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

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

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.

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

Newton-Gauss Algorithm of Robust Weighted Total Least Squares Model

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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.

Least-squares approximation of an improper correlation matrix by a proper one

NARCIS (Netherlands)

Knol, Dirk L.; ten Berge, Jos M.F.

1989-01-01

An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based upon a solution for Mosier's oblique Procrustes rotation problem offered by ten Berge and Nevels. A necessary and

A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems.

Science.gov (United States)

Kazemi, Mahdi; Arefi, Mohammad Mehdi

2017-03-01

In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

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

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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.

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.

New recursive-least-squares algorithms for nonlinear active control of sound and vibration using neural networks.

Science.gov (United States)

Bouchard, M

2001-01-01

In recent years, a few articles describing the use of neural networks for nonlinear active control of sound and vibration were published. Using a control structure with two multilayer feedforward neural networks (one as a nonlinear controller and one as a nonlinear plant model), steepest descent algorithms based on two distinct gradient approaches were introduced for the training of the controller network. The two gradient approaches were sometimes called the filtered-x approach and the adjoint approach. Some recursive-least-squares algorithms were also introduced, using the adjoint approach. In this paper, an heuristic procedure is introduced for the development of recursive-least-squares algorithms based on the filtered-x and the adjoint gradient approaches. This leads to the development of new recursive-least-squares algorithms for the training of the controller neural network in the two networks structure. These new algorithms produce a better convergence performance than previously published algorithms. Differences in the performance of algorithms using the filtered-x and the adjoint gradient approaches are discussed in the paper. The computational load of the algorithms discussed in the paper is evaluated for multichannel systems of nonlinear active control. Simulation results are presented to compare the convergence performance of the algorithms, showing the convergence gain provided by the new algorithms.

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

Science.gov (United States)

Schaffrin, Burkhard; Felus, Yaron A.

2008-06-01

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

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

Science.gov (United States)

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

2008-11-11

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

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

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.

Does model fit decrease the uncertainty of the data in comparison with a general non-model least squares fit?

International Nuclear Information System (INIS)

Pronyaev, V.G.

2003-01-01

The information entropy is taken as a measure of knowledge about the object and the reduced univariante variance as a common measure of uncertainty. Covariances in the model versus non-model least square fits are discussed

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

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ELİF BULUT

2013-06-01

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

Least-Squares Approximation of an Improper Correlation Matrix by a Proper One.

Science.gov (United States)

Knol, Dirk L.; ten Berge, Jos M. F.

1989-01-01

An algorithm, based on a solution for C. I. Mosier's oblique Procrustes rotation problem, is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. Results are of interest for missing value and tetrachoric correlation, indefinite matrix correlation, and constrained…

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

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

Single Directional SMO Algorithm for Least Squares Support Vector Machines

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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.

Least-squares fit of a linear combination of functions

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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.

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.

Application of the tuning algorithm with the least squares approximation to the suboptimal control algorithm for integrating objects

Science.gov (United States)

Kuzishchin, V. F.; Merzlikina, E. I.; Van Va, Hoang

2017-11-01

The problem of PID and PI-algorithms tuning by means of the approximation by the least square method of the frequency response of a linear algorithm to the sub-optimal algorithm is considered. The advantage of the method is that the parameter values are obtained through one cycle of calculation. Recommendations how to choose the parameters of the least square method taking into consideration the plant dynamics are given. The parameters mentioned are the time constant of the filter, the approximation frequency range and the correction coefficient for the time delay parameter. The problem is considered for integrating plants for some practical cases (the level control system in a boiler drum). The transfer function of the suboptimal algorithm is determined relating to the disturbance that acts in the point of the control impact input, it is typical for thermal plants. In the recommendations it is taken into consideration that the overregulation for the transient process when the setpoint is changed is also limited. In order to compare the results the systems under consideration are also calculated by the classical method with the limited frequency oscillation index. The results given in the paper can be used by specialists dealing with tuning systems with the integrating plants.

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 approximation of an improper by a proper correlation matrix using a semi-infinite convex program

NARCIS (Netherlands)

Knol, Dirk L.; ten Berge, Jos M.F.

1987-01-01

An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based on a solution for C. I. Mosier's oblique Procrustes rotation problem offered by J. M. F. ten Berge and K. Nevels (1977).

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 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)

Polynomial curve fitting for control rod worth using least square numerical analysis

International Nuclear Information System (INIS)

Muhammad Husamuddin Abdul Khalil; Mark Dennis Usang; Julia Abdul Karim; Mohd Amin Sharifuldin Salleh

2012-01-01

RTP must have sufficient excess reactivity to compensate the negative reactivity feedback effects such as those caused by the fuel temperature and power defects of reactivity, fuel burn-up and to allow full power operation for predetermined period of time. To compensate this excess reactivity, it is necessary to introduce an amount of negative reactivity by adjusting or controlling the control rods at will. Control rod worth depends largely upon the value of the neutron flux at the location of the rod and reflected by a polynomial curve. Purpose of this paper is to rule out the polynomial curve fitting using least square numerical techniques via MATLAB compatible language. (author)

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

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

Douglas Gardner, C.

1980-01-01

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

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.

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)

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.

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)

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)

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

Science.gov (United States)

Mizutani, Eiji; Demmel, James W

2003-01-01

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

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.

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.

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

Extension of least squares spectral resolution algorithm to high-resolution lipidomics data

Energy Technology Data Exchange (ETDEWEB)

Zeng, Ying-Xu [Department of Chemistry, University of Bergen, PO Box 7803, N-5020 Bergen (Norway); Mjøs, Svein Are, E-mail: svein.mjos@kj.uib.no [Department of Chemistry, University of Bergen, PO Box 7803, N-5020 Bergen (Norway); David, Fabrice P.A. [Bioinformatics and Biostatistics Core Facility, School of Life Sciences, Ecole Polytechnique Fédérale de Lausanne (EPFL) and Swiss Institute of Bioinformatics (SIB), Lausanne (Switzerland); Schmid, Adrien W. [Proteomics Core Facility, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne (Switzerland)

2016-03-31

Lipidomics, which focuses on the global study of molecular lipids in biological systems, has been driven tremendously by technical advances in mass spectrometry (MS) instrumentation, particularly high-resolution MS. This requires powerful computational tools that handle the high-throughput lipidomics data analysis. To address this issue, a novel computational tool has been developed for the analysis of high-resolution MS data, including the data pretreatment, visualization, automated identification, deconvolution and quantification of lipid species. The algorithm features the customized generation of a lipid compound library and mass spectral library, which covers the major lipid classes such as glycerolipids, glycerophospholipids and sphingolipids. Next, the algorithm performs least squares resolution of spectra and chromatograms based on the theoretical isotope distribution of molecular ions, which enables automated identification and quantification of molecular lipid species. Currently, this methodology supports analysis of both high and low resolution MS as well as liquid chromatography-MS (LC-MS) lipidomics data. The flexibility of the methodology allows it to be expanded to support more lipid classes and more data interpretation functions, making it a promising tool in lipidomic data analysis. - Highlights: • A flexible strategy for analyzing MS and LC-MS data of lipid molecules is proposed. • Isotope distribution spectra of theoretically possible compounds were generated. • High resolution MS and LC-MS data were resolved by least squares spectral resolution. • The method proposed compounds that are likely to occur in the analyzed samples. • The proposed compounds matched results from manual interpretation of fragment spectra.

Extension of least squares spectral resolution algorithm to high-resolution lipidomics data

International Nuclear Information System (INIS)

Zeng, Ying-Xu; Mjøs, Svein Are; David, Fabrice P.A.; Schmid, Adrien W.

2016-01-01

Lipidomics, which focuses on the global study of molecular lipids in biological systems, has been driven tremendously by technical advances in mass spectrometry (MS) instrumentation, particularly high-resolution MS. This requires powerful computational tools that handle the high-throughput lipidomics data analysis. To address this issue, a novel computational tool has been developed for the analysis of high-resolution MS data, including the data pretreatment, visualization, automated identification, deconvolution and quantification of lipid species. The algorithm features the customized generation of a lipid compound library and mass spectral library, which covers the major lipid classes such as glycerolipids, glycerophospholipids and sphingolipids. Next, the algorithm performs least squares resolution of spectra and chromatograms based on the theoretical isotope distribution of molecular ions, which enables automated identification and quantification of molecular lipid species. Currently, this methodology supports analysis of both high and low resolution MS as well as liquid chromatography-MS (LC-MS) lipidomics data. The flexibility of the methodology allows it to be expanded to support more lipid classes and more data interpretation functions, making it a promising tool in lipidomic data analysis. - Highlights: • A flexible strategy for analyzing MS and LC-MS data of lipid molecules is proposed. • Isotope distribution spectra of theoretically possible compounds were generated. • High resolution MS and LC-MS data were resolved by least squares spectral resolution. • The method proposed compounds that are likely to occur in the analyzed samples. • The proposed compounds matched results from manual interpretation of fragment spectra.

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.

Respiratory mechanics by least squares fitting in mechanically ventilated patients: application on flow-limited COPD patients.

Science.gov (United States)

Volta, Carlo A; Marangoni, Elisabetta; Alvisi, Valentina; Capuzzo, Maurizia; Ragazzi, Riccardo; Pavanelli, Lina; Alvisi, Raffaele

2002-01-01

Although computerized methods of analyzing respiratory system mechanics such as the least squares fitting method have been used in various patient populations, no conclusive data are available in patients with chronic obstructive pulmonary disease (COPD), probably because they may develop expiratory flow limitation (EFL). This suggests that respiratory mechanics be determined only during inspiration. Eight-bed multidisciplinary ICU of a teaching hospital. Eight non-flow-limited postvascular surgery patients and eight flow-limited COPD patients. Patients were sedated, paralyzed for diagnostic purposes, and ventilated in volume control ventilation with constant inspiratory flow rate. Data on resistance, compliance, and dynamic intrinsic positive end-expiratory pressure (PEEPi,dyn) obtained by applying the least squares fitting method during inspiration, expiration, and the overall breathing cycle were compared with those obtained by the traditional method (constant flow, end-inspiratory occlusion method). Our results indicate that (a) the presence of EFL markedly decreases the precision of resistance and compliance values measured by the LSF method, (b) the determination of respiratory variables during inspiration allows the calculation of respiratory mechanics in flow limited COPD patients, and (c) the LSF method is able to detect the presence of PEEPi,dyn if only inspiratory data are used.

The derivation of vector magnetic fields from Stokes profiles - Integral versus least squares fitting techniques

Science.gov (United States)

Ronan, R. S.; Mickey, D. L.; Orrall, F. Q.

1987-01-01

The results of two methods for deriving photospheric vector magnetic fields from the Zeeman effect, as observed in the Fe I line at 6302.5 A at high spectral resolution (45 mA), are compared. The first method does not take magnetooptical effects into account, but determines the vector magnetic field from the integral properties of the Stokes profiles. The second method is an iterative least-squares fitting technique which fits the observed Stokes profiles to the profiles predicted by the Unno-Rachkovsky solution to the radiative transfer equation. For sunspot fields above about 1500 gauss, the two methods are found to agree in derived azimuthal and inclination angles to within about + or - 20 deg.

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.

LOGISTIC FUNCTION PROFILE FIT: A least-squares program for fitting interface profiles to an extended logistic function

International Nuclear Information System (INIS)

Kirchhoff, William H.

2012-01-01

The extended logistic function provides a physically reasonable description of interfaces such as depth profiles or line scans of surface topological or compositional features. It describes these interfaces with the minimum number of parameters, namely, position, width, and asymmetry. Logistic Function Profile Fit (LFPF) is a robust, least-squares fitting program in which the nonlinear extended logistic function is linearized by a Taylor series expansion (equivalent to a Newton–Raphson approach) with no apparent introduction of bias in the analysis. The program provides reliable confidence limits for the parameters when systematic errors are minimal and provides a display of the residuals from the fit for the detection of systematic errors. The program will aid researchers in applying ASTM E1636-10, “Standard practice for analytically describing sputter-depth-profile and linescan-profile data by an extended logistic function,” and may also prove useful in applying ISO 18516: 2006, “Surface chemical analysis—Auger electron spectroscopy and x-ray photoelectron spectroscopy—determination of lateral resolution.” Examples are given of LFPF fits to a secondary ion mass spectrometry depth profile, an Auger surface line scan, and synthetic data generated to exhibit known systematic errors for examining the significance of such errors to the extrapolation of partial profiles.

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

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

Science.gov (United States)

Xu, Yu-Lin

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

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.

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

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.

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.

Identifying ambiguous prostate gland contours from histology using capsule shape information and least squares curve fitting

Energy Technology Data Exchange (ETDEWEB)

Hussein, Rania [DigiPen Institute of Technology, Department of Computer Engineering, Redmond, WA (United States); McKenzie, Frederic D. [Old Dominion University, Department of Electrical and Computer Engineering, Norfolk, VA (United States)

2007-12-15

To obtain an accurate assessment of the percentage and depth of extra-capsular soft tissue removed with the prostate by the various surgical techniques in order to help surgeons in determining the appropriateness of different surgical approaches. This can be enhanced by an accurate and automated means of identifying the prostate gland contour. To facilitate 3D reconstruction and, ultimately, more accurate analyses, it is essential for us to identify the capsule boundary that separates the prostate gland tissue from its extra-capsular tissue. However, the capsule is sometimes unrecognizable due to the naturally occurring intrusion of muscle and connective tissue into the prostate gland. At these regions where the capsule disappears, its contour can be arbitrarily created with a continuing contour line based on the natural shape of the prostate. We utilize an algorithm based on a least squares curve fitting technique that uses a prostate shape equation to merge previously detected capsule parts with the shape equation to produce an approximated curve that represents the prostate capsule. We have tested our algorithm using three different shapes on 13 histologic prostate slices that are cut at different locations from the apex. The best result shows a 90% average contour match when compared to pathologist-drawn contours. We believe that automatically identifying histologic prostate contours will lead to increased objective analyses of surgical margins and extracapsular spread of cancer. Our results show that this is achievable. (orig.)

Identifying ambiguous prostate gland contours from histology using capsule shape information and least squares curve fitting

International Nuclear Information System (INIS)

Hussein, Rania; McKenzie, Frederic D.

2007-01-01

To obtain an accurate assessment of the percentage and depth of extra-capsular soft tissue removed with the prostate by the various surgical techniques in order to help surgeons in determining the appropriateness of different surgical approaches. This can be enhanced by an accurate and automated means of identifying the prostate gland contour. To facilitate 3D reconstruction and, ultimately, more accurate analyses, it is essential for us to identify the capsule boundary that separates the prostate gland tissue from its extra-capsular tissue. However, the capsule is sometimes unrecognizable due to the naturally occurring intrusion of muscle and connective tissue into the prostate gland. At these regions where the capsule disappears, its contour can be arbitrarily created with a continuing contour line based on the natural shape of the prostate. We utilize an algorithm based on a least squares curve fitting technique that uses a prostate shape equation to merge previously detected capsule parts with the shape equation to produce an approximated curve that represents the prostate capsule. We have tested our algorithm using three different shapes on 13 histologic prostate slices that are cut at different locations from the apex. The best result shows a 90% average contour match when compared to pathologist-drawn contours. We believe that automatically identifying histologic prostate contours will lead to increased objective analyses of surgical margins and extracapsular spread of cancer. Our results show that this is achievable. (orig.)

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

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.

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.

Baseline correction combined partial least squares algorithm and its application in on-line Fourier transform infrared quantitative analysis.

Science.gov (United States)

Peng, Jiangtao; Peng, Silong; Xie, Qiong; Wei, Jiping

2011-04-01

In order to eliminate the lower order polynomial interferences, a new quantitative calibration algorithm "Baseline Correction Combined Partial Least Squares (BCC-PLS)", which combines baseline correction and conventional PLS, is proposed. By embedding baseline correction constraints into PLS weights selection, the proposed calibration algorithm overcomes the uncertainty in baseline correction and can meet the requirement of on-line attenuated total reflectance Fourier transform infrared (ATR-FTIR) quantitative analysis. The effectiveness of the algorithm is evaluated by the analysis of glucose and marzipan ATR-FTIR spectra. BCC-PLS algorithm shows improved prediction performance over PLS. The root mean square error of cross-validation (RMSECV) on marzipan spectra for the prediction of the moisture is found to be 0.53%, w/w (range 7-19%). The sugar content is predicted with a RMSECV of 2.04%, w/w (range 33-68%). Copyright © 2011 Elsevier B.V. All rights reserved.

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 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...

Analysis of quantile regression as alternative to ordinary least squares

OpenAIRE

Ibrahim Abdullahi; Abubakar Yahaya

2015-01-01

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

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

Fitting of two and three variant polynomials from experimental data through the least squares method. (Using of the codes AJUS-2D, AJUS-3D and LEGENDRE-2D)

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. (Author) 10 refs

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

Analysis of Shift and Deformation of Planar Surfaces Using the Least Squares Plane

Directory of Open Access Journals (Sweden)

Hrvoje Matijević

2006-12-01

Full Text Available Modern methods of measurement developed on the basis of advanced reflectorless distance measurement have paved the way for easier detection and analysis of shift and deformation. A large quantity of collected data points will often require a mathematical model of the surface that fits best into these. Although this can be a complex task, in the case of planar surfaces it is easily done, enabling further processing and analysis of measurement results. The paper describes the fitting of a plane to a set of collected points using the least squares distance, with previously excluded outliers via the RANSAC algorithm. Based on that, a method for analysis of the deformation and shift of planar surfaces is also described.

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).

Least mean square fourth based microgrid state estimation algorithm using the internet of things technology.

