariate Gaussian Distribution and Multivariate Gaussian Distribution; the latter was developed with the Monte Carlo method using a programming language called 'R...

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.

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...

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

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.

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.

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...

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

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.

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.

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

Multi-Gaussian fitting for pulse waveform using Weighted Least Squares and multi-criteria decision making method.

Science.gov (United States)

Wang, Lu; Xu, Lisheng; Feng, Shuting; Meng, Max Q-H; Wang, Kuanquan

2013-11-01

Analysis of pulse waveform is a low cost, non-invasive method for obtaining vital information related to the conditions of the cardiovascular system. In recent years, different Pulse Decomposition Analysis (PDA) methods have been applied to disclose the pathological mechanisms of the pulse waveform. All these methods decompose single-period pulse waveform into a constant number (such as 3, 4 or 5) of individual waves. Furthermore, those methods do not pay much attention to the estimation error of the key points in the pulse waveform. The estimation of human vascular conditions depends on the key points' positions of pulse wave. In this paper, we propose a Multi-Gaussian (MG) model to fit real pulse waveforms using an adaptive number (4 or 5 in our study) of Gaussian waves. The unknown parameters in the MG model are estimated by the Weighted Least Squares (WLS) method and the optimized weight values corresponding to different sampling points are selected by using the Multi-Criteria Decision Making (MCDM) method. Performance of the MG model and the WLS method has been evaluated by fitting 150 real pulse waveforms of five different types. The resulting Normalized Root Mean Square Error (NRMSE) was less than 2.0% and the estimation accuracy for the key points was satisfactory, demonstrating that our proposed method is effective in compressing, synthesizing and analyzing pulse waveforms. Copyright © 2013 Elsevier Ltd. All rights reserved.

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

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.

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.

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.

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.

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.

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

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.

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)

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.

Application of a mixed Galerkin/least-squares method to axisymetric shell problems subjected to arbitrary loading

International Nuclear Information System (INIS)

Loula, A.F.D.; Toledo, E.M.; Franca, L.P.; Garcia, E.L.M.

1989-08-01

A variationaly consistent finite element formulation for constrained problems free from shear or membrane locking is applied to axisymetric shells subjected to arbitrary loading. The governing equations are writen according to Love's classical theory for a problem of bending of axisymetric thin and moderately thick shells accounting for shear deformation. The mixed variational formulation, in terms of stresses and displacements here presented consists of classical Galerkin method plus mesh-dependent least-square type terms employed with equal-order finite element polynomials. The additional terms enhance stability and accuracy of the original Galerkin method, as already proven theoretically and confirmed trough numerical experiments. Numerical results of some examples are presented to demonstrate the good stability and accuracy of the formulation. (author) [pt

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.

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.

Calculating the parameters of experimental data Gauss distribution using the least square fit method and evaluation of their accuracy

International Nuclear Information System (INIS)

Guseva, E.V.; Peregudov, V.N.

1982-01-01

The FITGAV program for calculation of parameters of the Gauss curve describing experimental data is considered. The calculations are based on the least square fit method. The estimations of errors in the parameter determination as a function of experimental data sample volume and their statistical significance are obtained. The curve fit using 100 points occupies less than 1 s at the SM-4 type computer

Stable Galerkin versus equal-order Galerkin least-squares elements for the stokes flow problem

International Nuclear Information System (INIS)

Franca, L.P.; Frey, S.L.; Sampaio, R.

1989-11-01

Numerical experiments are performed for the stokes flow problem employing a stable Galerkin method and a Galerkin/Least-squares method with equal-order elements. Error estimates for the methods tested herein are reviewed. The numerical results presented attest the good stability properties of all methods examined herein. (A.C.A.S.) [pt

Fitting of two and three variate polynomials from experimental data through the least squares method

International Nuclear Information System (INIS)

Sanchez-Miro, J.J.; Sanz-Martin, J.C.

1994-01-01

Obtaining polynomial fittings from observational data in two and three dimensions is an interesting and practical task. Such an arduous problem suggests the development of an automatic code. The main novelty we provide lies in the generalization of the classical least squares method in three FORTRAN 77 programs usable in any sampling problem. Furthermore, we introduce the orthogonal 2D-Legendre function in the fitting process. These FORTRAN 77 programs are equipped with the options to calculate the approximation quality standard indicators, obviously generalized to two and three dimensions (correlation nonlinear factor, confidence intervals, cuadratic mean error, and so on). The aim of this paper is to rectify the absence of fitting algorithms for more than one independent variable in mathematical libraries

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

Improved variable reduction in partial least squares modelling based on predictive-property-ranked variables and adaptation of partial least squares complexity.

Science.gov (United States)

Andries, Jan P M; Vander Heyden, Yvan; Buydens, Lutgarde M C

2011-10-31

The calibration performance of partial least squares for one response variable (PLS1) can be improved by elimination of uninformative variables. Many methods are based on so-called predictive variable properties, which are functions of various PLS-model parameters, and which may change during the variable reduction process. In these methods variable reduction is made on the variables ranked in descending order for a given variable property. The methods start with full spectrum modelling. Iteratively, until a specified number of remaining variables is reached, the variable with the smallest property value is eliminated; a new PLS model is calculated, followed by a renewed ranking of the variables. The Stepwise Variable Reduction methods using Predictive-Property-Ranked Variables are denoted as SVR-PPRV. In the existing SVR-PPRV methods the PLS model complexity is kept constant during the variable reduction process. In this study, three new SVR-PPRV methods are proposed, in which a possibility for decreasing the PLS model complexity during the variable reduction process is build in. Therefore we denote our methods as PPRVR-CAM methods (Predictive-Property-Ranked Variable Reduction with Complexity Adapted Models). The selective and predictive abilities of the new methods are investigated and tested, using the absolute PLS regression coefficients as predictive property. They were compared with two modifications of existing SVR-PPRV methods (with constant PLS model complexity) and with two reference methods: uninformative variable elimination followed by either a genetic algorithm for PLS (UVE-GA-PLS) or an interval PLS (UVE-iPLS). The performance of the methods is investigated in conjunction with two data sets from near-infrared sources (NIR) and one simulated set. The selective and predictive performances of the variable reduction methods are compared statistically using the Wilcoxon signed rank test. The three newly developed PPRVR-CAM methods were able to retain

Space-time least-squares Petrov-Galerkin projection in nonlinear model reduction.

Energy Technology Data Exchange (ETDEWEB)

Choi, Youngsoo [Sandia National Laboratories (SNL-CA), Livermore, CA (United States). Extreme-scale Data Science and Analytics Dept.; Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Carlberg, Kevin Thomas [Sandia National Laboratories (SNL-CA), Livermore, CA (United States). Extreme-scale Data Science and Analytics Dept.

2017-09-01

Our work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply Petrov-Galerkin projection in the spatial dimension and subsequently apply time integration to numerically resolve the resulting low-dimensional dynamical system, the proposed method applies projection in space and time simultaneously. To accomplish this, the method first introduces a low-dimensional space-time trial subspace, which can be obtained by computing tensor decompositions of state-snapshot data. The method then computes discrete-optimal approximations in this space-time trial subspace by minimizing the residual arising after time discretization over all space and time in a weighted ℓ²-norm. This norm can be de ned to enable complexity reduction (i.e., hyper-reduction) in time, which leads to space-time collocation and space-time GNAT variants of the ST-LSPG method. Advantages of the approach relative to typical spatial-projection-based nonlinear model reduction methods such as Galerkin projection and least-squares Petrov-Galerkin projection include: (1) a reduction of both the spatial and temporal dimensions of the dynamical system, (2) the removal of spurious temporal modes (e.g., unstable growth) from the state space, and (3) error bounds that exhibit slower growth in time. Numerical examples performed on model problems in fluid dynamics demonstrate the ability of the method to generate orders-of-magnitude computational savings relative to spatial-projection-based reduced-order models without sacrificing accuracy.

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.

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.

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.

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…

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)…

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

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.

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.

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...

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

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.

Numerical Analysis of the Reaction-diffusion Equation for Soluble Starch and Dextrin as Substrates of Immobilized Amyloglucosidase in a Porous Support by Using Least Square Method

Directory of Open Access Journals (Sweden)

Ali Izadi

2015-10-01

Full Text Available In this study, substrates concentration profile has been studied in a porous matrix containing immobilized amyloglucosidase for glucose production. This analysis has been performed by using of an analytical method called Least Square Method and results have been compared with numerical solution. Effects of effective diffusivity (, Michael's constant (, maximum reaction rate ( and initial substrate concentration ( are studied on Soluble Starch and Dextrin concentration in the spherical support. Outcomes reveal that Least Square Method has an excellent agreement with numerical solution and in the center of support, substrate concentration is minimum and increasing of effective diffusivity and Michael's constant reduce the Soluble Starch and Dextrin profile gradient.

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.

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.

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...

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.

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.