Science.gov (United States)

Rana, Md Masud

2017-01-01

This paper proposes an innovative internet of things (IoT) based communication framework for monitoring microgrid under the condition of packet dropouts in measurements. First of all, the microgrid incorporating the renewable distributed energy resources is represented by a state-space model. The IoT embedded wireless sensor network is adopted to sense the system states. Afterwards, the information is transmitted to the energy management system using the communication network. Finally, the least mean square fourth algorithm is explored for estimating the system states. The effectiveness of the developed approach is verified through numerical simulations.

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.

Proportionate-type normalized last mean square algorithms

CERN Document Server

Wagner, Kevin

2013-01-01

The topic of this book is proportionate-type normalized least mean squares (PtNLMS) adaptive filtering algorithms, which attempt to estimate an unknown impulse response by adaptively giving gains proportionate to an estimate of the impulse response and the current measured error. These algorithms offer low computational complexity and fast convergence times for sparse impulse responses in network and acoustic echo cancellation applications. New PtNLMS algorithms are developed by choosing gains that optimize user-defined criteria, such as mean square error, at all times. PtNLMS algorithms ar

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.

An improved algorithm for the determination of the system parameters of a visual binary by least squares

International Nuclear Information System (INIS)

Xu, Yu-Lin.

1988-01-01

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

Damped least square based genetic algorithm with Gaussian distribution of damping factor for singularity-robust inverse kinematics

International Nuclear Information System (INIS)

Phuoc, Le Minh; Lee, Suk Han; Kim, Hun Mo; Martinet, Philippe

2008-01-01

Robot inverse kinematics based on Jacobian inversion encounters critical issues of kinematic singularities. In this paper, several techniques based on damped least squares are proposed to lead robot pass through kinematic singularities without excessive joint velocities. Unlike other work in which the same damping factor is used for all singular vectors, this paper proposes a different damping coefficient for each singular vector based on corresponding singular value of the Jacobian. Moreover, a continuous distribution of damping factor following Gaussian function guarantees the continuous in joint velocities. A genetic algorithm is utilized to search for the best maximum damping factor and singular region, which used to require ad hoc searching in other works. As a result, end effector tracking error, which is inherited from damped least squares by introducing damping factors, is minimized. The effectiveness of our approach is compared with other methods in both non-redundant robot and redundant robot

Damped least square based genetic algorithm with Gaussian distribution of damping factor for singularity-robust inverse kinematics

Energy Technology Data Exchange (ETDEWEB)

Phuoc, Le Minh; Lee, Suk Han; Kim, Hun Mo [Sungkyunkwan University, Suwon (Korea, Republic of); Martinet, Philippe [Blaise Pascal University, Clermont-Ferrand Cedex (France)

2008-07-15

Robot inverse kinematics based on Jacobian inversion encounters critical issues of kinematic singularities. In this paper, several techniques based on damped least squares are proposed to lead robot pass through kinematic singularities without excessive joint velocities. Unlike other work in which the same damping factor is used for all singular vectors, this paper proposes a different damping coefficient for each singular vector based on corresponding singular value of the Jacobian. Moreover, a continuous distribution of damping factor following Gaussian function guarantees the continuous in joint velocities. A genetic algorithm is utilized to search for the best maximum damping factor and singular region, which used to require ad hoc searching in other works. As a result, end effector tracking error, which is inherited from damped least squares by introducing damping factors, is minimized. The effectiveness of our approach is compared with other methods in both non-redundant robot and redundant robot

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

Science.gov (United States)

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

2009-06-01

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

Least mean square fourth based microgrid state estimation algorithm using the internet of things technology.

Directory of Open Access Journals (Sweden)

Md Masud Rana

Full Text Available This paper proposes an innovative internet of things (IoT based communication framework for monitoring microgrid under the condition of packet dropouts in measurements. First of all, the microgrid incorporating the renewable distributed energy resources is represented by a state-space model. The IoT embedded wireless sensor network is adopted to sense the system states. Afterwards, the information is transmitted to the energy management system using the communication network. Finally, the least mean square fourth algorithm is explored for estimating the system states. The effectiveness of the developed approach is verified through numerical simulations.

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-12-15

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

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

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.

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

Science.gov (United States)

de Renstrom, Pawel Brückman; Haywood, Stephen

2006-04-01

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

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.

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.

Application of the Polynomial-Based Least Squares and Total Least Squares Models for the Attenuated Total Reflection Fourier Transform Infrared Spectra of Binary Mixtures of Hydroxyl Compounds.

Science.gov (United States)

Shan, Peng; Peng, Silong; Zhao, Yuhui; Tang, Liang

2016-03-01

An analysis of binary mixtures of hydroxyl compound by Attenuated Total Reflection Fourier transform infrared spectroscopy (ATR FT-IR) and classical least squares (CLS) yield large model error due to the presence of unmodeled components such as H-bonded components. To accommodate these spectral variations, polynomial-based least squares (LSP) and polynomial-based total least squares (TLSP) are proposed to capture the nonlinear absorbance-concentration relationship. LSP is based on assuming that only absorbance noise exists; while TLSP takes both absorbance noise and concentration noise into consideration. In addition, based on different solving strategy, two optimization algorithms (limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm and Levenberg-Marquardt (LM) algorithm) are combined with TLSP and then two different TLSP versions (termed as TLSP-LBFGS and TLSP-LM) are formed. The optimum order of each nonlinear model is determined by cross-validation. Comparison and analyses of the four models are made from two aspects: absorbance prediction and concentration prediction. The results for water-ethanol solution and ethanol-ethyl lactate solution show that LSP, TLSP-LBFGS, and TLSP-LM can, for both absorbance prediction and concentration prediction, obtain smaller root mean square error of prediction than CLS. Additionally, they can also greatly enhance the accuracy of estimated pure component spectra. However, from the view of concentration prediction, the Wilcoxon signed rank test shows that there is no statistically significant difference between each nonlinear model and CLS. © The Author(s) 2016.

Fitting polynomial surfaces to triangular meshes with Voronoi Squared Distance Minimization

KAUST Repository

Nivoliers, Vincent; Yan, Dongming; Lé vy, Bruno L.

2011-01-01

This paper introduces Voronoi Squared Distance Minimization (VSDM), an algorithm that fits a surface to an input mesh. VSDM minimizes an objective function that corresponds to a Voronoi-based approximation of the overall squared distance function

Fitting polynomial surfaces to triangular meshes with Voronoi squared distance minimization

KAUST Repository

Nivoliers, Vincent; Yan, Dongming; Lé vy, Bruno L.

2012-01-01

This paper introduces Voronoi squared distance minimization (VSDM), an algorithm that fits a surface to an input mesh. VSDM minimizes an objective function that corresponds to a Voronoi-based approximation of the overall squared distance function

Beam-hardening correction by a surface fitting and phase classification by a least square support vector machine approach for tomography images of geological samples

Science.gov (United States)

Khan, F.; Enzmann, F.; Kersten, M.

2015-12-01

In X-ray computed microtomography (μXCT) image processing is the most important operation prior to image analysis. Such processing mainly involves artefact reduction and image segmentation. We propose a new two-stage post-reconstruction procedure of an image of a geological rock core obtained by polychromatic cone-beam μXCT technology. In the first stage, the beam-hardening (BH) is removed applying a best-fit quadratic surface algorithm to a given image data set (reconstructed slice), which minimizes the BH offsets of the attenuation data points from that surface. The final BH-corrected image is extracted from the residual data, or the difference between the surface elevation values and the original grey-scale values. For the second stage, we propose using a least square support vector machine (a non-linear classifier algorithm) to segment the BH-corrected data as a pixel-based multi-classification task. A combination of the two approaches was used to classify a complex multi-mineral rock sample. The Matlab code for this approach is provided in the Appendix. A minor drawback is that the proposed segmentation algorithm may become computationally demanding in the case of a high dimensional training data set.

DEM GENERATION FROM HIGH RESOLUTION SATELLITE IMAGES THROUGH A NEW 3D LEAST SQUARES MATCHING ALGORITHM

Directory of Open Access Journals (Sweden)

T. Kim

2012-09-01

Full Text Available Automated generation of digital elevation models (DEMs from high resolution satellite images (HRSIs has been an active research topic for many years. However, stereo matching of HRSIs, in particular based on image-space search, is still difficult due to occlusions and building facades within them. Object-space matching schemes, proposed to overcome these problem, often are very time consuming and critical to the dimensions of voxels. In this paper, we tried a new least square matching (LSM algorithm that works in a 3D object space. The algorithm starts with an initial height value on one location of the object space. From this 3D point, the left and right image points are projected. The true height is calculated by iterative least squares estimation based on the grey level differences between the left and right patches centred on the projected left and right points. We tested the 3D LSM to the Worldview images over 'Terrassa Sud' provided by the ISPRS WG I/4. We also compared the performance of the 3D LSM with the correlation matching based on 2D image space and the correlation matching based on 3D object space. The accuracy of the DEM from each method was analysed against the ground truth. Test results showed that 3D LSM offers more accurate DEMs over the conventional matching algorithms. Results also showed that 3D LSM is sensitive to the accuracy of initial height value to start the estimation. We combined the 3D COM and 3D LSM for accurate and robust DEM generation from HRSIs. The major contribution of this paper is that we proposed and validated that LSM can be applied to object space and that the combination of 3D correlation and 3D LSM can be a good solution for automated DEM generation from HRSIs.

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...

Due Date Assignment in a Dynamic Job Shop with the Orthogonal Kernel Least Squares Algorithm

Science.gov (United States)

Yang, D. H.; Hu, L.; Qian, Y.

2017-06-01

Meeting due dates is a key goal in the manufacturing industries. This paper proposes a method for due date assignment (DDA) by using the Orthogonal Kernel Least Squares Algorithm (OKLSA). A simulation model is built to imitate the production process of a highly dynamic job shop. Several factors describing job characteristics and system state are extracted as attributes to predict job flow-times. A number of experiments under conditions of varying dispatching rules and 90% shop utilization level have been carried out to evaluate the effectiveness of OKLSA applied for DDA. The prediction performance of OKLSA is compared with those of five conventional DDA models and back-propagation neural network (BPNN). The experimental results indicate that OKLSA is statistically superior to other DDA models in terms of mean absolute lateness and root mean squares lateness in most cases. The only exception occurs when the shortest processing time rule is used for dispatching jobs, the difference between OKLSA and BPNN is not statistically significant.

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.

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)

An Algorithm for Online Inertia Identification and Load Torque Observation via Adaptive Kalman Observer-Recursive Least Squares

Directory of Open Access Journals (Sweden)

Ming Yang

2018-03-01

Full Text Available In this paper, an on-line parameter identification algorithm to iteratively compute the numerical values of inertia and load torque is proposed. Since inertia and load torque are strongly coupled variables due to the degenerate-rank problem, it is hard to estimate relatively accurate values for them in the cases such as when load torque variation presents or one cannot obtain a relatively accurate priori knowledge of inertia. This paper eliminates this problem and realizes ideal online inertia identification regardless of load condition and initial error. The algorithm in this paper integrates a full-order Kalman Observer and Recursive Least Squares, and introduces adaptive controllers to enhance the robustness. It has a better performance when iteratively computing load torque and moment of inertia. Theoretical sensitivity analysis of the proposed algorithm is conducted. Compared to traditional methods, the validity of the proposed algorithm is proved by simulation and experiment results.

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

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.

Construction of an accurate quartic force field by using generalised least-squares fitting and experimental design

International Nuclear Information System (INIS)

Carbonniere, Philippe; Begue, Didier; Dargelos, Alain; Pouchan, Claude

2004-01-01

In this work we present an attractive least-squares fitting procedure which allows for the calculation of a quartic force field by jointly using energy, gradient, and Hessian data, obtained from electronic wave function calculations on a suitably chosen grid of points. We use the experimental design to select the grid points: a 'simplex-sum' of Box and Behnken grid was chosen for its efficiency and accuracy. We illustrate the numerical implementations of the method by using the energy and gradient data for H 2 O and H 2 CO. The B3LYP/cc-pVTZ quartic force field performed from 11 and 44 simplex-sum configurations shows excellent agreement in comparison to the classical 44 and 168 energy calculations

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

CARS Spectral Fitting with Multiple Resonant Species using Sparse Libraries

Science.gov (United States)

Cutler, Andrew D.; Magnotti, Gaetano

2010-01-01

The dual pump CARS technique is often used in the study of turbulent flames. Fast and accurate algorithms are needed for fitting dual-pump CARS spectra for temperature and multiple chemical species. This paper describes the development of such an algorithm. The algorithm employs sparse libraries, whose size grows much more slowly with number of species than a conventional library. The method was demonstrated by fitting synthetic "experimental" spectra containing 4 resonant species (N2, O2, H2 and CO2), both with noise and without it, and by fitting experimental spectra from a H2-air flame produced by a Hencken burner. In both studies, weighted least squares fitting of signal, as opposed to least squares fitting signal or square-root signal, was shown to produce the least random error and minimize bias error in the fitted parameters.

Least square regularized regression in sum space.

Science.gov (United States)

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

2013-04-01

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

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.

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.

Estimating the Acquisition Price of Enshi Yulu Young Tea Shoots Using Near-Infrared Spectroscopy by the Back Propagation Artificial Neural Network Model in Conjunction with Backward Interval Partial Least Squares Algorithm

Science.gov (United States)

Wang, Sh.-P.; Gong, Z.-M.; Su, X.-Zh.; Liao, J.-Zh.

2017-09-01

Near infrared spectroscopy and the back propagation artificial neural network model in conjunction with backward interval partial least squares algorithm were used to estimate the purchasing price of Enshi yulu young tea shoots. The near-infrared spectra regions most relevant to the tea shoots price model (5700.5-5935.8, 7613.6-7848.9, 8091.8-8327.1, 8331-8566.2, 9287.5-9522.5, and 9526.6-9761.9 cm-1) were selected using backward interval partial least squares algorithm. The first five principal components that explained 99.96% of the variability in those selected spectral data were then used to calibrate the back propagation artificial neural tea shoots purchasing price model. The performance of this model (coefficient of determination for prediction 0.9724; root-mean-square error of prediction 4.727) was superior to those of the back propagation artificial neural model (coefficient of determination for prediction 0.8653, root-mean-square error of prediction 5.125) and the backward interval partial least squares model (coefficient of determination for prediction 0.5932, root-mean-square error of prediction 25.125). The acquisition price model with the combined backward interval partial least squares-back propagation artificial neural network algorithms can evaluate the price of Enshi yulu tea shoots accurately, quickly and objectively.

A Hybrid Least Square Support Vector Machine Model with Parameters Optimization for Stock Forecasting

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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.

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

Science.gov (United States)

Zeb, Salman; Yousaf, Muhammad

2017-01-01

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

A New Hybrid Approach for Wind Speed Prediction Using Fast Block Least Mean Square Algorithm and Artificial Neural Network

Directory of Open Access Journals (Sweden)

Ummuhan Basaran Filik

2016-01-01

Full Text Available A new hybrid wind speed prediction approach, which uses fast block least mean square (FBLMS algorithm and artificial neural network (ANN method, is proposed. FBLMS is an adaptive algorithm which has reduced complexity with a very fast convergence rate. A hybrid approach is proposed which uses two powerful methods: FBLMS and ANN method. In order to show the efficiency and accuracy of the proposed approach, seven-year real hourly collected wind speed data sets belonging to Turkish State Meteorological Service of Bozcaada and Eskisehir regions are used. Two different ANN structures are used to compare with this approach. The first six-year data is handled as a train set; the remaining one-year hourly data is handled as test data. Mean absolute error (MAE and root mean square error (RMSE are used for performance evaluations. It is shown for various cases that the performance of the new hybrid approach gives better results than the different conventional ANN structure.

Annual Electric Load Forecasting by a Least Squares Support Vector Machine with a Fruit Fly Optimization Algorithm

Directory of Open Access Journals (Sweden)

Bao Wang

2012-11-01

Full Text Available The accuracy of annual electric load forecasting plays an important role in the economic and social benefits of electric power systems. The least squares support vector machine (LSSVM has been proven to offer strong potential in forecasting issues, particularly by employing an appropriate meta-heuristic algorithm to determine the values of its two parameters. However, these meta-heuristic algorithms have the drawbacks of being hard to understand and reaching the global optimal solution slowly. As a novel meta-heuristic and evolutionary algorithm, the fruit fly optimization algorithm (FOA has the advantages of being easy to understand and fast convergence to the global optimal solution. Therefore, to improve the forecasting performance, this paper proposes a LSSVM-based annual electric load forecasting model that uses FOA to automatically determine the appropriate values of the two parameters for the LSSVM model. By taking the annual electricity consumption of China as an instance, the computational result shows that the LSSVM combined with FOA (LSSVM-FOA outperforms other alternative methods, namely single LSSVM, LSSVM combined with coupled simulated annealing algorithm (LSSVM-CSA, generalized regression neural network (GRNN and regression model.

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.

An Incremental Weighted Least Squares Approach to Surface Lights Fields

Science.gov (United States)

Coombe, Greg; Lastra, Anselmo

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

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....

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

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,…

'AJUSTAR' a interactive processor for to Fit, by means of least squares, one variable polinomials (arbitrary degree) at experimental points

International Nuclear Information System (INIS)

Sanchez Miro, J.J.; Pena, J.