A modified Generalized Least Squares method for large scale nuclear data evaluation

Energy Technology Data Exchange (ETDEWEB)

Schnabel, Georg [Irfu, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette (France); Atominstitut, TU Wien, Vienna (Austria); Leeb, Helmut [Atominstitut, TU Wien, Vienna (Austria)

2017-01-01

Nuclear data evaluation aims to provide estimates and uncertainties in the form of covariance matrices of cross sections and related quantities. Many practitioners use the Generalized Least Squares (GLS) formulas to combine experimental data and results of model calculations in order to determine reliable estimates and covariance matrices. A prerequisite to apply the GLS formulas is the construction of a prior covariance matrix for the observables from a set of model calculations. Modern nuclear model codes are able to provide predictions for a large number of observables. However, the inclusion of all observables may lead to a prior covariance matrix of intractable size. Therefore, we introduce mathematically equivalent versions of the GLS formulas to avoid the construction of the prior covariance matrix. Experimental data can be incrementally incorporated into the evaluation process, hence there is no upper limit on their amount. We demonstrate the modified GLS method in a tentative evaluation involving about three million observables using the code TALYS. The revised scheme is well suited as building block of a database application providing evaluated nuclear data. Updating with new experimental data is feasible and users can query estimates and correlations of arbitrary subsets of the observables stored in the database.

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

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.

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

Phase-unwrapping algorithm by a rounding-least-squares approach

Science.gov (United States)

Juarez-Salazar, Rigoberto; Robledo-Sanchez, Carlos; Guerrero-Sanchez, Fermin

2014-02-01

A simple and efficient phase-unwrapping algorithm based on a rounding procedure and a global least-squares minimization is proposed. Instead of processing the gradient of the wrapped phase, this algorithm operates over the gradient of the phase jumps by a robust and noniterative scheme. Thus, the residue-spreading and over-smoothing effects are reduced. The algorithm's performance is compared with four well-known phase-unwrapping methods: minimum cost network flow (MCNF), fast Fourier transform (FFT), quality-guided, and branch-cut. A computer simulation and experimental results show that the proposed algorithm reaches a high-accuracy level than the MCNF method by a low-computing time similar to the FFT phase-unwrapping method. Moreover, since the proposed algorithm is simple, fast, and user-free, it could be used in metrological interferometric and fringe-projection automatic real-time applications.

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.

Determination of the longitudinal modulus of elasticity in structural sawn wooden beams by the least squares method

Directory of Open Access Journals (Sweden)

André Luis Christoforo

2012-12-01

Full Text Available This paper proposes an alternative method of calculation based on the Least Squares Method to determine the longitudinal modulus of elasticity in structural-sized wooden beams. The developed equations require knowledge of three points of displacements, allowing greater reliability on the dependent variable when using the static four-point bending test. Using the Jatobá (Hymenaea sp wood in the study, the methodology proposed here was used in combination with a simplified one, requiring knowledge of displacement only at the midpoint of the beam in order to compare the results among them. Results show statistical equivalence between the models, indicating a good approximation of the simplified model for calculating the modulus of elasticity in wooden structural bending here evaluated.

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.

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.

Quantitative Analysis of Adulterations in Oat Flour by FT-NIR Spectroscopy, Incomplete Unbalanced Randomized Block Design, and Partial Least Squares

Directory of Open Access Journals (Sweden)

Ning Wang

2014-01-01

Full Text Available This paper developed a rapid and nondestructive method for quantitative analysis of a cheaper adulterant (wheat flour in oat flour by NIR spectroscopy and chemometrics. Reflectance FT-NIR spectra in the range of 4000 to 12000 cm−1 of 300 oat flour objects adulterated with wheat flour were measured. The doping levels of wheat flour ranged from 5% to 50% (w/w. To ensure the generalization performance of the method, both the oat and the wheat flour samples were collected from different producing areas and an incomplete unbalanced randomized block (IURB design was performed to include the significant variations that may be encountered in future samples. Partial least squares regression (PLSR was used to develop calibration models for predicting the levels of wheat flour. Different preprocessing methods including smoothing, taking second-order derivative (D2, and standard normal variate (SNV transformation were investigated to improve the model accuracy of PLS. The root mean squared error of Monte Carlo cross-validation (RMSEMCCV and root mean squared error of prediction (RMSEP were 1.921 and 1.975 (%, w/w by D2-PLS, respectively. The results indicate that NIR and chemometrics can provide a rapid method for quantitative analysis of wheat flour in oat flour.

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.

A Galerkin least squares approach to viscoelastic flow.