1991-01-01

In this repport is offered, to scientist and technical people, a numeric tool consisting in a FORTRAN program, of interactive use, with destination to make lineal 'least squares', fittings on any set of empirical observations. The method based in the orthogonal functions (for discrete case), instead of direct solving the equations system, is used. The procedure includes also the optionally facilities of: variable change, direct interpolation, correlation non linear factor, 'weights' of the points, confidence intervals (Scheffe, Miller, Student), and plotting results. (Author). 10 refs

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

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

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

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.

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.

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

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.

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

Multiple Harmonics Fitting Algorithms Applied to Periodic Signals Based on Hilbert-Huang Transform

Directory of Open Access Journals (Sweden)

Hui Wang

2013-01-01

Full Text Available A new generation of multipurpose measurement equipment is transforming the role of computers in instrumentation. The new features involve mixed devices, such as kinds of sensors, analog-to-digital and digital-to-analog converters, and digital signal processing techniques, that are able to substitute typical discrete instruments like multimeters and analyzers. Signal-processing applications frequently use least-squares (LS sine-fitting algorithms. Periodic signals may be interpreted as a sum of sine waves with multiple frequencies: the Fourier series. This paper describes a new sine fitting algorithm that is able to fit a multiharmonic acquired periodic signal. By means of a “sinusoidal wave” whose amplitude and phase are both transient, the “triangular wave” can be reconstructed on the basis of Hilbert-Huang transform (HHT. This method can be used to test effective number of bits (ENOBs of analog-to-digital converter (ADC, avoiding the trouble of selecting initial value of the parameters and working out the nonlinear equations. The simulation results show that the algorithm is precise and efficient. In the case of enough sampling points, even under the circumstances of low-resolution signal with the harmonic distortion existing, the root mean square (RMS error between the sampling data of original “triangular wave” and the corresponding points of fitting “sinusoidal wave” is marvelously small. That maybe means, under the circumstances of any periodic signal, that ENOBs of high-resolution ADC can be tested accurately.

Electric Load Forecasting Based on a Least Squares Support Vector Machine with Fuzzy Time Series and Global Harmony Search Algorithm

Directory of Open Access Journals (Sweden)

Yan Hong Chen

2016-01-01

Full Text Available This paper proposes a new electric load forecasting model by hybridizing the fuzzy time series (FTS and global harmony search algorithm (GHSA with least squares support vector machines (LSSVM, namely GHSA-FTS-LSSVM model. Firstly, the fuzzy c-means clustering (FCS algorithm is used to calculate the clustering center of each cluster. Secondly, the LSSVM is applied to model the resultant series, which is optimized by GHSA. Finally, a real-world example is adopted to test the performance of the proposed model. In this investigation, the proposed model is verified using experimental datasets from the Guangdong Province Industrial Development Database, and results are compared against autoregressive integrated moving average (ARIMA model and other algorithms hybridized with LSSVM including genetic algorithm (GA, particle swarm optimization (PSO, harmony search, and so on. The forecasting results indicate that the proposed GHSA-FTS-LSSVM model effectively generates more accurate predictive results.

An improved partial least-squares regression method for Raman spectroscopy

Science.gov (United States)

Momenpour Tehran Monfared, Ali; Anis, Hanan

2017-10-01

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

The Short-Term Power Load Forecasting Based on Sperm Whale Algorithm and Wavelet Least Square Support Vector Machine with DWT-IR for Feature Selection

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Jin-peng Liu

2017-07-01

Full Text Available Short-term power load forecasting is an important basis for the operation of integrated energy system, and the accuracy of load forecasting directly affects the economy of system operation. To improve the forecasting accuracy, this paper proposes a load forecasting system based on wavelet least square support vector machine and sperm whale algorithm. Firstly, the methods of discrete wavelet transform and inconsistency rate model (DWT-IR are used to select the optimal features, which aims to reduce the redundancy of input vectors. Secondly, the kernel function of least square support vector machine LSSVM is replaced by wavelet kernel function for improving the nonlinear mapping ability of LSSVM. Lastly, the parameters of W-LSSVM are optimized by sperm whale algorithm, and the short-term load forecasting method of W-LSSVM-SWA is established. Additionally, the example verification results show that the proposed model outperforms other alternative methods and has a strong effectiveness and feasibility in short-term power load forecasting.

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

Time Scale in Least Square Method

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Özgür Yeniay

2014-01-01

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

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

Science.gov (United States)

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

2018-03-26

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

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

International Nuclear Information System (INIS)

Pan, Bing; Wu, Dafang; Wang, Zhaoyang

2012-01-01

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

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

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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.

Robust regularized least-squares beamforming approach to signal estimation

KAUST Repository

Suliman, Mohamed Abdalla Elhag

2017-05-12

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

Derivation of decay heat benchmarks for U235 and Pu239 by a least squares fit to measured data

International Nuclear Information System (INIS)

Tobias, A.

1989-05-01

A least squares technique used by previous authors has been applied to an extended set of available decay heat measurements for both U235 and Pu239 to yield simultaneous fits to the corresponding beta, gamma and total decay heat. The analysis takes account of both systematic and statistical uncertainties, including correlations, via calculations which use covariance matrices constructed for the measured data. The results of the analysis are given in the form of beta, gamma and total decay heat estimates following fission pulses and a range of irradiation times in both U235 and Pu239. These decay heat estimates are considered to form a consistent set of benchmarks for use in the assessment of summation calculations. (author)

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

Science.gov (United States)

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

1980-06-01

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

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

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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

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.

Resimulation of noise: a precision estimator for least square error curve-fitting tested for axial strain time constant imaging

Science.gov (United States)

Nair, S. P.; Righetti, R.

2015-05-01

Recent elastography techniques focus on imaging information on properties of materials which can be modeled as viscoelastic or poroelastic. These techniques often require the fitting of temporal strain data, acquired from either a creep or stress-relaxation experiment to a mathematical model using least square error (LSE) parameter estimation. It is known that the strain versus time relationships for tissues undergoing creep compression have a non-linear relationship. In non-linear cases, devising a measure of estimate reliability can be challenging. In this article, we have developed and tested a method to provide non linear LSE parameter estimate reliability: which we called Resimulation of Noise (RoN). RoN provides a measure of reliability by estimating the spread of parameter estimates from a single experiment realization. We have tested RoN specifically for the case of axial strain time constant parameter estimation in poroelastic media. Our tests show that the RoN estimated precision has a linear relationship to the actual precision of the LSE estimator. We have also compared results from the RoN derived measure of reliability against a commonly used reliability measure: the correlation coefficient (CorrCoeff). Our results show that CorrCoeff is a poor measure of estimate reliability for non-linear LSE parameter estimation. While the RoN is specifically tested only for axial strain time constant imaging, a general algorithm is provided for use in all LSE parameter estimation.

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.

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.

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

Science.gov (United States)

Sen, Symal K.; Shaykhian, Gholam Ali

2011-01-01

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

Passive shimming of a superconducting magnet using the L1-norm regularized least square algorithm.

Science.gov (United States)

Kong, Xia; Zhu, Minhua; Xia, Ling; Wang, Qiuliang; Li, Yi; Zhu, Xuchen; Liu, Feng; Crozier, Stuart

2016-02-01

The uniformity of the static magnetic field B0 is of prime importance for an MRI system. The passive shimming technique is usually applied to improve the uniformity of the static field by optimizing the layout of a series of steel shims. The steel pieces are fixed in the drawers in the inner bore of the superconducting magnet, and produce a magnetizing field in the imaging region to compensate for the inhomogeneity of the B0 field. In practice, the total mass of steel used for shimming should be minimized, in addition to the field uniformity requirement. This is because the presence of steel shims may introduce a thermal stability problem. The passive shimming procedure is typically realized using the linear programming (LP) method. The LP approach however, is generally slow and also has difficulty balancing the field quality and the total amount of steel for shimming. In this paper, we have developed a new algorithm that is better able to balance the dual constraints of field uniformity and the total mass of the shims. The least square method is used to minimize the magnetic field inhomogeneity over the imaging surface with the total mass of steel being controlled by an L1-norm based constraint. The proposed algorithm has been tested with practical field data, and the results show that, with similar computational cost and mass of shim material, the new algorithm achieves superior field uniformity (43% better for the test case) compared with the conventional linear programming approach. Copyright © 2016 Elsevier Inc. All rights reserved.

Circular contour retrieval in real-world conditions by higher order statistics and an alternating-least squares algorithm

Science.gov (United States)

Jiang, Haiping; Marot, Julien; Fossati, Caroline; Bourennane, Salah

2011-12-01

In real-world conditions, contours are most often blurred in digital images because of acquisition conditions such as movement, light transmission environment, and defocus. Among image segmentation methods, Hough transform requires a computational load which increases with the number of noise pixels, level set methods also require a high computational load, and some other methods assume that the contours are one-pixel wide. For the first time, we retrieve the characteristics of multiple possibly concentric blurred circles. We face correlated noise environment, to get closer to real-world conditions. For this, we model a blurred circle by a few parameters--center coordinates, radius, and spread--which characterize its mean position and gray level variations. We derive the signal model which results from signal generation on circular antenna. Linear antennas provide the center coordinates. To retrieve the circle radii, we adapt the second-order statistics TLS-ESPRIT method for non-correlated noise environment, and propose a novel version of TLS-ESPRIT based on higher-order statistics for correlated noise environment. Then, we derive a least-squares criterion and propose an alternating least-squares algorithm to retrieve simultaneously all spread values of concentric circles. Experiments performed on hand-made and real-world images show that the proposed methods outperform the Hough transform and a level set method dedicated to blurred contours in terms of computational load. Moreover, the proposed model and optimization method provide the information of the contour grey level variations.

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

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

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.

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.

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.

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.

Fitting polynomial surfaces to triangular meshes with Voronoi squared distance minimization

KAUST Repository

Nivoliers, Vincent

2012-11-06

This paper introduces Voronoi squared distance minimization (VSDM), an algorithm that fits a surface to an input mesh. VSDM minimizes an objective function that corresponds to a Voronoi-based approximation of the overall squared distance function between the surface and the input mesh (SDM). This objective function is a generalization of the one minimized by centroidal Voronoi tessellation, and can be minimized by a quasi-Newton solver. VSDM naturally adapts the orientation of the mesh elements to best approximate the input, without estimating any differential quantities. Therefore, it can be applied to triangle soups or surfaces with degenerate triangles, topological noise and sharp features. Applications of fitting quad meshes and polynomial surfaces to input triangular meshes are demonstrated. © 2012 Springer-Verlag London.

SIOB: a FORTRAN code for least-squares shape fitting several neutron transmission measurements using the Breit--Wigner multilevel formula. [For IBM-360/91

Energy Technology Data Exchange (ETDEWEB)

de Saussure, G.; Olsen, D. K.; Perez, R. B.

1978-05-01

The FORTRAN-IV code SIOB was developed to least-square fit the shape of neutron transmission curves. Any number of measurements on a common energy scale for different sample thicknesses can be simultaneously fitted. The computed transmission curves can be broadened with either a Gaussian or a rectangular resolution function or both, with the resolution width a function of energy. The total cross section is expressed as a sum of single-level or multilevel Breit--Wigner terms and Doppler broadened by using the fast interpolation routine QUICKW. The number of data points, resonance levels, and variables which can be handled simultaneously is only limited by the overall dimensions of two arrays in the program and by the stability of the matrix inversion. In a test problem seven transmissions each with 3750 data points were simultaneously fitted with 74 resonances and 110 variable parameters. The problem took 47 min of CPU time on an IBM-360/91, for 3 iterations. 3 figures, 2 tables.

Classification of Ultrasonic NDE Signals Using the Expectation Maximization (EM) and Least Mean Square (LMS) Algorithms

International Nuclear Information System (INIS)

Kim, Dae Won

2005-01-01

Ultrasonic inspection methods are widely used for detecting flaws in materials. The signal analysis step plays a crucial part in the data interpretation process. A number of signal processing methods have been proposed to classify ultrasonic flaw signals. One of the more popular methods involves the extraction of an appropriate set of features followed by the use of a neural network for the classification of the signals in the feature spare. This paper describes an alternative approach which uses the least mean square (LMS) method and exportation maximization (EM) algorithm with the model based deconvolution which is employed for classifying nondestructive evaluation (NDE) signals from steam generator tubes in a nuclear power plant. The signals due to cracks and deposits are not significantly different. These signals must be discriminated to prevent from happening a huge disaster such as contamination of water or explosion. A model based deconvolution has been described to facilitate comparison of classification results. The method uses the space alternating generalized expectation maximiBation (SAGE) algorithm ill conjunction with the Newton-Raphson method which uses the Hessian parameter resulting in fast convergence to estimate the time of flight and the distance between the tube wall and the ultrasonic sensor. Results using these schemes for the classification of ultrasonic signals from cracks and deposits within steam generator tubes are presented and showed a reasonable performances

Forecasting of Energy Consumption in China Based on Ensemble Empirical Mode Decomposition and Least Squares Support Vector Machine Optimized by Improved Shuffled Frog Leaping Algorithm

Directory of Open Access Journals (Sweden)

Shuyu Dai

2018-04-01

Full Text Available For social development, energy is a crucial material whose consumption affects the stable and sustained development of the natural environment and economy. Currently, China has become the largest energy consumer in the world. Therefore, establishing an appropriate energy consumption prediction model and accurately forecasting energy consumption in China have practical significance, and can provide a scientific basis for China to formulate a reasonable energy production plan and energy-saving and emissions-reduction-related policies to boost sustainable development. For forecasting the energy consumption in China accurately, considering the main driving factors of energy consumption, a novel model, EEMD-ISFLA-LSSVM (Ensemble Empirical Mode Decomposition and Least Squares Support Vector Machine Optimized by Improved Shuffled Frog Leaping Algorithm, is proposed in this article. The prediction accuracy of energy consumption is influenced by various factors. In this article, first considering population, GDP (Gross Domestic Product, industrial structure (the proportion of the second industry added value, energy consumption structure, energy intensity, carbon emissions intensity, total imports and exports and other influencing factors of energy consumption, the main driving factors of energy consumption are screened as the model input according to the sorting of grey relational degrees to realize feature dimension reduction. Then, the original energy consumption sequence of China is decomposed into multiple subsequences by Ensemble Empirical Mode Decomposition for de-noising. Next, the ISFLA-LSSVM (Least Squares Support Vector Machine Optimized by Improved Shuffled Frog Leaping Algorithm model is adopted to forecast each subsequence, and the prediction sequences are reconstructed to obtain the forecasting result. After that, the data from 1990 to 2009 are taken as the training set, and the data from 2010 to 2016 are taken as the test set to make an

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

Non-linear least squares curve fitting of a simple theoretical model to radioimmunoassay dose-response data using a mini-computer

International Nuclear Information System (INIS)

Wilkins, T.A.; Chadney, D.C.; Bryant, J.; Palmstroem, S.H.; Winder, R.L.

1977-01-01

Using the simple univalent antigen univalent-antibody equilibrium model the dose-response curve of a radioimmunoassay (RIA) may be expressed as a function of Y, X and the four physical parameters of the idealised system. A compact but powerful mini-computer program has been written in BASIC for rapid iterative non-linear least squares curve fitting and dose interpolation with this function. In its simplest form the program can be operated in an 8K byte mini-computer. The program has been extensively tested with data from 10 different assay systems (RIA and CPBA) for measurement of drugs and hormones ranging in molecular size from thyroxine to insulin. For each assay system the results have been analysed in terms of (a) curve fitting biases and (b) direct comparison with manual fitting. In all cases the quality of fitting was remarkably good in spite of the fact that the chemistry of each system departed significantly from one or more of the assumptions implicit in the model used. A mathematical analysis of departures from the model's principal assumption has provided an explanation for this somewhat unexpected observation. The essential features of this analysis are presented in this paper together with the statistical analyses of the performance of the program. From these and the results obtained to date in the routine quality control of these 10 assays, it is concluded that the method of curve fitting and dose interpolation presented in this paper is likely to be of general applicability. (orig.) [de

Combining Approach in Stages with Least Squares for fits of data in hyperelasticity

Science.gov (United States)

Beda, Tibi

2006-10-01

The present work concerns a method of continuous approximation by block of a continuous function; a method of approximation combining the Approach in Stages with the finite domains Least Squares. An identification procedure by sub-domains: basic generating functions are determined step-by-step permitting their weighting effects to be felt. This procedure allows one to be in control of the signs and to some extent of the optimal values of the parameters estimated, and consequently it provides a unique set of solutions that should represent the real physical parameters. Illustrations and comparisons are developed in rubber hyperelastic modeling. To cite this article: T. Beda, C. R. Mecanique 334 (2006).

A wavelet and least square filter based spatial-spectral denoising approach of hyperspectral imagery

Science.gov (United States)

Li, Ting; Chen, Xiao-Mei; Chen, Gang; Xue, Bo; Ni, Guo-Qiang

2009-11-01

Noise reduction is a crucial step in hyperspectral imagery pre-processing. Based on sensor characteristics, the noise of hyperspectral imagery represents in both spatial and spectral domain. However, most prevailing denosing techniques process the imagery in only one specific domain, which have not utilized multi-domain nature of hyperspectral imagery. In this paper, a new spatial-spectral noise reduction algorithm is proposed, which is based on wavelet analysis and least squares filtering techniques. First, in the spatial domain, a new stationary wavelet shrinking algorithm with improved threshold function is utilized to adjust the noise level band-by-band. This new algorithm uses BayesShrink for threshold estimation, and amends the traditional soft-threshold function by adding shape tuning parameters. Comparing with soft or hard threshold function, the improved one, which is first-order derivable and has a smooth transitional region between noise and signal, could save more details of image edge and weaken Pseudo-Gibbs. Then, in the spectral domain, cubic Savitzky-Golay filter based on least squares method is used to remove spectral noise and artificial noise that may have been introduced in during the spatial denoising. Appropriately selecting the filter window width according to prior knowledge, this algorithm has effective performance in smoothing the spectral curve. The performance of the new algorithm is experimented on a set of Hyperion imageries acquired in 2007. The result shows that the new spatial-spectral denoising algorithm provides more significant signal-to-noise-ratio improvement than traditional spatial or spectral method, while saves the local spectral absorption features better.