Energy Technology Data Exchange (ETDEWEB)

Rao, Rekha R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Schunk, Peter Randall [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2015-10-01

A Galerkin/least-squares stabilization technique is applied to a discrete Elastic Viscous Stress Splitting formulation of for viscoelastic flow. From this, a possible viscoelastic stabilization method is proposed. This method is tested with the flow of an Oldroyd-B fluid past a rigid cylinder, where it is found to produce inaccurate drag coefficients. Furthermore, it fails for relatively low Weissenberg number indicating it is not suited for use as a general algorithm. In addition, a decoupled approach is used as a way separating the constitutive equation from the rest of the system. A Pressure Poisson equation is used when the velocity and pressure are sought to be decoupled, but this fails to produce a solution when inflow/outflow boundaries are considered. However, a coupled pressure-velocity equation with a decoupled constitutive equation is successful for the flow past a rigid cylinder and seems to be suitable as a general-use algorithm.

From least squares to multilevel modeling: A graphical introduction to Bayesian inference

Science.gov (United States)

Loredo, Thomas J.

2016-01-01

This tutorial presentation will introduce some of the key ideas and techniques involved in applying Bayesian methods to problems in astrostatistics. The focus will be on the big picture: understanding the foundations (interpreting probability, Bayes's theorem, the law of total probability and marginalization), making connections to traditional methods (propagation of errors, least squares, chi-squared, maximum likelihood, Monte Carlo simulation), and highlighting problems where a Bayesian approach can be particularly powerful (Poisson processes, density estimation and curve fitting with measurement error). The "graphical" component of the title reflects an emphasis on pictorial representations of some of the math, but also on the use of graphical models (multilevel or hierarchical models) for analyzing complex data. Code for some examples from the talk will be available to participants, in Python and in the Stan probabilistic programming language.

Modeling and forecasting monthly movement of annual average solar insolation based on the least-squares Fourier-model

International Nuclear Information System (INIS)

Yang, Zong-Chang

2014-01-01

Highlights: • Introduce a finite Fourier-series model for evaluating monthly movement of annual average solar insolation. • Present a forecast method for predicting its movement based on the extended Fourier-series model in the least-squares. • Shown its movement is well described by a low numbers of harmonics with approximately 6-term Fourier series. • Predict its movement most fitting with less than 6-term Fourier series. - Abstract: Solar insolation is one of the most important measurement parameters in many fields. Modeling and forecasting monthly movement of annual average solar insolation is of increasingly importance in areas of engineering, science and economics. In this study, Fourier-analysis employing finite Fourier-series is proposed for evaluating monthly movement of annual average solar insolation and extended in the least-squares for forecasting. The conventional Fourier analysis, which is the most common analysis method in the frequency domain, cannot be directly applied for prediction. Incorporated with the least-square method, the introduced Fourier-series model is extended to predict its movement. The extended Fourier-series forecasting model obtains its optimums Fourier coefficients in the least-square sense based on its previous monthly movements. The proposed method is applied to experiments and yields satisfying results in the different cities (states). It is indicated that monthly movement of annual average solar insolation is well described by a low numbers of harmonics with approximately 6-term Fourier series. The extended Fourier forecasting model predicts the monthly movement of annual average solar insolation most fitting with less than 6-term Fourier series

A Comparative Investigation of the Combined Effects of Pre-Processing, Wavelength Selection, and Regression Methods on Near-Infrared Calibration Model Performance.

Science.gov (United States)

Wan, Jian; Chen, Yi-Chieh; Morris, A Julian; Thennadil, Suresh N

2017-07-01

Near-infrared (NIR) spectroscopy is being widely used in various fields ranging from pharmaceutics to the food industry for analyzing chemical and physical properties of the substances concerned. Its advantages over other analytical techniques include available physical interpretation of spectral data, nondestructive nature and high speed of measurements, and little or no need for sample preparation. The successful application of NIR spectroscopy relies on three main aspects: pre-processing of spectral data to eliminate nonlinear variations due to temperature, light scattering effects and many others, selection of those wavelengths that contribute useful information, and identification of suitable calibration models using linear/nonlinear regression . Several methods have been developed for each of these three aspects and many comparative studies of different methods exist for an individual aspect or some combinations. However, there is still a lack of comparative studies for the interactions among these three aspects, which can shed light on what role each aspect plays in the calibration and how to combine various methods of each aspect together to obtain the best calibration model. This paper aims to provide such a comparative study based on four benchmark data sets using three typical pre-processing methods, namely, orthogonal signal correction (OSC), extended multiplicative signal correction (EMSC) and optical path-length estimation and correction (OPLEC); two existing wavelength selection methods, namely, stepwise forward selection (SFS) and genetic algorithm optimization combined with partial least squares regression for spectral data (GAPLSSP); four popular regression methods, namely, partial least squares (PLS), least absolute shrinkage and selection operator (LASSO), least squares support vector machine (LS-SVM), and Gaussian process regression (GPR). The comparative study indicates that, in general, pre-processing of spectral data can play a significant

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.

Discussion About Nonlinear Time Series Prediction Using Least Squares Support Vector Machine

International Nuclear Information System (INIS)

Xu Ruirui; Bian Guoxing; Gao Chenfeng; Chen Tianlun

2005-01-01

The least squares support vector machine (LS-SVM) is used to study the nonlinear time series prediction. First, the parameter γ and multi-step prediction capabilities of the LS-SVM network are discussed. Then we employ clustering method in the model to prune the number of the support values. The learning rate and the capabilities of filtering noise for LS-SVM are all greatly improved.

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.

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.

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.

Proton Exchange Membrane Fuel Cell Modelling Using Moving Least Squares Technique

Directory of Open Access Journals (Sweden)

Radu Tirnovan

2009-07-01

Full Text Available Proton exchange membrane fuel cell, with low polluting emissions, is a great alternative to replace the traditional electrical power sources for automotive applications or for small stationary consumers. This paper presents a numerical method, for the fuel cell modelling, based on moving least squares (MLS. Experimental data have been used for developing an approximated model of the PEMFC function of the current density, air inlet pressure and operating temperature of the fuel cell. The method can be applied for modelling others fuel cell sub-systems, such as the compressor. The method can be used for off-line or on-line identification of the PEMFC stack.

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.

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.

Multivariate fault isolation of batch processes via variable selection in partial least squares discriminant analysis.

Science.gov (United States)

Yan, Zhengbing; Kuang, Te-Hui; Yao, Yuan

2017-09-01

In recent years, multivariate statistical monitoring of batch processes has become a popular research topic, wherein multivariate fault isolation is an important step aiming at the identification of the faulty variables contributing most to the detected process abnormality. Although contribution plots have been commonly used in statistical fault isolation, such methods suffer from the smearing effect between correlated variables. In particular, in batch process monitoring, the high autocorrelations and cross-correlations that exist in variable trajectories make the smearing effect unavoidable. To address such a problem, a variable selection-based fault isolation method is proposed in this research, which transforms the fault isolation problem into a variable selection problem in partial least squares discriminant analysis and solves it by calculating a sparse partial least squares model. As different from the traditional methods, the proposed method emphasizes the relative importance of each process variable. Such information may help process engineers in conducting root-cause diagnosis. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

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.

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.

Multisource least-squares migration of marine streamer and land data with frequency-division encoding

KAUST Repository

Huang, Yunsong; Schuster, Gerard T.

2012-01-01

Multisource migration of phase-encoded supergathers has shown great promise in reducing the computational cost of conventional migration. The accompanying crosstalk noise, in addition to the migration footprint, can be reduced by least-squares inversion. But the application of this approach to marine streamer data is hampered by the mismatch between the limited number of live traces/shot recorded in the field and the pervasive number of traces generated by the finite-difference modelling method. This leads to a strong mismatch in the misfit function and results in strong artefacts (crosstalk) in the multisource least-squares migration image. To eliminate this noise, we present a frequency-division multiplexing (FDM) strategy with iterative least-squares migration (ILSM) of supergathers. The key idea is, at each ILSM iteration, to assign a unique frequency band to each shot gather. In this case there is no overlap in the crosstalk spectrum of each migrated shot gather m(x, ω i), so the spectral crosstalk product m(x, ω i)m(x, ω j) =δ i, j is zero, unless i=j. Our results in applying this method to 2D marine data for a SEG/EAGE salt model show better resolved images than standard migration computed at about 1/10 th of the cost. Similar results are achieved after applying this method to synthetic data for a 3D SEG/EAGE salt model, except the acquisition geometry is similar to that of a marine OBS survey. Here, the speedup of this method over conventional migration is more than 10. We conclude that multisource migration for a marine geometry can be successfully achieved by a frequency-division encoding strategy, as long as crosstalk-prone sources are segregated in their spectral content. This is both the strength and the potential limitation of this method. © 2012 European Association of Geoscientists & Engineers.