Quantum algorithm for linear regression

Science.gov (United States)

Wang, Guoming

2017-07-01

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

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.

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....

Short-Term Load Forecasting Based on Wavelet Transform and Least Squares Support Vector Machine Optimized by Fruit Fly Optimization Algorithm

Directory of Open Access Journals (Sweden)

Wei Sun

2015-01-01

Full Text Available Electric power is a kind of unstorable energy concerning the national welfare and the people’s livelihood, the stability of which is attracting more and more attention. Because the short-term power load is always interfered by various external factors with the characteristics like high volatility and instability, a single model is not suitable for short-term load forecasting due to low accuracy. In order to solve this problem, this paper proposes a new model based on wavelet transform and the least squares support vector machine (LSSVM which is optimized by fruit fly algorithm (FOA for short-term load forecasting. Wavelet transform is used to remove error points and enhance the stability of the data. Fruit fly algorithm is applied to optimize the parameters of LSSVM, avoiding the randomness and inaccuracy to parameters setting. The result of implementation of short-term load forecasting demonstrates that the hybrid model can be used in the short-term forecasting of the power system.

Icing Forecasting of High Voltage Transmission Line Using Weighted Least Square Support Vector Machine with Fireworks Algorithm for Feature Selection

Directory of Open Access Journals (Sweden)

Tiannan Ma

2016-12-01

Full Text Available Accurate forecasting of icing thickness has great significance for ensuring the security and stability of the power grid. In order to improve the forecasting accuracy, this paper proposes an icing forecasting system based on the fireworks algorithm and weighted least square support vector machine (W-LSSVM. The method of the fireworks algorithm is employed to select the proper input features with the purpose of eliminating redundant influence. In addition, the aim of the W-LSSVM model is to train and test the historical data-set with the selected features. The capability of this proposed icing forecasting model and framework is tested through simulation experiments using real-world icing data from the monitoring center of the key laboratory of anti-ice disaster, Hunan, South China. The results show that the proposed W-LSSVM-FA method has a higher prediction accuracy and it may be a promising alternative for icing thickness forecasting.

Exploring the limits of cryospectroscopy: Least-squares based approaches for analyzing the self-association of HCl

Science.gov (United States)

De Beuckeleer, Liene I.; Herrebout, Wouter A.

2016-02-01

To rationalize the concentration dependent behavior observed for a large spectral data set of HCl recorded in liquid argon, least-squares based numerical methods are developed and validated. In these methods, for each wavenumber a polynomial is used to mimic the relation between monomer concentrations and measured absorbances. Least-squares fitting of higher degree polynomials tends to overfit and thus leads to compensation effects where a contribution due to one species is compensated for by a negative contribution of another. The compensation effects are corrected for by carefully analyzing, using AIC and BIC information criteria, the differences observed between consecutive fittings when the degree of the polynomial model is systematically increased, and by introducing constraints prohibiting negative absorbances to occur for the monomer or for one of the oligomers. The method developed should allow other, more complicated self-associating systems to be analyzed with a much higher accuracy than before.

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 Constrained Least Squares Approach to Mobile Positioning: Algorithms and Optimality

Science.gov (United States)

Cheung, KW; So, HC; Ma, W.-K.; Chan, YT

2006-12-01

The problem of locating a mobile terminal has received significant attention in the field of wireless communications. Time-of-arrival (TOA), received signal strength (RSS), time-difference-of-arrival (TDOA), and angle-of-arrival (AOA) are commonly used measurements for estimating the position of the mobile station. In this paper, we present a constrained weighted least squares (CWLS) mobile positioning approach that encompasses all the above described measurement cases. The advantages of CWLS include performance optimality and capability of extension to hybrid measurement cases (e.g., mobile positioning using TDOA and AOA measurements jointly). Assuming zero-mean uncorrelated measurement errors, we show by mean and variance analysis that all the developed CWLS location estimators achieve zero bias and the Cramér-Rao lower bound approximately when measurement error variances are small. The asymptotic optimum performance is also confirmed by simulation results.

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.

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

Directory of Open Access Journals (Sweden)

Baoguo Yu

2016-01-01

Full Text Available In the wireless sensor network (WSN localization methods based on Received Signal Strength Indicator (RSSI, it is usually required to determine the parameters of the radio signal propagation model before estimating the distance between the anchor node and an unknown node with reference to their communication RSSI value. And finally we use a localization algorithm to estimate the location of the unknown node. However, this localization method, though high in localization accuracy, has weaknesses such as complex working procedure and poor system versatility. Concerning these defects, a self-adaptive WSN localization method based on least square is proposed, which uses the least square criterion to estimate the parameters of radio signal propagation model, which positively reduces the computation amount in the estimation process. The experimental results show that the proposed self-adaptive localization method outputs a high processing efficiency while satisfying the high localization accuracy requirement. Conclusively, the proposed method is of definite practical value.

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)).

Multi-phase classification by a least-squares support vector machine approach in tomography images of geological samples

Science.gov (United States)

Khan, Faisal; Enzmann, Frieder; Kersten, Michael

2016-03-01

Image processing of X-ray-computed polychromatic cone-beam micro-tomography (μXCT) data of geological samples mainly involves artefact reduction and phase segmentation. For the former, the main beam-hardening (BH) artefact is removed by applying a best-fit quadratic surface algorithm to a given image data set (reconstructed slice), which minimizes the BH offsets of the attenuation data points from that surface. A Matlab code for this approach is provided in the Appendix. The final BH-corrected image is extracted from the residual data or from the difference between the surface elevation values and the original grey-scale values. For the segmentation, we propose a novel least-squares support vector machine (LS-SVM, an algorithm for pixel-based multi-phase classification) approach. A receiver operating characteristic (ROC) analysis was performed on BH-corrected and uncorrected samples to show that BH correction is in fact an important prerequisite for accurate multi-phase classification. The combination of the two approaches was thus used to classify successfully three different more or less complex multi-phase rock core samples.

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)

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

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

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

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.

A fitting algorithm based on simulated annealing techniques for efficiency calibration of HPGe detectors using different mathematical functions

Energy Technology Data Exchange (ETDEWEB)

Hurtado, S. [Servicio de Radioisotopos, Centro de Investigacion, Tecnologia e Innovacion (CITIUS), Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla (Spain)], E-mail: shurtado@us.es; Garcia-Leon, M. [Departamento de Fisica Atomica, Molecular y Nuclear, Facultad de Fisica, Universidad de Sevilla, Aptd. 1065, 41080 Sevilla (Spain); Garcia-Tenorio, R. [Departamento de Fisica Aplicada II, E.T.S.A. Universidad de Sevilla, Avda, Reina Mercedes 2, 41012 Sevilla (Spain)

2008-09-11

In this work several mathematical functions are compared in order to perform the full-energy peak efficiency calibration of HPGe detectors using a 126cm{sup 3} HPGe coaxial detector and gamma-ray energies ranging from 36 to 1460 keV. Statistical tests and Monte Carlo simulations were used to study the performance of the fitting curve equations. Furthermore the fitting procedure of these complex functional forms to experimental data is a non-linear multi-parameter minimization problem. In gamma-ray spectrometry usually non-linear least-squares fitting algorithms (Levenberg-Marquardt method) provide a fast convergence while minimizing {chi}{sub R}{sup 2}, however, sometimes reaching only local minima. In order to overcome that shortcoming a hybrid algorithm based on simulated annealing (HSA) techniques is proposed. Additionally a new function is suggested that models the efficiency curve of germanium detectors in gamma-ray spectrometry.

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

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.

Quantitative analysis of Ni2+/Ni3+ in Li[NixMnyCoz]O2 cathode materials: Non-linear least-squares fitting of XPS spectra

Science.gov (United States)

Fu, Zewei; Hu, Juntao; Hu, Wenlong; Yang, Shiyu; Luo, Yunfeng

2018-05-01

Quantitative analysis of Ni2+/Ni3+ using X-ray photoelectron spectroscopy (XPS) is important for evaluating the crystal structure and electrochemical performance of Lithium-nickel-cobalt-manganese oxide (Li[NixMnyCoz]O2, NMC). However, quantitative analysis based on Gaussian/Lorentzian (G/L) peak fitting suffers from the challenges of reproducibility and effectiveness. In this study, the Ni2+ and Ni3+ standard samples and a series of NMC samples with different Ni doping levels were synthesized. The Ni2+/Ni3+ ratios in NMC were quantitatively analyzed by non-linear least-squares fitting (NLLSF). Two Ni 2p overall spectra of synthesized Li [Ni0.33Mn0.33Co0.33]O2(NMC111) and bulk LiNiO2 were used as the Ni2+ and Ni3+ reference standards. Compared to G/L peak fitting, the fitting parameters required no adjustment, meaning that the spectral fitting process was free from operator dependence and the reproducibility was improved. Comparison of residual standard deviation (STD) showed that the fitting quality of NLLSF was superior to that of G/L peaks fitting. Overall, these findings confirmed the reproducibility and effectiveness of the NLLSF method in XPS quantitative analysis of Ni2+/Ni3+ ratio in Li[NixMnyCoz]O2 cathode materials.

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

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...

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.

Distributed weighted least-squares estimation with fast convergence for large-scale systems☆

Science.gov (United States)

Marelli, Damián Edgardo; Fu, Minyue

2015-01-01

In this paper we study a distributed weighted least-squares estimation problem for a large-scale system consisting of a network of interconnected sub-systems. Each sub-system is concerned with a subset of the unknown parameters and has a measurement linear in the unknown parameters with additive noise. The distributed estimation task is for each sub-system to compute the globally optimal estimate of its own parameters using its own measurement and information shared with the network through neighborhood communication. We first provide a fully distributed iterative algorithm to asymptotically compute the global optimal estimate. The convergence rate of the algorithm will be maximized using a scaling parameter and a preconditioning method. This algorithm works for a general network. For a network without loops, we also provide a different iterative algorithm to compute the global optimal estimate which converges in a finite number of steps. We include numerical experiments to illustrate the performances of the proposed methods. PMID:25641976

Distributed weighted least-squares estimation with fast convergence for large-scale systems.

Science.gov (United States)

Marelli, Damián Edgardo; Fu, Minyue

2015-01-01

In this paper we study a distributed weighted least-squares estimation problem for a large-scale system consisting of a network of interconnected sub-systems. Each sub-system is concerned with a subset of the unknown parameters and has a measurement linear in the unknown parameters with additive noise. The distributed estimation task is for each sub-system to compute the globally optimal estimate of its own parameters using its own measurement and information shared with the network through neighborhood communication. We first provide a fully distributed iterative algorithm to asymptotically compute the global optimal estimate. The convergence rate of the algorithm will be maximized using a scaling parameter and a preconditioning method. This algorithm works for a general network. For a network without loops, we also provide a different iterative algorithm to compute the global optimal estimate which converges in a finite number of steps. We include numerical experiments to illustrate the performances of the proposed methods.

Group-wise partial least square regression

NARCIS (Netherlands)

Camacho, José; Saccenti, Edoardo

2018-01-01

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

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.

Lossless medical image compression using geometry-adaptive partitioning and least square-based prediction.

Science.gov (United States)

Song, Xiaoying; Huang, Qijun; Chang, Sheng; He, Jin; Wang, Hao

2018-06-01

To improve the compression rates for lossless compression of medical images, an efficient algorithm, based on irregular segmentation and region-based prediction, is proposed in this paper. Considering that the first step of a region-based compression algorithm is segmentation, this paper proposes a hybrid method by combining geometry-adaptive partitioning and quadtree partitioning to achieve adaptive irregular segmentation for medical images. Then, least square (LS)-based predictors are adaptively designed for each region (regular subblock or irregular subregion). The proposed adaptive algorithm not only exploits spatial correlation between pixels but it utilizes local structure similarity, resulting in efficient compression performance. Experimental results show that the average compression performance of the proposed algorithm is 10.48, 4.86, 3.58, and 0.10% better than that of JPEG 2000, CALIC, EDP, and JPEG-LS, respectively. Graphical abstract ᅟ.

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 ...

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.

Joint Estimation of the Electric Vehicle Power Battery State of Charge Based on the Least Squares Method and the Kalman Filter Algorithm

Directory of Open Access Journals (Sweden)

Xiangwei Guo

2016-02-01

Full Text Available An estimation of the power battery state of charge (SOC is related to the energy management, the battery cycle life and the use cost of electric vehicles. When a lithium-ion power battery is used in an electric vehicle, the SOC displays a very strong time-dependent nonlinearity under the influence of random factors, such as the working conditions and the environment. Hence, research on estimating the SOC of a power battery for an electric vehicle is of great theoretical significance and application value. In this paper, according to the dynamic response of the power battery terminal voltage during a discharging process, the second-order RC circuit is first used as the equivalent model of the power battery. Subsequently, on the basis of this model, the least squares method (LS with a forgetting factor and the adaptive unscented Kalman filter (AUKF algorithm are used jointly in the estimation of the power battery SOC. Simulation experiments show that the joint estimation algorithm proposed in this paper has higher precision and convergence of the initial value error than a single AUKF algorithm.

PROPOSED MODIFICATIONS OF K2-TEMPERATURE RELATION AND LEAST SQUARES ESTIMATES OF BOD (BIOCHEMICAL OXYGEN DEMAND) PARAMETERS

Science.gov (United States)

A technique is presented for finding the least squares estimates for the ultimate biochemical oxygen demand (BOD) and rate coefficient for the BOD reaction without resorting to complicated computer algorithms or subjective graphical methods. This may be used in stream water quali...

Least-squares wave-front reconstruction of Shack-Hartmann sensors and shearing interferometers using multigrid techniques

International Nuclear Information System (INIS)

Baker, K.L.

2005-01-01

This article details a multigrid algorithm that is suitable for least-squares wave-front reconstruction of Shack-Hartmann and shearing interferometer wave-front sensors. The algorithm detailed in this article is shown to scale with the number of subapertures in the same fashion as fast Fourier transform techniques, making it suitable for use in applications requiring a large number of subapertures and high Strehl ratio systems such as for high spatial frequency characterization of high-density plasmas, optics metrology, and multiconjugate and extreme adaptive optics systems

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)

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.

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

Directory of Open Access Journals (Sweden)

Engin Cemal MENGÜÇ

2018-03-01

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

Curve Fitting via the Criterion of Least Squares. Applications of Algebra and Elementary Calculus to Curve Fitting. [and] Linear Programming in Two Dimensions: I. Applications of High School Algebra to Operations Research. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 321, 453.

Science.gov (United States)

Alexander, John W., Jr.; Rosenberg, Nancy S.

This document consists of two modules. The first of these views applications of algebra and elementary calculus to curve fitting. The user is provided with information on how to: 1) construct scatter diagrams; 2) choose an appropriate function to fit specific data; 3) understand the underlying theory of least squares; 4) use a computer program to…

Optimization on Paddy Crops in Central Java (with Solver, SVD on Least Square and ACO (Ant Colony Algorithm))

Science.gov (United States)

Parhusip, H. A.; Trihandaru, S.; Susanto, B.; Prasetyo, S. Y. J.; Agus, Y. H.; Simanjuntak, B. H.

2017-03-01

Several algorithms and objective functions on paddy crops have been studied to get optimal paddy crops in Central Java based on the data given from Surakarta and Boyolali. The algorithms are linear solver, least square and Ant Colony Algorithms (ACO) to develop optimization procedures on paddy crops modelled with Modified GSTAR (Generalized Space-Time Autoregressive) and nonlinear models where the nonlinear models are quadratic and power functions. The studied data contain paddy crops from Surakarta and Boyolali determining the best period of planting in the year 1992-2012 for Surakarta where 3 periods for planting are known and the optimal amount of paddy crops in Boyolali in the year 2008-2013. Having these analyses may guide the local agriculture government to give a decision on rice sustainability in its region. The best period for planting in Surakarta is observed, i.e. the best period is in September-December based on the data 1992-2012 by considering the planting area, the cropping area, and the paddy crops are the most important factors to be taken into account. As a result, we can refer the paddy crops in this best period (about 60.4 thousand tons per year) as the optimal results in 1992-2012 where the used objective function is quadratic. According to the research, the optimal paddy crops in Boyolali about 280 thousand tons per year where the studied factors are the amount of rainfalls, the harvested area and the paddy crops in 2008-2013. In this case, linear and power functions are studied to be the objective functions. Compared to all studied algorithms, the linear solver is still recommended to be an optimization tool for a local agriculture government to predict paddy crops in future.

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.

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

Multi-frequency Phase Unwrap from Noisy Data: Adaptive Least Squares Approach

Science.gov (United States)

Katkovnik, Vladimir; Bioucas-Dias, José

2010-04-01

Multiple frequency interferometry is, basically, a phase acquisition strategy aimed at reducing or eliminating the ambiguity of the wrapped phase observations or, equivalently, reducing or eliminating the fringe ambiguity order. In multiple frequency interferometry, the phase measurements are acquired at different frequencies (or wavelengths) and recorded using the corresponding sensors (measurement channels). Assuming that the absolute phase to be reconstructed is piece-wise smooth, we use a nonparametric regression technique for the phase reconstruction. The nonparametric estimates are derived from a local least squares criterion, which, when applied to the multifrequency data, yields denoised (filtered) phase estimates with extended ambiguity (periodized), compared with the phase ambiguities inherent to each measurement frequency. The filtering algorithm is based on local polynomial (LPA) approximation for design of nonlinear filters (estimators) and adaptation of these filters to unknown smoothness of the spatially varying absolute phase [9]. For phase unwrapping, from filtered periodized data, we apply the recently introduced robust (in the sense of discontinuity preserving) PUMA unwrapping algorithm [1]. Simulations give evidence that the proposed algorithm yields state-of-the-art performance for continuous as well as for discontinues phase surfaces, enabling phase unwrapping in extraordinary difficult situations when all other algorithms fail.