Multisource least-squares migration of marine streamer and land data with frequency-division encoding

KAUST Repository

Huang, Yunsong

2012-05-22

Multisource migration of phase-encoded supergathers has shown great promise in reducing the computational cost of conventional migration. The accompanying crosstalk noise, in addition to the migration footprint, can be reduced by least-squares inversion. But the application of this approach to marine streamer data is hampered by the mismatch between the limited number of live traces/shot recorded in the field and the pervasive number of traces generated by the finite-difference modelling method. This leads to a strong mismatch in the misfit function and results in strong artefacts (crosstalk) in the multisource least-squares migration image. To eliminate this noise, we present a frequency-division multiplexing (FDM) strategy with iterative least-squares migration (ILSM) of supergathers. The key idea is, at each ILSM iteration, to assign a unique frequency band to each shot gather. In this case there is no overlap in the crosstalk spectrum of each migrated shot gather m(x, ω i), so the spectral crosstalk product m(x, ω i)m(x, ω j) =δ i, j is zero, unless i=j. Our results in applying this method to 2D marine data for a SEG/EAGE salt model show better resolved images than standard migration computed at about 1/10 th of the cost. Similar results are achieved after applying this method to synthetic data for a 3D SEG/EAGE salt model, except the acquisition geometry is similar to that of a marine OBS survey. Here, the speedup of this method over conventional migration is more than 10. We conclude that multisource migration for a marine geometry can be successfully achieved by a frequency-division encoding strategy, as long as crosstalk-prone sources are segregated in their spectral content. This is both the strength and the potential limitation of this method. © 2012 European Association of Geoscientists & Engineers.

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 ...

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.

Multisource least-squares reverse-time migration with structure-oriented filtering

Science.gov (United States)

Fan, Jing-Wen; Li, Zhen-Chun; Zhang, Kai; Zhang, Min; Liu, Xue-Tong

2016-09-01

The technology of simultaneous-source acquisition of seismic data excited by several sources can significantly improve the data collection efficiency. However, direct imaging of simultaneous-source data or blended data may introduce crosstalk noise and affect the imaging quality. To address this problem, we introduce a structure-oriented filtering operator as preconditioner into the multisource least-squares reverse-time migration (LSRTM). The structure-oriented filtering operator is a nonstationary filter along structural trends that suppresses crosstalk noise while maintaining structural information. The proposed method uses the conjugate-gradient method to minimize the mismatch between predicted and observed data, while effectively attenuating the interference noise caused by exciting several sources simultaneously. Numerical experiments using synthetic data suggest that the proposed method can suppress the crosstalk noise and produce highly accurate images.

A principal-component and least-squares method for allocating polycyclic aromatic hydrocarbons in sediment to multiple sources

International Nuclear Information System (INIS)

Burns, W.A.; Mankiewicz, P.J.; Bence, A.E.; Page, D.S.; Parker, K.R.

1997-01-01

A method was developed to allocate polycyclic aromatic hydrocarbons (PAHs) in sediment samples to the PAH sources from which they came. The method uses principal-component analysis to identify possible sources and a least-squares model to find the source mix that gives the best fit of 36 PAH analytes in each sample. The method identified 18 possible PAH sources in a large set of field data collected in Prince William Sound, Alaska, USA, after the 1989 Exxon Valdez oil spill, including diesel oil, diesel soot, spilled crude oil in various weathering states, natural background, creosote, and combustion products from human activities and forest fires. Spill oil was generally found to be a small increment of the natural background in subtidal sediments, whereas combustion products were often the predominant sources for subtidal PAHs near sites of past or present human activity. The method appears to be applicable to other situations, including other spills

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.

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

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.

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.

Least square fitting of low resolution gamma ray spectra with cubic B-spline basis functions

International Nuclear Information System (INIS)

Zhu Menghua; Liu Lianggang; Qi Dongxu; You Zhong; Xu Aoao

2009-01-01

In this paper, the least square fitting method with the cubic B-spline basis functions is derived to reduce the influence of statistical fluctuations in the gamma ray spectra. The derived procedure is simple and automatic. The results show that this method is better than the convolution method with a sufficient reduction of statistical fluctuation. (authors)

A Local Weighted Nearest Neighbor Algorithm and a Weighted and Constrained Least-Squared Method for Mixed Odor Analysis by Electronic Nose Systems

Directory of Open Access Journals (Sweden)

Jyuo-Min Shyu

2010-11-01

Full Text Available A great deal of work has been done to develop techniques for odor analysis by electronic nose systems. These analyses mostly focus on identifying a particular odor by comparing with a known odor dataset. However, in many situations, it would be more practical if each individual odorant could be determined directly. This paper proposes two methods for such odor components analysis for electronic nose systems. First, a K-nearest neighbor (KNN-based local weighted nearest neighbor (LWNN algorithm is proposed to determine the components of an odor. According to the component analysis, the odor training data is firstly categorized into several groups, each of which is represented by its centroid. The examined odor is then classified as the class of the nearest centroid. The distance between the examined odor and the centroid is calculated based on a weighting scheme, which captures the local structure of each predefined group. To further determine the concentration of each component, odor models are built by regressions. Then, a weighted and constrained least-squares (WCLS method is proposed to estimate the component concentrations. Experiments were carried out to assess the effectiveness of the proposed methods. The LWNN algorithm is able to classify mixed odors with different mixing ratios, while the WCLS method can provide good estimates on component concentrations.

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.

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.

A least-squares/finite element method for the numerical solution of the Navier–Stokes-Cahn–Hilliard system modeling the motion of the contact line

KAUST Repository

He, Qiaolin; Glowinski, Roland; Wang, Xiao Ping

2011-01-01

element space approximation with a time discretization by operator-splitting. To solve the Cahn-Hilliard part of the problem, we use a least-squares/conjugate gradient method. We also show that the scheme has the total energy decaying in time property

TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods

Energy Technology Data Exchange (ETDEWEB)

Bouaricha, A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.; Schnabel, R.B. [Colorado Univ., Boulder, CO (United States). Dept. of Computer Science

1996-12-31

This paper describes a modular software package for solving systems of nonlinear equations and nonlinear least squares problems, using a new class of methods called tensor methods. It is intended for small to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or approximate it by finite differences at each iteration. The software allows the user to select between a tensor method and a standard method based upon a linear model. The tensor method models F({ital x}) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies, a line search and a two- dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small and medium-sized problems in iterations and function evaluations.

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.

The current strain distribution in the North China Basin of eastern China by least-squares collocation

Science.gov (United States)

Wu, J. C.; Tang, H. W.; Chen, Y. Q.; Li, Y. X.

2006-07-01

In this paper, the velocities of 154 stations obtained in 2001 and 2003 GPS survey campaigns are applied to formulate a continuous velocity field by the least-squares collocation method. The strain rate field obtained by the least-squares collocation method shows more clear deformation patterns than that of the conventional discrete triangle method. The significant deformation zones obtained are mainly located in three places, to the north of Tangshan, between Tianjing and Shijiazhuang, and to the north of Datong, which agree with the places of the Holocene active deformation zones obtained by geological investigations. The maximum shear strain rate is located at latitude 38.6°N and longitude 116.8°E, with a magnitude of 0.13 ppm/a. The strain rate field obtained can be used for earthquake prediction research in the North China Basin.

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.

Battery state-of-charge estimation using approximate least squares

Science.gov (United States)

Unterrieder, C.; Zhang, C.; Lunglmayr, M.; Priewasser, R.; Marsili, S.; Huemer, M.

2015-03-01

In recent years, much effort has been spent to extend the runtime of battery-powered electronic applications. In order to improve the utilization of the available cell capacity, high precision estimation approaches for battery-specific parameters are needed. In this work, an approximate least squares estimation scheme is proposed for the estimation of the battery state-of-charge (SoC). The SoC is determined based on the prediction of the battery's electromotive force. The proposed approach allows for an improved re-initialization of the Coulomb counting (CC) based SoC estimation method. Experimental results for an implementation of the estimation scheme on a fuel gauge system on chip are illustrated. Implementation details and design guidelines are presented. The performance of the presented concept is evaluated for realistic operating conditions (temperature effects, aging, standby current, etc.). For the considered test case of a GSM/UMTS load current pattern of a mobile phone, the proposed method is able to re-initialize the CC-method with a high accuracy, while state-of-the-art methods fail to perform a re-initialization.

Gompertz: A Scilab Program for Estimating Gompertz Curve Using Gauss-Newton Method of Least Squares

Directory of Open Access Journals (Sweden)

Surajit Ghosh Dastidar

2006-04-01

Full Text Available A computer program for estimating Gompertz curve using Gauss-Newton method of least squares is described in detail. It is based on the estimation technique proposed in Reddy (1985. The program is developed using Scilab (version 3.1.1, a freely available scientific software package that can be downloaded from http://www.scilab.org/. Data is to be fed into the program from an external disk file which should be in Microsoft Excel format. The output will contain sample size, tolerance limit, a list of initial as well as the final estimate of the parameters, standard errors, value of Gauss-Normal equations namely GN1 GN2 and GN3 , No. of iterations, variance(σ2 , Durbin-Watson statistic, goodness of fit measures such as R2 , D value, covariance matrix and residuals. It also displays a graphical output of the estimated curve vis a vis the observed curve. It is an improved version of the program proposed in Dastidar (2005.