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.

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.

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

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

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

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.

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....

Vis-NIR spectrometric determination of Brix and sucrose in sugar production samples using kernel partial least squares with interval selection based on the successive projections algorithm.

Science.gov (United States)

de Almeida, Valber Elias; de Araújo Gomes, Adriano; de Sousa Fernandes, David Douglas; Goicoechea, Héctor Casimiro; Galvão, Roberto Kawakami Harrop; Araújo, Mario Cesar Ugulino

2018-05-01

This paper proposes a new variable selection method for nonlinear multivariate calibration, combining the Successive Projections Algorithm for interval selection (iSPA) with the Kernel Partial Least Squares (Kernel-PLS) modelling technique. The proposed iSPA-Kernel-PLS algorithm is employed in a case study involving a Vis-NIR spectrometric dataset with complex nonlinear features. The analytical problem consists of determining Brix and sucrose content in samples from a sugar production system, on the basis of transflectance spectra. As compared to full-spectrum Kernel-PLS, the iSPA-Kernel-PLS models involve a smaller number of variables and display statistically significant superiority in terms of accuracy and/or bias in the predictions. Published by Elsevier B.V.

Online Least Squares One-Class Support Vector Machines-Based Abnormal Visual Event Detection

Directory of Open Access Journals (Sweden)

Tian Wang

2013-12-01

Full Text Available The abnormal event detection problem is an important subject in real-time video surveillance. In this paper, we propose a novel online one-class classification algorithm, online least squares one-class support vector machine (online LS-OC-SVM, combined with its sparsified version (sparse online LS-OC-SVM. LS-OC-SVM extracts a hyperplane as an optimal description of training objects in a regularized least squares sense. The online LS-OC-SVM learns a training set with a limited number of samples to provide a basic normal model, then updates the model through remaining data. In the sparse online scheme, the model complexity is controlled by the coherence criterion. The online LS-OC-SVM is adopted to handle the abnormal event detection problem. Each frame of the video is characterized by the covariance matrix descriptor encoding the moving information, then is classified into a normal or an abnormal frame. Experiments are conducted, on a two-dimensional synthetic distribution dataset and a benchmark video surveillance dataset, to demonstrate the promising results of the proposed online LS-OC-SVM method.

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

Science.gov (United States)

Khawaja, Taimoor Saleem

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

Obtention of the parameters of the Voigt function using the least square fit method; Obtencion de los parametros de la funcion Voigt empleando el metodo de minimos cuadrados

Energy Technology Data Exchange (ETDEWEB)

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

1990-01-15

The fundamental parameters of the Voigt function are determined: lorentzian wide ({gamma}{sub L}) and gaussian wide ({gamma}{sub G}) with an error for almost all the cases inferior to 1% in the intervals 0.01 {<=} {gamma}{sub L} / {gamma}{sub G} {<=}1 and 0.3 {<=} {gamma}{sub G} / {gamma}{sub 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)

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.

Customer demand prediction of service-oriented manufacturing using the least square support vector machine optimized by particle swarm optimization algorithm

Science.gov (United States)

Cao, Jin; Jiang, Zhibin; Wang, Kangzhou

2017-07-01

Many nonlinear customer satisfaction-related factors significantly influence the future customer demand for service-oriented manufacturing (SOM). To address this issue and enhance the prediction accuracy, this article develops a novel customer demand prediction approach for SOM. The approach combines the phase space reconstruction (PSR) technique with the optimized least square support vector machine (LSSVM). First, the prediction sample space is reconstructed by the PSR to enrich the time-series dynamics of the limited data sample. Then, the generalization and learning ability of the LSSVM are improved by the hybrid polynomial and radial basis function kernel. Finally, the key parameters of the LSSVM are optimized by the particle swarm optimization algorithm. In a real case study, the customer demand prediction of an air conditioner compressor is implemented. Furthermore, the effectiveness and validity of the proposed approach are demonstrated by comparison with other classical predication approaches.

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.

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 highly accurate dynamic contact angle algorithm for drops on inclined surface based on ellipse-fitting.

Science.gov (United States)

Xu, Z N; Wang, S Y

2015-02-01

To improve the accuracy in the calculation of dynamic contact angle for drops on the inclined surface, a significant number of numerical drop profiles on the inclined surface with different inclination angles, drop volumes, and contact angles are generated based on the finite difference method, a least-squares ellipse-fitting algorithm is used to calculate the dynamic contact angle. The influences of the above three factors are systematically investigated. The results reveal that the dynamic contact angle errors, including the errors of the left and right contact angles, evaluated by the ellipse-fitting algorithm tend to increase with inclination angle/drop volume/contact angle. If the drop volume and the solid substrate are fixed, the errors of the left and right contact angles increase with inclination angle. After performing a tremendous amount of computation, the critical dimensionless drop volumes corresponding to the critical contact angle error are obtained. Based on the values of the critical volumes, a highly accurate dynamic contact angle algorithm is proposed and fully validated. Within nearly the whole hydrophobicity range, it can decrease the dynamic contact angle error in the inclined plane method to less than a certain value even for different types of liquids.

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.

8th International Conference on Partial Least Squares and Related Methods

CERN Document Server

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

2016-01-01

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

Motion-compensated cone beam computed tomography using a conjugate gradient least-squares algorithm and electrical impedance tomography imaging motion data.

Science.gov (United States)

Pengpen, T; Soleimani, M

2015-06-13

Cone beam computed tomography (CBCT) is an imaging modality that has been used in image-guided radiation therapy (IGRT). For applications such as lung radiation therapy, CBCT images are greatly affected by the motion artefacts. This is mainly due to low temporal resolution of CBCT. Recently, a dual modality of electrical impedance tomography (EIT) and CBCT has been proposed, in which the high temporal resolution EIT imaging system provides motion data to a motion-compensated algebraic reconstruction technique (ART)-based CBCT reconstruction software. High computational time associated with ART and indeed other variations of ART make it less practical for real applications. This paper develops a motion-compensated conjugate gradient least-squares (CGLS) algorithm for CBCT. A motion-compensated CGLS offers several advantages over ART-based methods, including possibilities for explicit regularization, rapid convergence and parallel computations. This paper for the first time demonstrates motion-compensated CBCT reconstruction using CGLS and reconstruction results are shown in limited data CBCT considering only a quarter of the full dataset. The proposed algorithm is tested using simulated motion data in generic motion-compensated CBCT as well as measured EIT data in dual EIT-CBCT imaging. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Depth profiles of defects in Ar-iondashirradiated steels determined by a least-squares fit of S parameters from variable-energy positron annihilation

Science.gov (United States)

Aruga, Takeo; Takamura, Saburo; Nakata, Kiyotomo; Ito, Yasuo

1995-01-01

Using a new method for reconstructing the depth profile of defects in an iondashirradiated sample by using slow positrons, the depth profiles of vacancy-type defects in 316 stainless steel samples, irradiated with 250 keV Ar ions to a dose of 7.5 × 10 19 m -2 at room temperature, have been calculated from Doppler-broadening S parameters measured as a function of positron energies up to 16 keV. Without assuming any type of shape for the defect profiles, such as Gaussian, the defect profiling is done using a least-squares fitting method. The resulting profile suggests that in as-irradiated 316 stainless steel samples with lower carbon content, the defect distribution peaks at a depth four times larger than that of the ion range. After annealing at a high temperature of 1253 K for 0.5 h, the fitted profile shows that the peak around the average ion range is highly enhanced. While in the steel added with 0.3 wt% titanium, the profile exhibits almost no peak after annealing at 1073 K. The results indicate that the radiationdashproduced vacancy clusters are stabilized by the implanted Ar atoms more effectively in the Ti-free steel than in the Ti-added steel.

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.

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.

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.

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.

Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

Science.gov (United States)

Orr, Jeb S.

2012-01-01

A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed

Robust Homography Estimation Based on Nonlinear Least Squares Optimization

Directory of Open Access Journals (Sweden)

Wei Mou

2014-01-01

Full Text Available The homography between image pairs is normally estimated by minimizing a suitable cost function given 2D keypoint correspondences. The correspondences are typically established using descriptor distance of keypoints. However, the correspondences are often incorrect due to ambiguous descriptors which can introduce errors into following homography computing step. There have been numerous attempts to filter out these erroneous correspondences, but it is unlikely to always achieve perfect matching. To deal with this problem, we propose a nonlinear least squares optimization approach to compute homography such that false matches have no or little effect on computed homography. Unlike normal homography computation algorithms, our method formulates not only the keypoints’ geometric relationship but also their descriptor similarity into cost function. Moreover, the cost function is parametrized in such a way that incorrect correspondences can be simultaneously identified while the homography is computed. Experiments show that the proposed approach can perform well even with the presence of a large number of outliers.

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

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

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.

Facial Expression Recognition using Multiclass Ensemble Least-Square Support Vector Machine

Science.gov (United States)

Lawi, Armin; Sya'Rani Machrizzandi, M.

2018-03-01

Facial expression is one of behavior characteristics of human-being. The use of biometrics technology system with facial expression characteristics makes it possible to recognize a person’s mood or emotion. The basic components of facial expression analysis system are face detection, face image extraction, facial classification and facial expressions recognition. This paper uses Principal Component Analysis (PCA) algorithm to extract facial features with expression parameters, i.e., happy, sad, neutral, angry, fear, and disgusted. Then Multiclass Ensemble Least-Squares Support Vector Machine (MELS-SVM) is used for the classification process of facial expression. The result of MELS-SVM model obtained from our 185 different expression images of 10 persons showed high accuracy level of 99.998% using RBF kernel.

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.

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.

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

Chi-squared goodness of fit tests with applications

CERN Document Server

Balakrishnan, N; Nikulin, MS

2013-01-01

Chi-Squared Goodness of Fit Tests with Applications provides a thorough and complete context for the theoretical basis and implementation of Pearson's monumental contribution and its wide applicability for chi-squared goodness of fit tests. The book is ideal for researchers and scientists conducting statistical analysis in processing of experimental data as well as to students and practitioners with a good mathematical background who use statistical methods. The historical context, especially Chapter 7, provides great insight into importance of this subject with an authoritative author team

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

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

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

Modeling and control of PEMFC based on least squares support vector machines

International Nuclear Information System (INIS)

Li Xi; Cao Guangyi; Zhu Xinjian

2006-01-01

The proton exchange membrane fuel cell (PEMFC) is one of the most important power supplies. The operating temperature of the stack is an important controlled variable, which impacts the performance of the PEMFC. In order to improve the generating performance of the PEMFC, prolong its life and guarantee safety, credibility and low cost of the PEMFC system, it must be controlled efficiently. A nonlinear predictive control algorithm based on a least squares support vector machine (LS-SVM) model is presented for a family of complex systems with severe nonlinearity, such as the PEMFC, in this paper. The nonlinear off line model of the PEMFC is built by a LS-SVM model with radial basis function (RBF) kernel so as to implement nonlinear predictive control of the plant. During PEMFC operation, the off line model is linearized at each sampling instant, and the generalized predictive control (GPC) algorithm is applied to the predictive control of the plant. Experimental results demonstrate the effectiveness and advantages of this approach

Comparison of remove-compute-restore and least squares modification of Stokes' formula techniques to quasi-geoid determination over the Auvergne test area

DEFF Research Database (Denmark)

Yildiz, H.; Forsberg, René; Ågren, J.

2012-01-01

The remove-compute-restore (RCR) technique for regional geoid determination implies that both topography and low-degree global geopotential model signals are removed before computation and restored after Stokes' integration or Least Squares Collocation (LSC) solution. The Least Squares Modification...... area. All methods showed a reasonable agreement with GPS-levelling data, in the order of a 3-3.5 cm in the central region having relatively smooth topography, which is consistent with the accuracies of GPS and levelling. When a 1-parameter fit is used, the FFT method using kernel modification performs...

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.

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.

Fitting of two and three variant polynomials from experimental data through the least squares method. (Using of the codes AJUS-2D, AJUS-3D and LEGENDRE-2D); Ajuste de polinomios en dos y tres variables independientes por el metodo de minimos cuadrados. (Desarrollo de los codigos AJUS-2D, AJUS-3D y LEGENDRE-2D)

Energy Technology Data Exchange (ETDEWEB)

Sanchez Miro, J J; Sanz Martin, J C

1994-07-01

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. (Author) 10 refs.

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

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.

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

Online Identification of Multivariable Discrete Time Delay Systems Using a Recursive Least Square Algorithm

Directory of Open Access Journals (Sweden)

Saïda Bedoui

2013-01-01

Full Text Available This paper addresses the problem of simultaneous identification of linear discrete time delay multivariable systems. This problem involves both the estimation of the time delays and the dynamic parameters matrices. In fact, we suggest a new formulation of this problem allowing defining the time delay and the dynamic parameters in the same estimated vector and building the corresponding observation vector. Then, we use this formulation to propose a new method to identify the time delays and the parameters of these systems using the least square approach. Convergence conditions and statistics properties of the proposed method are also developed. Simulation results are presented to illustrate the performance of the proposed method. An application of the developed approach to compact disc player arm is also suggested in order to validate simulation results.

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.

A comparative analysis of the EEDF obtained by Regularization and by Least square fit methods; Un analisis comparativo de la EEDF obtenido por metodos de regularizacion y por un ajuste de minimos cuadrados

Energy Technology Data Exchange (ETDEWEB)

Gutierrez T, C.; Flores Ll, H. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico)

2004-07-01

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)

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.

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.

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.

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

Science.gov (United States)

Long, Rebecca G

2008-10-01

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

Short-term traffic flow prediction model using particle swarm optimization–based combined kernel function-least squares support vector machine combined with chaos theory

Directory of Open Access Journals (Sweden)

Qiang Shang

2016-08-01

Full Text Available Short-term traffic flow prediction is an important part of intelligent transportation systems research and applications. For further improving the accuracy of short-time traffic flow prediction, a novel hybrid prediction model (multivariate phase space reconstruction–combined kernel function-least squares support vector machine based on multivariate phase space reconstruction and combined kernel function-least squares support vector machine is proposed. The C-C method is used to determine the optimal time delay and the optimal embedding dimension of traffic variables’ (flow, speed, and occupancy time series for phase space reconstruction. The G-P method is selected to calculate the correlation dimension of attractor which is an important index for judging chaotic characteristics of the traffic variables’ series. The optimal input form of combined kernel function-least squares support vector machine model is determined by multivariate phase space reconstruction, and the model’s parameters are optimized by particle swarm optimization algorithm. Finally, case validation is carried out using the measured data of an expressway in Xiamen, China. The experimental results suggest that the new proposed model yields better predictions compared with similar models (combined kernel function-least squares support vector machine, multivariate phase space reconstruction–generalized kernel function-least squares support vector machine, and phase space reconstruction–combined kernel function-least squares support vector machine, which indicates that the new proposed model exhibits stronger prediction ability and robustness.

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

Science.gov (United States)

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

2016-04-01

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

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.

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.

Least Squares Magnetic-Field Optimization for Portable Nuclear Magnetic Resonance Magnet Design

International Nuclear Information System (INIS)

Paulsen, Jeffrey L; Franck, John; Demas, Vasiliki; Bouchard, Louis-S.

2008-01-01

Single-sided and mobile nuclear magnetic resonance (NMR) sensors have the advantages of portability, low cost, and low power consumption compared to conventional high-field NMR and magnetic resonance imaging (MRI) systems. We present fast, flexible, and easy-to-implement target field algorithms for mobile NMR and MRI magnet design. The optimization finds a global optimum in a cost function that minimizes the error in the target magnetic field in the sense of least squares. When the technique is tested on a ring array of permanent-magnet elements, the solution matches the classical dipole Halbach solution. For a single-sided handheld NMR sensor, the algorithm yields a 640 G field homogeneous to 16,100 ppm across a 1.9 cc volume located 1.5 cm above the top of the magnets and homogeneous to 32,200 ppm over a 7.6 cc volume. This regime is adequate for MRI applications. We demonstrate that the homogeneous region can be continuously moved away from the sensor by rotating magnet rod elements, opening the way for NMR sensors with adjustable 'sensitive volumes'

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

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

Lameness detection challenges in automated milking systems addressed with partial least squares discriminant analysis

DEFF Research Database (Denmark)

Garcia, Emanuel; Klaas, Ilka Christine; Amigo Rubio, Jose Manuel

2014-01-01

Lameness is prevalent in dairy herds. It causes decreased animal welfare and leads to higher production costs. This study explored data from an automatic milking system (AMS) to model on-farm gait scoring from a commercial farm. A total of 88 cows were gait scored once per week, for 2 5-wk periods......). The reference gait scoring error was estimated in the first week of the study and was, on average, 15%. Two partial least squares discriminant analysis models were fitted to parity 1 and parity 2 groups, respectively, to assign the lameness class according to the predicted probability of being lame (score 3...