Gompertz: A Scilab Program for Estimating Gompertz Curve Using Gauss-Newton Method of Least Squares

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Surajit Ghosh Dastidar

2006-04-01

Full Text Available A computer program for estimating Gompertz curve using Gauss-Newton method of least squares is described in detail. It is based on the estimation technique proposed in Reddy (1985. The program is developed using Scilab (version 3.1.1, a freely available scientific software package that can be downloaded from http://www.scilab.org/. Data is to be fed into the program from an external disk file which should be in Microsoft Excel format. The output will contain sample size, tolerance limit, a list of initial as well as the final estimate of the parameters, standard errors, value of Gauss-Normal equations namely GN1 GN2 and GN3, No. of iterations, variance(σ2, Durbin-Watson statistic, goodness of fit measures such as R2, D value, covariance matrix and residuals. It also displays a graphical output of the estimated curve vis a vis the observed curve. It is an improved version of the program proposed in Dastidar (2005.

Study of the convergence behavior of the complex kernel least mean square algorithm.

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Paul, Thomas K; Ogunfunmi, Tokunbo

2013-09-01

The complex kernel least mean square (CKLMS) algorithm is recently derived and allows for online kernel adaptive learning for complex data. Kernel adaptive methods can be used in finding solutions for neural network and machine learning applications. The derivation of CKLMS involved the development of a modified Wirtinger calculus for Hilbert spaces to obtain the cost function gradient. We analyze the convergence of the CKLMS with different kernel forms for complex data. The expressions obtained enable us to generate theory-predicted mean-square error curves considering the circularity of the complex input signals and their effect on nonlinear learning. Simulations are used for verifying the analysis results.

Time series modeling with pruned multi-layer perceptron and 2-stage damped least-squares method

International Nuclear Information System (INIS)

Voyant, Cyril; Tamas, Wani; Paoli, Christophe; Balu, Aurélia; Muselli, Marc; Nivet, Marie-Laure; Notton, Gilles

2014-01-01

A Multi-Layer Perceptron (MLP) defines a family of artificial neural networks often used in TS modeling and forecasting. Because of its ''black box'' aspect, many researchers refuse to use it. Moreover, the optimization (often based on the exhaustive approach where ''all'' configurations are tested) and learning phases of this artificial intelligence tool (often based on the Levenberg-Marquardt algorithm; LMA) are weaknesses of this approach (exhaustively and local minima). These two tasks must be repeated depending on the knowledge of each new problem studied, making the process, long, laborious and not systematically robust. In this paper a pruning process is proposed. This method allows, during the training phase, to carry out an inputs selecting method activating (or not) inter-nodes connections in order to verify if forecasting is improved. We propose to use iteratively the popular damped least-squares method to activate inputs and neurons. A first pass is applied to 10% of the learning sample to determine weights significantly different from 0 and delete other. Then a classical batch process based on LMA is used with the new MLP. The validation is done using 25 measured meteorological TS and cross-comparing the prediction results of the classical LMA and the 2-stage LMA

Comparison of least squares and exponential sine sweep methods for Parallel Hammerstein Models estimation

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Rebillat, Marc; Schoukens, Maarten

2018-05-01

Linearity is a common assumption for many real-life systems, but in many cases the nonlinear behavior of systems cannot be ignored and must be modeled and estimated. Among the various existing classes of nonlinear models, Parallel Hammerstein Models (PHM) are interesting as they are at the same time easy to interpret as well as to estimate. One way to estimate PHM relies on the fact that the estimation problem is linear in the parameters and thus that classical least squares (LS) estimation algorithms can be used. In that area, this article introduces a regularized LS estimation algorithm inspired on some of the recently developed regularized impulse response estimation techniques. Another mean to estimate PHM consists in using parametric or non-parametric exponential sine sweeps (ESS) based methods. These methods (LS and ESS) are founded on radically different mathematical backgrounds but are expected to tackle the same issue. A methodology is proposed here to compare them with respect to (i) their accuracy, (ii) their computational cost, and (iii) their robustness to noise. Tests are performed on simulated systems for several values of methods respective parameters and of signal to noise ratio. Results show that, for a given set of data points, the ESS method is less demanding in computational resources than the LS method but that it is also less accurate. Furthermore, the LS method needs parameters to be set in advance whereas the ESS method is not subject to conditioning issues and can be fully non-parametric. In summary, for a given set of data points, ESS method can provide a first, automatic, and quick overview of a nonlinear system than can guide more computationally demanding and precise methods, such as the regularized LS one proposed here.

Evaluation of the prediction precision capability of partial least squares regression approach for analysis of high alloy steel by laser induced breakdown spectroscopy

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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).

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.

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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.