Image reconstruction for an electrical capacitance tomography system based on a least-squares support vector machine and a self-adaptive particle swarm optimization algorithm

International Nuclear Information System (INIS)

Chen, Xia; Hu, Hong-li; Liu, Fei; Gao, Xiang Xiang

2011-01-01

The task of image reconstruction for an electrical capacitance tomography (ECT) system is to determine the permittivity distribution and hence the phase distribution in a pipeline by measuring the electrical capacitances between sets of electrodes placed around its periphery. In view of the nonlinear relationship between the permittivity distribution and capacitances and the limited number of independent capacitance measurements, image reconstruction for ECT is a nonlinear and ill-posed inverse problem. To solve this problem, a new image reconstruction method for ECT based on a least-squares support vector machine (LS-SVM) combined with a self-adaptive particle swarm optimization (PSO) algorithm is presented. Regarded as a special small sample theory, the SVM avoids the issues appearing in artificial neural network methods such as difficult determination of a network structure, over-learning and under-learning. However, the SVM performs differently with different parameters. As a relatively new population-based evolutionary optimization technique, PSO is adopted to realize parameters' effective selection with the advantages of global optimization and rapid convergence. This paper builds up a 12-electrode ECT system and a pneumatic conveying platform to verify this image reconstruction algorithm. Experimental results indicate that the algorithm has good generalization ability and high-image reconstruction quality

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.

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

Discrete least squares polynomial approximation with random evaluations - application to PDEs with Random parameters

KAUST Repository

Nobile, Fabio

2015-01-07

We consider a general problem F(u, y) = 0 where u is the unknown solution, possibly Hilbert space valued, and y a set of uncertain parameters. We specifically address the situation in which the parameterto-solution map u(y) is smooth, however y could be very high (or even infinite) dimensional. In particular, we are interested in cases in which F is a differential operator, u a Hilbert space valued function and y a distributed, space and/or time varying, random field. We aim at reconstructing the parameter-to-solution map u(y) from random noise-free or noisy observations in random points by discrete least squares on polynomial spaces. The noise-free case is relevant whenever the technique is used to construct metamodels, based on polynomial expansions, for the output of computer experiments. In the case of PDEs with random parameters, the metamodel is then used to approximate statistics of the output quantity. We discuss the stability of discrete least squares on random points show convergence estimates both in expectation and probability. We also present possible strategies to select, either a-priori or by adaptive algorithms, sequences of approximating polynomial spaces that allow to reduce, and in some cases break, the curse of dimensionality

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.

Sustainability Evaluation of Power Grid Construction Projects Using Improved TOPSIS and Least Square Support Vector Machine with Modified Fly Optimization Algorithm

Directory of Open Access Journals (Sweden)

Dongxiao Niu

2018-01-01

Full Text Available The electric power industry is of great significance in promoting social and economic development and improving people’s living standards. Power grid construction is a necessary part of infrastructure construction, whose sustainability plays an important role in economic development, environmental protection and social progress. In order to effectively evaluate the sustainability of power grid construction projects, in this paper, we first identified 17 criteria from four dimensions including economy, technology, society and environment to establish the evaluation criteria system. After that, the grey incidence analysis was used to modify the traditional Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS, which made it possible to evaluate the sustainability of electric power construction projects based on visual angle of similarity and nearness. Then, in order to simplify the procedure of experts scoring and computation, on the basis of evaluation results of the improved TOPSIS, the model using Modified Fly Optimization Algorithm (MFOA to optimize the Least Square Support Vector Machine (LSSVM was established. Finally, a numerical example was given to demonstrate the effectiveness of the proposed model.

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.

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

Directory of Open Access Journals (Sweden)

Ade Widyaningsih

2015-04-01

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

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

Directory of Open Access Journals (Sweden)

Ade Widyaningsih

2014-06-01

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

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 ...

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.

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

International Nuclear Information System (INIS)

Aspinall, J.

1982-01-01

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

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 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

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.

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

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.

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.

A deterministic iterative least-squares algorithm for beam weight optimization in conformal radiotherapy

International Nuclear Information System (INIS)

Chen Yan; Michalski, Darek; Houser, Christopher; Galvin, James M.

2002-01-01

Currently, inverse treatment planning in conformal radiotherapy is, in part, a trial-and-error process due to the interplay of many competing criteria for obtaining a clinically acceptable dose distribution. A new method is developed for beam weight optimization that incorporates clinically relevant nonlinear and linear constraints. The process is driven by a nonlinear, quasi-quadratic objective function and the solution space is defined by a set of linear constraints. At each step of iteration, the optimization problem is linearized by a self-consistent approximation that is local to the existing dose distribution. The dose distribution is then improved by solving a series of constrained least-squares problems using an established method until all prescribed constraints are satisfied. This differs from the current approaches in that it does not rely on the search for the global minimum of a specific objective function. Essentially, our proposed objective function can be construed as a functional that comprises a class of dose-based quadratic objective functions. Empirical adjustment for appropriate model parameters in the construction of objective function is minimized, since these parameters are in effect adaptively adjusted during optimization. The method is robust in solving difficult clinical cases using either aperture or pencil beam based planning techniques for intensity-modulated radiation therapy. (author)

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.

Ajustar: A interactive processor for to fit, by means of least squares, one variable polynomials (arbitrary degree) at experimental points

International Nuclear Information System (INIS)

Sanchez Miro, J. J.; Pena Gutierrez, J.

1991-01-01

In this report is offered, to scientist and technical people, a numeric tool consisting in a FORTRAN program, of interactive use, with destination to make lineal l east squares , fittings on any set of empirical observations. The method based in the orthogonal functions (for discrete case), instead of direct solving the equations system, is used. The procedure includes also the optionally facilities of: variable change, direct interpolation, correlation non linear factor, w eights o f the points, confidence intervals (Schelle, Miller, Student), and plotting results. (Author) 10 refs

Weighted Least Squares Techniques for Improved Received Signal Strength Based Localization

Directory of Open Access Journals (Sweden)

José R. Casar

2011-09-01

Full Text Available The practical deployment of wireless positioning systems requires minimizing the calibration procedures while improving the location estimation accuracy. Received Signal Strength localization techniques using propagation channel models are the simplest alternative, but they are usually designed under the assumption that the radio propagation model is to be perfectly characterized a priori. In practice, this assumption does not hold and the localization results are affected by the inaccuracies of the theoretical, roughly calibrated or just imperfect channel models used to compute location. In this paper, we propose the use of weighted multilateration techniques to gain robustness with respect to these inaccuracies, reducing the dependency of having an optimal channel model. In particular, we propose two weighted least squares techniques based on the standard hyperbolic and circular positioning algorithms that specifically consider the accuracies of the different measurements to obtain a better estimation of the position. These techniques are compared to the standard hyperbolic and circular positioning techniques through both numerical simulations and an exhaustive set of real experiments on different types of wireless networks (a wireless sensor network, a WiFi network and a Bluetooth network. The algorithms not only produce better localization results with a very limited overhead in terms of computational cost but also achieve a greater robustness to inaccuracies in channel modeling.

Least Squares Neural Network-Based Wireless E-Nose System Using an SnO₂ Sensor Array.

Science.gov (United States)

Shahid, Areej; Choi, Jong-Hyeok; Rana, Abu Ul Hassan Sarwar; Kim, Hyun-Seok

2018-05-06

Over the last few decades, the development of the electronic nose (E-nose) for detection and quantification of dangerous and odorless gases, such as methane (CH₄) and carbon monoxide (CO), using an array of SnO₂ gas sensors has attracted considerable attention. This paper addresses sensor cross sensitivity by developing a classifier and estimator using an artificial neural network (ANN) and least squares regression (LSR), respectively. Initially, the ANN was implemented using a feedforward pattern recognition algorithm to learn the collective behavior of an array as the signature of a particular gas. In the second phase, the classified gas was quantified by minimizing the mean square error using LSR. The combined approach produced 98.7% recognition probability, with 95.5 and 94.4% estimated gas concentration accuracies for CH₄ and CO, respectively. The classifier and estimator parameters were deployed in a remote microcontroller for the actualization of a wireless E-nose system.

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...

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

International Nuclear Information System (INIS)

Shuke, Noriyuki

1991-01-01

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

Identifying multiple outliers in linear regression: robust fit and clustering approach

International Nuclear Information System (INIS)

Robiah Adnan; Mohd Nor Mohamad; Halim Setan

2001-01-01

This research provides a clustering based approach for determining potential candidates for outliers. This is modification of the method proposed by Serbert et. al (1988). It is based on using the single linkage clustering algorithm to group the standardized predicted and residual values of data set fit by least trimmed of squares (LTS). (Author)

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

A Precise Lane Detection Algorithm Based on Top View Image Transformation and Least-Square Approaches

Directory of Open Access Journals (Sweden)

Byambaa Dorj

2016-01-01

Full Text Available The next promising key issue of the automobile development is a self-driving technique. One of the challenges for intelligent self-driving includes a lane-detecting and lane-keeping capability for advanced driver assistance systems. This paper introduces an efficient and lane detection method designed based on top view image transformation that converts an image from a front view to a top view space. After the top view image transformation, a Hough transformation technique is integrated by using a parabolic model of a curved lane in order to estimate a parametric model of the lane in the top view space. The parameters of the parabolic model are estimated by utilizing a least-square approach. The experimental results show that the newly proposed lane detection method with the top view transformation is very effective in estimating a sharp and curved lane leading to a precise self-driving capability.

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.

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.

LEAST SQUARE APPROACH FOR ESTIMATING OF LAND SURFACE TEMPERATURE FROM LANDSAT-8 SATELLITE DATA USING RADIATIVE TRANSFER EQUATION

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Y. Jouybari-Moghaddam

2017-09-01

Full Text Available Land Surface Temperature (LST is one of the significant variables measured by remotely sensed data, and it is applied in many environmental and Geoscience studies. The main aim of this study is to develop an algorithm to retrieve the LST from Landsat-8 satellite data using Radiative Transfer Equation (RTE. However, LST can be retrieved from RTE, but, since the RTE has two unknown parameters including LST and surface emissivity, estimating LST from RTE is an under the determined problem. In this study, in order to solve this problem, an approach is proposed an equation set includes two RTE based on Landsat-8 thermal bands (i.e.: band 10 and 11 and two additional equations based on the relation between the Normalized Difference Vegetation Index (NDVI and emissivity of Landsat-8 thermal bands by using simulated data for Landsat-8 bands. The iterative least square approach was used for solving the equation set. The LST derived from proposed algorithm is evaluated by the simulated dataset, built up by MODTRAN. The result shows the Root Mean Squared Error (RMSE is less than 1.18°K. Therefore; the proposed algorithm can be a suitable and robust method to retrieve the LST from Landsat-8 satellite data.

Least Square Approach for Estimating of Land Surface Temperature from LANDSAT-8 Satellite Data Using Radiative Transfer Equation

Science.gov (United States)

Jouybari-Moghaddam, Y.; Saradjian, M. R.; Forati, A. M.

2017-09-01

Land Surface Temperature (LST) is one of the significant variables measured by remotely sensed data, and it is applied in many environmental and Geoscience studies. The main aim of this study is to develop an algorithm to retrieve the LST from Landsat-8 satellite data using Radiative Transfer Equation (RTE). However, LST can be retrieved from RTE, but, since the RTE has two unknown parameters including LST and surface emissivity, estimating LST from RTE is an under the determined problem. In this study, in order to solve this problem, an approach is proposed an equation set includes two RTE based on Landsat-8 thermal bands (i.e.: band 10 and 11) and two additional equations based on the relation between the Normalized Difference Vegetation Index (NDVI) and emissivity of Landsat-8 thermal bands by using simulated data for Landsat-8 bands. The iterative least square approach was used for solving the equation set. The LST derived from proposed algorithm is evaluated by the simulated dataset, built up by MODTRAN. The result shows the Root Mean Squared Error (RMSE) is less than 1.18°K. Therefore; the proposed algorithm can be a suitable and robust method to retrieve the LST from Landsat-8 satellite data.

The application of bayesian statistic in data fit processing

International Nuclear Information System (INIS)

Guan Xingyin; Li Zhenfu; Song Zhaohui

2010-01-01

The rationality and disadvantage of least squares fitting that is usually used in data processing is analyzed, and the theory and commonly method that Bayesian statistic is applied in data processing is shown in detail. As it is proved in analysis, Bayesian approach avoid the limitative hypothesis that least squares fitting has in data processing, and the result has traits that it is more scientific and more easily understood, may replace the least squares fitting to apply in data processing. (authors)

A constrained robust least squares approach for contaminant release history identification

Science.gov (United States)

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

2006-04-01

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

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.

Application of numerical methods in spectroscopy : fitting of the curve of thermoluminescence

International Nuclear Information System (INIS)

RANDRIAMANALINA, S.

1999-01-01

The method of non linear least squares is one of the mathematical tools widely employed in spectroscopy, it is used for the determination of parameters of a model. In other hand, the spline function is among fitting functions that introduce the smallest error. It is used for the calculation of the area under the curve. We present an application of these methods, with the details of the corresponding algorithms, to the fitting of the thermoluminescence curve. [fr

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.

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.

Geodesic least squares regression for scaling studies in magnetic confinement fusion

International Nuclear Information System (INIS)

Verdoolaege, Geert

2015-01-01

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

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

Wavelet-LMS algorithm-based echo cancellers

Science.gov (United States)

Seetharaman, Lalith K.; Rao, Sathyanarayana S.

2002-12-01

This paper presents Echo Cancellers based on the Wavelet-LMS Algorithm. The performance of the Least Mean Square Algorithm in Wavelet transform domain is observed and its application in Echo cancellation is analyzed. The Widrow-Hoff Least Mean Square Algorithm is most widely used algorithm for Adaptive filters that function as Echo Cancellers. The present day communication signals are widely non-stationary in nature and some errors crop up when Least Mean Square Algorithm is used for the Echo Cancellers handling such signals. The analysis of non-stationary signals often involves a compromise between how well transitions or discontinuities can be located. The multi-scale or multi-resolution of signal analysis, which is the essence of wavelet transform, makes Wavelets popular in non-stationary signal analysis. In this paper, we present a Wavelet-LMS algorithm wherein the wavelet coefficients of a signal are modified adaptively using the Least Mean Square Algorithm and then reconstructed to give an Echo-free signal. The Echo Canceller based on this Algorithm is found to have a better convergence and a comparatively lesser MSE (Mean Square error).

Regularized plane-wave least-squares Kirchhoff migration

KAUST Repository

Wang, Xin

2013-09-22

A Kirchhoff least-squares migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images. A regularization term is included that accounts for mispositioning of reflectors due to errors in the velocity model. Both synthetic and field results show that: 1) LSM with a reflectivity model common for all the plane-wave gathers provides the best image when the migration velocity model is accurate, but it is more sensitive to the velocity errors, 2) the regularized plane-wave LSM is more robust in the presence of velocity errors, and 3) LSM achieves both computational and IO saving by plane-wave encoding compared to shot-domain LSM for the models tested.

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.

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

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

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

Iterative raw measurements restoration method with penalized weighted least squares approach for low-dose CT

Science.gov (United States)

Takahashi, Hisashi; Goto, Taiga; Hirokawa, Koichi; Miyazaki, Osamu

2014-03-01

Statistical iterative reconstruction and post-log data restoration algorithms for CT noise reduction have been widely studied and these techniques have enabled us to reduce irradiation doses while maintaining image qualities. In low dose scanning, electronic noise becomes obvious and it results in some non-positive signals in raw measurements. The nonpositive signal should be converted to positive signal so that it can be log-transformed. Since conventional conversion methods do not consider local variance on the sinogram, they have difficulty of controlling the strength of the filtering. Thus, in this work, we propose a method to convert the non-positive signal to the positive signal by mainly controlling the local variance. The method is implemented in two separate steps. First, an iterative restoration algorithm based on penalized weighted least squares is used to mitigate the effect of electronic noise. The algorithm preserves the local mean and reduces the local variance induced by the electronic noise. Second, smoothed raw measurements by the iterative algorithm are converted to the positive signal according to a function which replaces the non-positive signal with its local mean. In phantom studies, we confirm that the proposed method properly preserves the local mean and reduce the variance induced by the electronic noise. Our technique results in dramatically reduced shading artifacts and can also successfully cooperate with the post-log data filter to reduce streak artifacts.

Improved prediction of drug-target interactions using regularized least squares integrating with kernel fusion technique

Energy Technology Data Exchange (ETDEWEB)

Hao, Ming; Wang, Yanli, E-mail: ywang@ncbi.nlm.nih.gov; Bryant, Stephen H., E-mail: bryant@ncbi.nlm.nih.gov

2016-02-25

Identification of drug-target interactions (DTI) is a central task in drug discovery processes. In this work, a simple but effective regularized least squares integrating with nonlinear kernel fusion (RLS-KF) algorithm is proposed to perform DTI predictions. Using benchmark DTI datasets, our proposed algorithm achieves the state-of-the-art results with area under precision–recall curve (AUPR) of 0.915, 0.925, 0.853 and 0.909 for enzymes, ion channels (IC), G protein-coupled receptors (GPCR) and nuclear receptors (NR) based on 10 fold cross-validation. The performance can further be improved by using a recalculated kernel matrix, especially for the small set of nuclear receptors with AUPR of 0.945. Importantly, most of the top ranked interaction predictions can be validated by experimental data reported in the literature, bioassay results in the PubChem BioAssay database, as well as other previous studies. Our analysis suggests that the proposed RLS-KF is helpful for studying DTI, drug repositioning as well as polypharmacology, and may help to accelerate drug discovery by identifying novel drug targets. - Graphical abstract: Flowchart of the proposed RLS-KF algorithm for drug-target interaction predictions. - Highlights: • A nonlinear kernel fusion algorithm is proposed to perform drug-target interaction predictions. • Performance can further be improved by using the recalculated kernel. • Top predictions can be validated by experimental data.

Improved prediction of drug-target interactions using regularized least squares integrating with kernel fusion technique

International Nuclear Information System (INIS)

Hao, Ming; Wang, Yanli; Bryant, Stephen H.

2016-01-01

Identification of drug-target interactions (DTI) is a central task in drug discovery processes. In this work, a simple but effective regularized least squares integrating with nonlinear kernel fusion (RLS-KF) algorithm is proposed to perform DTI predictions. Using benchmark DTI datasets, our proposed algorithm achieves the state-of-the-art results with area under precision–recall curve (AUPR) of 0.915, 0.925, 0.853 and 0.909 for enzymes, ion channels (IC), G protein-coupled receptors (GPCR) and nuclear receptors (NR) based on 10 fold cross-validation. The performance can further be improved by using a recalculated kernel matrix, especially for the small set of nuclear receptors with AUPR of 0.945. Importantly, most of the top ranked interaction predictions can be validated by experimental data reported in the literature, bioassay results in the PubChem BioAssay database, as well as other previous studies. Our analysis suggests that the proposed RLS-KF is helpful for studying DTI, drug repositioning as well as polypharmacology, and may help to accelerate drug discovery by identifying novel drug targets. - Graphical abstract: Flowchart of the proposed RLS-KF algorithm for drug-target interaction predictions. - Highlights: • A nonlinear kernel fusion algorithm is proposed to perform drug-target interaction predictions. • Performance can further be improved by using the recalculated kernel. • Top predictions can be validated by experimental data.

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.

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.

Skeletonized Least Squares Wave Equation Migration

KAUST Repository

Zhan, Ge

2010-10-17

The theory for skeletonized least squares wave equation migration (LSM) is presented. The key idea is, for an assumed velocity model, the source‐side Green\\'s function and the geophone‐side Green\\'s function are computed by a numerical solution of the wave equation. Only the early‐arrivals of these Green\\'s functions are saved and skeletonized to form the migration Green\\'s function (MGF) by convolution. Then the migration image is obtained by a dot product between the recorded shot gathers and the MGF for every trial image point. The key to an efficient implementation of iterative LSM is that at each conjugate gradient iteration, the MGF is reused and no new finitedifference (FD) simulations are needed to get the updated migration image. It is believed that this procedure combined with phase‐encoded multi‐source technology will allow for the efficient computation of wave equation LSM images in less time than that of conventional reverse time migration (RTM).

Elastic least-squares reverse time migration

KAUST Repository

Feng, Zongcai

2017-03-08

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

Elastic least-squares reverse time migration

KAUST Repository

Feng, Zongcai; Schuster, Gerard T.

2017-01-01

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

Improving imaging quality using least-squares reverse time migration: application to data from Bohai basin

KAUST Repository

Zhang, Hao; Liu, Qiancheng; Wu, Jizhong

2017-01-01

Least-squares reverse time migration (LSRTM) is a seismic imaging technique based on linear inversion, which usually aims to improve the quality of seismic image through removing the acquisition footprint, suppressing migration artifacts, and enhancing resolution. LSRTM has been shown to produce migration images with better quality than those computed by conventional migration. In this paper, our derivation of LSRTM approximates the near-incident reflection coefficient with the normal-incident reflection coefficient, which shows that the reflectivity term defined is related to the normal-incident reflection coefficient and the background velocity. With reflected data, LSRTM is mainly sensitive to impedance perturbations. According to an approximate relationship between them, we reformulate the perturbation related system into a reflection-coefficient related one. Then, we seek the inverted image through linearized iteration. In the proposed algorithm, we only need the migration velocity for LSRTM considering that the density changes gently when compared with migration velocity. To validate our algorithms, we first apply it to a synthetic case and then a field data set. Both applications illustrate that our imaging results are of good quality.

Improving imaging quality using least-squares reverse time migration: application to data from Bohai basin

KAUST Repository

Zhang, Hao

2017-07-07

Least-squares reverse time migration (LSRTM) is a seismic imaging technique based on linear inversion, which usually aims to improve the quality of seismic image through removing the acquisition footprint, suppressing migration artifacts, and enhancing resolution. LSRTM has been shown to produce migration images with better quality than those computed by conventional migration. In this paper, our derivation of LSRTM approximates the near-incident reflection coefficient with the normal-incident reflection coefficient, which shows that the reflectivity term defined is related to the normal-incident reflection coefficient and the background velocity. With reflected data, LSRTM is mainly sensitive to impedance perturbations. According to an approximate relationship between them, we reformulate the perturbation related system into a reflection-coefficient related one. Then, we seek the inverted image through linearized iteration. In the proposed algorithm, we only need the migration velocity for LSRTM considering that the density changes gently when compared with migration velocity. To validate our algorithms, we first apply it to a synthetic case and then a field data set. Both applications illustrate that our imaging results are of good quality.

CURVE LSFIT, Gamma Spectrometer Calibration by Interactive Fitting Method

International Nuclear Information System (INIS)

Olson, D.G.

1992-01-01

1 - Description of program or function: CURVE and LSFIT are interactive programs designed to obtain the best data fit to an arbitrary curve. CURVE finds the type of fitting routine which produces the best curve. The types of fitting routines available are linear regression, exponential, logarithmic, power, least squares polynomial, and spline. LSFIT produces a reliable calibration curve for gamma ray spectrometry by using the uncertainty value associated with each data point. LSFIT is intended for use where an entire efficiency curve is to be made starting at 30 KeV and continuing to 1836 KeV. It creates calibration curves using up to three least squares polynomial fits to produce the best curve for photon energies above 120 KeV and a spline function to combine these fitted points with a best fit for points below 120 KeV. 2 - Method of solution: The quality of fit is tested by comparing the measured y-value to the y-value calculated from the fitted curve. The fractional difference between these two values is printed for the evaluation of the quality of the fit. 3 - Restrictions on the complexity of the problem - Maxima of: 2000 data points calibration curve output (LSFIT) 30 input data points 3 least squares polynomial fits (LSFIT) The least squares polynomial fit requires that the number of data points used exceed the degree of fit by at least two

Fitting PAC spectra with a hybrid algorithm

Energy Technology Data Exchange (ETDEWEB)

Alves, M. A., E-mail: mauro@sepn.org [Instituto de Aeronautica e Espaco (Brazil); Carbonari, A. W., E-mail: carbonar@ipen.br [Instituto de Pesquisas Energeticas e Nucleares (Brazil)

2008-01-15

A hybrid algorithm (HA) that blends features of genetic algorithms (GA) and simulated annealing (SA) was implemented for simultaneous fits of perturbed angular correlation (PAC) spectra. The main characteristic of the HA is the incorporation of a selection criterion based on SA into the basic structure of GA. The results obtained with the HA compare favorably with fits performed with conventional methods.

Implementation of a computationally efficient least-squares algorithm for highly under-determined three-dimensional diffuse optical tomography problems.

Science.gov (United States)

Yalavarthy, Phaneendra K; Lynch, Daniel R; Pogue, Brian W; Dehghani, Hamid; Paulsen, Keith D

2008-05-01

Three-dimensional (3D) diffuse optical tomography is known to be a nonlinear, ill-posed and sometimes under-determined problem, where regularization is added to the minimization to allow convergence to a unique solution. In this work, a generalized least-squares (GLS) minimization method was implemented, which employs weight matrices for both data-model misfit and optical properties to include their variances and covariances, using a computationally efficient scheme. This allows inversion of a matrix that is of a dimension dictated by the number of measurements, instead of by the number of imaging parameters. This increases the computation speed up to four times per iteration in most of the under-determined 3D imaging problems. An analytic derivation, using the Sherman-Morrison-Woodbury identity, is shown for this efficient alternative form and it is proven to be equivalent, not only analytically, but also numerically. Equivalent alternative forms for other minimization methods, like Levenberg-Marquardt (LM) and Tikhonov, are also derived. Three-dimensional reconstruction results indicate that the poor recovery of quantitatively accurate values in 3D optical images can also be a characteristic of the reconstruction algorithm, along with the target size. Interestingly, usage of GLS reconstruction methods reduces error in the periphery of the image, as expected, and improves by 20% the ability to quantify local interior regions in terms of the recovered optical contrast, as compared to LM methods. Characterization of detector photo-multiplier tubes noise has enabled the use of the GLS method for reconstructing experimental data and showed a promise for better quantification of target in 3D optical imaging. Use of these new alternative forms becomes effective when the ratio of the number of imaging property parameters exceeds the number of measurements by a factor greater than 2.

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

Directory of Open Access Journals (Sweden)

Ahmad Bilfarsah

2005-04-01

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

Inversion of Love wave phase velocity using smoothness-constrained least-squares technique; Heikatsuka seiyakutsuki saisho jijoho ni yoru love ha iso sokudo no inversion

Energy Technology Data Exchange (ETDEWEB)

Kawamura, S [Nippon Geophysical Prospecting Co. Ltd., Tokyo (Japan)

1996-10-01

Smoothness-constrained least-squares technique with ABIC minimization was applied to the inversion of phase velocity of surface waves during geophysical exploration, to confirm its usefulness. Since this study aimed mainly at the applicability of the technique, Love wave was used which is easier to treat theoretically than Rayleigh wave. Stable successive approximation solutions could be obtained by the repeated improvement of velocity model of S-wave, and an objective model with high reliability could be determined. While, for the inversion with simple minimization of the residuals squares sum, stable solutions could be obtained by the repeated improvement, but the judgment of convergence was very hard due to the smoothness-constraint, which might make the obtained model in a state of over-fitting. In this study, Love wave was used to examine the applicability of the smoothness-constrained least-squares technique with ABIC minimization. Applicability of this to Rayleigh wave will be investigated. 8 refs.

Time-Series INSAR: An Integer Least-Squares Approach For Distributed Scatterers

Science.gov (United States)

Samiei-Esfahany, Sami; Hanssen, Ramon F.

2012-01-01

The objective of this research is to extend the geode- tic mathematical model which was developed for persistent scatterers to a model which can exploit distributed scatterers (DS). The main focus is on the integer least- squares framework, and the main challenge is to include the decorrelation effect in the mathematical model. In order to adapt the integer least-squares mathematical model for DS we altered the model from a single master to a multi-master configuration and introduced the decorrelation effect stochastically. This effect is described in our model by a full covariance matrix. We propose to de- rive this covariance matrix by numerical integration of the (joint) probability distribution function (PDF) of interferometric phases. This PDF is a function of coherence values and can be directly computed from radar data. We show that the use of this model can improve the performance of temporal phase unwrapping of distributed scatterers.

A three-step algorithm for CANDECOMP/PARAFAC analysis of large data sets with multicollinearity

NARCIS (Netherlands)

Kiers, H.A.L.

1998-01-01

Fitting the CANDECOMP/PARAFAC model by the standard alternating least squares algorithm often requires very many iterations. One case in point is that of analysing data with mild to severe multicollinearity. If, in addition, the size of the data is large, the computation of one CANDECOMP/PARAFAC

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

DEFF Research Database (Denmark)

Gustavson, Fred G.; Wasniewski, Jerzy

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

Penalized weighted least-squares approach for low-dose x-ray computed tomography

Science.gov (United States)

Wang, Jing; Li, Tianfang; Lu, Hongbing; Liang, Zhengrong

2006-03-01

The noise of low-dose computed tomography (CT) sinogram follows approximately a Gaussian distribution with nonlinear dependence between the sample mean and variance. The noise is statistically uncorrelated among detector bins at any view angle. However the correlation coefficient matrix of data signal indicates a strong signal correlation among neighboring views. Based on above observations, Karhunen-Loeve (KL) transform can be used to de-correlate the signal among the neighboring views. In each KL component, a penalized weighted least-squares (PWLS) objective function can be constructed and optimal sinogram can be estimated by minimizing the objective function, followed by filtered backprojection (FBP) for CT image reconstruction. In this work, we compared the KL-PWLS method with an iterative image reconstruction algorithm, which uses the Gauss-Seidel iterative calculation to minimize the PWLS objective function in image domain. We also compared the KL-PWLS with an iterative sinogram smoothing algorithm, which uses the iterated conditional mode calculation to minimize the PWLS objective function in sinogram space, followed by FBP for image reconstruction. Phantom experiments show a comparable performance of these three PWLS methods in suppressing the noise-induced artifacts and preserving resolution in reconstructed images. Computer simulation concurs with the phantom experiments in terms of noise-resolution tradeoff and detectability in low contrast environment. The KL-PWLS noise reduction may have the advantage in computation for low-dose CT imaging, especially for dynamic high-resolution studies.

Eddy current characterization of small cracks using least square support vector machine

Science.gov (United States)

Chelabi, M.; Hacib, T.; Le Bihan, Y.; Ikhlef, N.; Boughedda, H.; Mekideche, M. R.

2016-04-01

Eddy current (EC) sensors are used for non-destructive testing since they are able to probe conductive materials. Despite being a conventional technique for defect detection and localization, the main weakness of this technique is that defect characterization, of the exact determination of the shape and dimension, is still a question to be answered. In this work, we demonstrate the capability of small crack sizing using signals acquired from an EC sensor. We report our effort to develop a systematic approach to estimate the size of rectangular and thin defects (length and depth) in a conductive plate. The achieved approach by the novel combination of a finite element method (FEM) with a statistical learning method is called least square support vector machines (LS-SVM). First, we use the FEM to design the forward problem. Next, an algorithm is used to find an adaptive database. Finally, the LS-SVM is used to solve the inverse problems, creating polynomial functions able to approximate the correlation between the crack dimension and the signal picked up from the EC sensor. Several methods are used to find the parameters of the LS-SVM. In this study, the particle swarm optimization (PSO) and genetic algorithm (GA) are proposed for tuning the LS-SVM. The results of the design and the inversions were compared to both simulated and experimental data, with accuracy experimentally verified. These suggested results prove the applicability of the presented approach.

Prediction of ferric iron precipitation in bioleaching process using partial least squares and artificial neural network

Directory of Open Access Journals (Sweden)

Golmohammadi Hassan

2013-01-01

Full Text Available A quantitative structure-property relationship (QSPR study based on partial least squares (PLS and artificial neural network (ANN was developed for the prediction of ferric iron precipitation in bioleaching process. The leaching temperature, initial pH, oxidation/reduction potential (ORP, ferrous concentration and particle size of ore were used as inputs to the network. The output of the model was ferric iron precipitation. The optimal condition of the neural network was obtained by adjusting various parameters by trial-and-error. After optimization and training of the network according to back-propagation algorithm, a 5-5-1 neural network was generated for prediction of ferric iron precipitation. The root mean square error for the neural network calculated ferric iron precipitation for training, prediction and validation set are 32.860, 40.739 and 35.890, respectively, which are smaller than those obtained by PLS model (180.972, 165.047 and 149.950, respectively. Results obtained reveal the reliability and good predictivity of neural network model for the prediction of ferric iron precipitation in bioleaching process.

Seismic time-lapse imaging using Interferometric least-squares migration

KAUST Repository

Sinha, Mrinal

2016-09-06

One of the problems with 4D surveys is that the environmental conditions change over time so that the experiment is insufficiently repeatable. To mitigate this problem, we propose the use of interferometric least-squares migration (ILSM) to estimate the migration image for the baseline and monitor surveys. Here, a known reflector is used as the reference reflector for ILSM. Results with synthetic and field data show that ILSM can eliminate artifacts caused by non-repeatability in time-lapse surveys.

Seismic time-lapse imaging using Interferometric least-squares migration

KAUST Repository

Sinha, Mrinal; Schuster, Gerard T.

2016-01-01

One of the problems with 4D surveys is that the environmental conditions change over time so that the experiment is insufficiently repeatable. To mitigate this problem, we propose the use of interferometric least-squares migration (ILSM) to estimate the migration image for the baseline and monitor surveys. Here, a known reflector is used as the reference reflector for ILSM. Results with synthetic and field data show that ILSM can eliminate artifacts caused by non-repeatability in time-lapse surveys.

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...

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%

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.

LBP-based penalized weighted least-squares approach to low-dose cone-beam computed tomography reconstruction

Science.gov (United States)

Ma, Ming; Wang, Huafeng; Liu, Yan; Zhang, Hao; Gu, Xianfeng; Liang, Zhengrong

2014-03-01

Cone-beam computed tomography (CBCT) has attracted growing interest of researchers in image reconstruction. The mAs level of the X-ray tube current, in practical application of CBCT, is mitigated in order to reduce the CBCT dose. The lowering of the X-ray tube current, however, results in the degradation of image quality. Thus, low-dose CBCT image reconstruction is in effect a noise problem. To acquire clinically acceptable quality of image, and keep the X-ray tube current as low as achievable in the meanwhile, some penalized weighted least-squares (PWLS)-based image reconstruction algorithms have been developed. One representative strategy in previous work is to model the prior information for solution regularization using an anisotropic penalty term. To enhance the edge preserving and noise suppressing in a finer scale, a novel algorithm combining the local binary pattern (LBP) with penalized weighted leastsquares (PWLS), called LBP-PWLS-based image reconstruction algorithm, is proposed in this work. The proposed LBP-PWLS-based algorithm adaptively encourages strong diffusion on the local spot/flat region around a voxel and less diffusion on edge/corner ones by adjusting the penalty for cost function, after the LBP is utilized to detect the region around the voxel as spot, flat and edge ones. The LBP-PWLS-based reconstruction algorithm was evaluated using the sinogram data acquired by a clinical CT scanner from the CatPhan® 600 phantom. Experimental results on the noiseresolution tradeoff measurement and other quantitative measurements demonstrated its feasibility and effectiveness in edge preserving and noise suppressing in comparison with a previous PWLS reconstruction algorithm.

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

Applying ISO 11929:2010 Standard to detection limit calculation in least-squares based multi-nuclide gamma-ray spectrum evaluation

Energy Technology Data Exchange (ETDEWEB)

Kanisch, G., E-mail: guenter.kanisch@hanse.net

2017-05-21

The concepts of ISO 11929 (2010) are applied to evaluation of radionuclide activities from more complex multi-nuclide gamma-ray spectra. From net peak areas estimated by peak fitting, activities and their standard uncertainties are calculated by weighted linear least-squares method with an additional step, where uncertainties of the design matrix elements are taken into account. A numerical treatment of the standard's uncertainty function, based on ISO 11929 Annex C.5, leads to a procedure for deriving decision threshold and detection limit values. The methods shown allow resolving interferences between radionuclide activities also in case of calculating detection limits where they can improve the latter by including more than one gamma line per radionuclide. The co'mmon single nuclide weighted mean is extended to an interference-corrected (generalized) weighted mean, which, combined with the least-squares method, allows faster detection limit calculations. In addition, a new grouped uncertainty budget was inferred, which for each radionuclide gives uncertainty budgets from seven main variables, such as net count rates, peak efficiencies, gamma emission intensities and others; grouping refers to summation over lists of peaks per radionuclide.

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

Energy Technology Data Exchange (ETDEWEB)

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

1996-12-31

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

Least-squares reverse time migration of marine data with frequency-selection encoding

KAUST Repository

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

2013-01-01

The phase-encoding technique can sometimes increase the efficiency of the least-squares reverse time migration (LSRTM) by more than one order of magnitude. However, traditional random encoding functions require all the encoded shots to share

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.

Partial Least Square with Savitzky Golay Derivative in Predicting Blood Hemoglobin Using Near Infrared Spectrum

Directory of Open Access Journals (Sweden)

Mohd Idrus Mohd Nazrul Effendy

2018-01-01

Full Text Available Near infrared spectroscopy (NIRS is a reliable technique that widely used in medical fields. Partial least square was developed to predict blood hemoglobin concentration using NIRS. The aims of this paper are (i to develop predictive model for near infrared spectroscopic analysis in blood hemoglobin prediction, (ii to establish relationship between blood hemoglobin and near infrared spectrum using a predictive model, (iii to evaluate the predictive accuracy of a predictive model based on root mean squared error (RMSE and coefficient of determination rp2. Partial least square with first order Savitzky Golay (SG derivative preprocessing (PLS-SGd1 showed the higher performance of predictions with RMSE = 0.7965 and rp2= 0.9206 in K-fold cross validation. Optimum number of latent variable (LV and frame length (f were 32 and 27 nm, respectively. These findings suggest that the relationship between blood hemoglobin and near infrared spectrum is strong, and the partial least square with first order SG derivative is able to predict the blood hemoglobin using near infrared spectral data.

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...

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...

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

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...

Elastic Model Transitions: a Hybrid Approach Utilizing Quadratic Inequality Constrained Least Squares (LSQI) and Direct Shape Mapping (DSM)

Science.gov (United States)

Jurenko, Robert J.; Bush, T. Jason; Ottander, John A.

2014-01-01

A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes both quadratically constrained least squares (LSQI) and Direct Shape Mapping (DSM) algorithms to determine physical displacements. This approach is applicable to the simulation of the elastic behavior of launch vehicles and other structures that utilize multiple LTI finite element model (FEM) derived mode sets that are propagated throughout time. The time invariant nature of the elastic data for discrete segments of the launch vehicle trajectory presents a problem of how to properly transition between models while preserving motion across the transition. In addition, energy may vary between flex models when using a truncated mode set. The LSQI-DSM algorithm can accommodate significant changes in energy between FEM models and carries elastic motion across FEM model transitions. Compared with previous approaches, the LSQI-DSM algorithm shows improvements ranging from a significant reduction to a complete removal of transients across FEM model transitions as well as maintaining elastic motion from the prior state.

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

Science.gov (United States)

Helmreich, James E.; Krog, K. Peter

2018-01-01

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

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

Securing a cyber physical system in nuclear power plants using least square approximation and computational geometric approach

International Nuclear Information System (INIS)

Gawand, Hemangi Laxman; Bhattacharjee, A. K.; Roy, Kallol

2017-01-01

In industrial plants such as nuclear power plants, system operations are performed by embedded controllers orchestrated by Supervisory Control and Data Acquisition (SCADA) software. A targeted attack (also termed a control aware attack) on the controller/SCADA software can lead a control system to operate in an unsafe mode or sometimes to complete shutdown of the plant. Such malware attacks can result in tremendous cost to the organization for recovery, cleanup, and maintenance activity. SCADA systems in operational mode generate huge log files. These files are useful in analysis of the plant behavior and diagnostics during an ongoing attack. However, they are bulky and difficult for manual inspection. Data mining techniques such as least squares approximation and computational methods can be used in the analysis of logs and to take proactive actions when required. This paper explores methodologies and algorithms so as to develop an effective monitoring scheme against control aware cyber attacks. It also explains soft computation techniques such as the computational geometric method and least squares approximation that can be effective in monitor design. This paper provides insights into diagnostic monitoring of its effectiveness by attack simulations on a four-tank model and using computation techniques to diagnose it. Cyber security of instrumentation and control systems used in nuclear power plants is of paramount importance and hence could be a possible target of such applications

Securing a cyber physical system in nuclear power plants using least square approximation and computational geometric approach

Energy Technology Data Exchange (ETDEWEB)

Gawand, Hemangi Laxman [Homi Bhabha National Institute, Computer Section, BARC, Mumbai (India); Bhattacharjee, A. K. [Reactor Control Division, BARC, Mumbai (India); Roy, Kallol [BHAVINI, Kalpakkam (India)

2017-04-15

In industrial plants such as nuclear power plants, system operations are performed by embedded controllers orchestrated by Supervisory Control and Data Acquisition (SCADA) software. A targeted attack (also termed a control aware attack) on the controller/SCADA software can lead a control system to operate in an unsafe mode or sometimes to complete shutdown of the plant. Such malware attacks can result in tremendous cost to the organization for recovery, cleanup, and maintenance activity. SCADA systems in operational mode generate huge log files. These files are useful in analysis of the plant behavior and diagnostics during an ongoing attack. However, they are bulky and difficult for manual inspection. Data mining techniques such as least squares approximation and computational methods can be used in the analysis of logs and to take proactive actions when required. This paper explores methodologies and algorithms so as to develop an effective monitoring scheme against control aware cyber attacks. It also explains soft computation techniques such as the computational geometric method and least squares approximation that can be effective in monitor design. This paper provides insights into diagnostic monitoring of its effectiveness by attack simulations on a four-tank model and using computation techniques to diagnose it. Cyber security of instrumentation and control systems used in nuclear power plants is of paramount importance and hence could be a possible target of such applications.

Securing a Cyber Physical System in Nuclear Power Plants Using Least Square Approximation and Computational Geometric Approach

Directory of Open Access Journals (Sweden)

Hemangi Laxman Gawand

2017-04-01

Full Text Available In industrial plants such as nuclear power plants, system operations are performed by embedded controllers orchestrated by Supervisory Control and Data Acquisition (SCADA software. A targeted attack (also termed a control aware attack on the controller/SCADA software can lead a control system to operate in an unsafe mode or sometimes to complete shutdown of the plant. Such malware attacks can result in tremendous cost to the organization for recovery, cleanup, and maintenance activity. SCADA systems in operational mode generate huge log files. These files are useful in analysis of the plant behavior and diagnostics during an ongoing attack. However, they are bulky and difficult for manual inspection. Data mining techniques such as least squares approximation and computational methods can be used in the analysis of logs and to take proactive actions when required. This paper explores methodologies and algorithms so as to develop an effective monitoring scheme against control aware cyber attacks. It also explains soft computation techniques such as the computational geometric method and least squares approximation that can be effective in monitor design. This paper provides insights into diagnostic monitoring of its effectiveness by attack simulations on a four-tank model and using computation techniques to diagnose it. Cyber security of instrumentation and control systems used in nuclear power plants is of paramount importance and hence could be a possible target of such applications.

A Monte Carlo Investigation of the Box-Cox Model and a Nonlinear Least Squares Alternative.

OpenAIRE

Showalter, Mark H

1994-01-01

This paper reports a Monte Carlo study of the Box-Cox model and a nonlinear least squares alternative. Key results include the following: the transformation parameter in the Box-Cox model appears to be inconsistently estimated in the presence of conditional heteroskedasticity; the constant term in both the Box-Cox and the nonlinear least squares models is poorly estimated in small samples; conditional mean forecasts tend to underestimate their true value in the Box-Cox model when the transfor...

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).

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...

Rapid classification of turmeric based on DNA fingerprint by near-infrared spectroscopy combined with moving window partial least squares-discrimination analysis

International Nuclear Information System (INIS)

Kasemsumran, Sumaporn; Suttiwijitpukdee, Nattaporn; Keeratinijakal, Vichein

2017-01-01

In this research, near-infrared (NIR) spectroscopy in combination with moving window partial least squares-discrimination analysis (MWPLS-DA) was utilized to discriminate the variety of turmeric based on DNA markers, which correlated to the quantity of curcuminoid. Curcuminoid was used as a marker compound in variety identification due to the most pharmacological properties of turmeric possessed from it. MWPLS-DA optimized informative NIR spectral regions for the fitting and prediction to {-1/1}-coded turmeric varieties, indicating variables in the development of latent variables in discrimination analysis. Consequently, MWPLS-DA benefited in the selection of combined informative NIR spectral regions of 1100 – 1260, 1300 – 1500 and 1880 – 2500 nm for classification modeling of turmeric variety with 148 calibration samples, and yielded the results better than that obtained from a partial least squares-discrimination analysis (PLS-DA) model built by using the whole NIR spectral region. An effective and rapid strategy of using NIR in combination with MWPLS-DA provided the best variety identification results of 100% in both specificity and total accuracy for 48 test samples. (author)

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.

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.

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-11-15

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

The reliability of nonlinear least-squares algorithm for data analysis of neural response activity during sinusoidal rotational stimulation in semicircular canal neurons.

Science.gov (United States)

Ren, Pengyu; Li, Bowen; Dong, Shiyao; Chen, Lin; Zhang, Yuelin

2018-01-01

Although many mathematical methods were used to analyze the neural activity under sinusoidal stimulation within linear response range in vestibular system, the reliabilities of these methods are still not reported, especially in nonlinear response range. Here we chose nonlinear least-squares algorithm (NLSA) with sinusoidal model to analyze the neural response of semicircular canal neurons (SCNs) during sinusoidal rotational stimulation (SRS) over a nonlinear response range. Our aim was to acquire a reliable mathematical method for data analysis under SRS in vestibular system. Our data indicated that the reliability of this method in an entire SCNs population was quite satisfactory. However, the reliability was strongly negatively depended on the neural discharge regularity. In addition, stimulation parameters were the vital impact factors influencing the reliability. The frequency had a significant negative effect but the amplitude had a conspicuous positive effect on the reliability. Thus, NLSA with sinusoidal model resulted a reliable mathematical tool for data analysis of neural response activity under SRS in vestibular system and more suitable for those under the stimulation with low frequency but high amplitude, suggesting that this method can be used in nonlinear response range. This method broke out of the restriction of neural activity analysis under nonlinear response range and provided a solid foundation for future study in nonlinear response range in vestibular system.

Soft sensor modelling by time difference, recursive partial least squares and adaptive model updating

International Nuclear Information System (INIS)

Fu, Y; Xu, O; Yang, W; Zhou, L; Wang, J

2017-01-01

To investigate time-variant and nonlinear characteristics in industrial processes, a soft sensor modelling method based on time difference, moving-window recursive partial least square (PLS) and adaptive model updating is proposed. In this method, time difference values of input and output variables are used as training samples to construct the model, which can reduce the effects of the nonlinear characteristic on modelling accuracy and retain the advantages of recursive PLS algorithm. To solve the high updating frequency of the model, a confidence value is introduced, which can be updated adaptively according to the results of the model performance assessment. Once the confidence value is updated, the model can be updated. The proposed method has been used to predict the 4-carboxy-benz-aldehyde (CBA) content in the purified terephthalic acid (PTA) oxidation reaction process. The results show that the proposed soft sensor modelling method can reduce computation effectively, improve prediction accuracy by making use of process information and reflect the process characteristics accurately. (paper)

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

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

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.

Fitting a function to time-dependent ensemble averaged data.

Science.gov (United States)

Fogelmark, Karl; Lomholt, Michael A; Irbäck, Anders; Ambjörnsson, Tobias

2018-05-03

Time-dependent ensemble averages, i.e., trajectory-based averages of some observable, are of importance in many fields of science. A crucial objective when interpreting such data is to fit these averages (for instance, squared displacements) with a function and extract parameters (such as diffusion constants). A commonly overlooked challenge in such function fitting procedures is that fluctuations around mean values, by construction, exhibit temporal correlations. We show that the only available general purpose function fitting methods, correlated chi-square method and the weighted least squares method (which neglects correlation), fail at either robust parameter estimation or accurate error estimation. We remedy this by deriving a new closed-form error estimation formula for weighted least square fitting. The new formula uses the full covariance matrix, i.e., rigorously includes temporal correlations, but is free of the robustness issues, inherent to the correlated chi-square method. We demonstrate its accuracy in four examples of importance in many fields: Brownian motion, damped harmonic oscillation, fractional Brownian motion and continuous time random walks. We also successfully apply our method, weighted least squares including correlation in error estimation (WLS-ICE), to particle tracking data. The WLS-ICE method is applicable to arbitrary fit functions, and we provide a publically available WLS-ICE software.

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

General least-squares fitting procedures to minimize the volume of a hyperellipsoid

International Nuclear Information System (INIS)

Wadlinger, E.A.

1979-01-01

Several methods for determining the shape parameters, which in two dimensions are the Courant-Snyder parameters, and the volume of an ellipse or hyperellipse that represent a set of phase-space points in a two or more dimensional hyperspace are presented. The ellipse parameters are useful for matching a beam to an accelerating or transport system and in studies of emittance growth. The fitting procedure minimizes the total volume of a hyperellipse by adjusting the ellipse shape parameters. The total volume is the sum of the individual particle volumes defined by the hyperellipse that passes through the phase-space point of a particle. A two-dimensional space is considered first; the results are then generalized to higher dimensions. Computer programs using these techniques were written. 1 figure

Implementation of the Least-Squares Lattice with Order and Forgetting Factor Estimation for FPGA

Czech Academy of Sciences Publication Activity Database

Pohl, Zdeněk; Tichý, Milan; Kadlec, Jiří

2008-01-01

Roč. 2008, č. 2008 (2008), s. 1-11 ISSN 1687-6172 R&D Projects: GA MŠk(CZ) 1M0567 EU Projects: European Commission(XE) 027611 - AETHER Program:FP6 Institutional research plan: CEZ:AV0Z10750506 Keywords : DSP * Least-squares lattice * order estimation * exponential forgetting factor estimation * FPGA implementation * scheduling * dynamic reconfiguration * microblaze Subject RIV: IN - Informatics, Computer Science Impact factor: 1.055, year: 2008 http://library.utia.cas.cz/separaty/2008/ZS/pohl-tichy-kadlec-implementation%20of%20the%20least-squares%20lattice%20with%20order%20and%20forgetting%20factor%20estimation%20for%20fpga.pdf

Unlocking interpretation in near infrared multivariate calibrations by orthogonal partial least squares.

Science.gov (United States)

Stenlund, Hans; Johansson, Erik; Gottfries, Johan; Trygg, Johan

2009-01-01

Near infrared spectroscopy (NIR) was developed primarily for applications such as the quantitative determination of nutrients in the agricultural and food industries. Examples include the determination of water, protein, and fat within complex samples such as grain and milk. Because of its useful properties, NIR analysis has spread to other areas such as chemistry and pharmaceutical production. NIR spectra consist of infrared overtones and combinations thereof, making interpretation of the results complicated. It can be very difficult to assign peaks to known constituents in the sample. Thus, multivariate analysis (MVA) has been crucial in translating spectral data into information, mainly for predictive purposes. Orthogonal partial least squares (OPLS), a new MVA method, has prediction and modeling properties similar to those of other MVA techniques, e.g., partial least squares (PLS), a method with a long history of use for the analysis of NIR data. OPLS provides an intrinsic algorithmic improvement for the interpretation of NIR data. In this report, four sets of NIR data were analyzed to demonstrate the improved interpretation provided by OPLS. The first two sets included simulated data to demonstrate the overall principles; the third set comprised a statistically replicated design of experiments (DoE), to demonstrate how instrumental difference could be accurately visualized and correctly attributed to Wood's anomaly phenomena; the fourth set was chosen to challenge the MVA by using data relating to powder mixing, a crucial step in the pharmaceutical industry prior to tabletting. Improved interpretation by OPLS was demonstrated for all four examples, as compared to alternative MVA approaches. It is expected that OPLS will be used mostly in applications where improved interpretation is crucial; one such area is process analytical technology (PAT). PAT involves fewer independent samples, i.e., batches, than would be associated with agricultural applications; in

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

Czech Academy of Sciences Publication Activity Database

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

2008-01-01

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

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.

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.

FITS: a function-fitting program

Energy Technology Data Exchange (ETDEWEB)

Balestrini, S.J.; Chezem, C.G.

1982-01-01

FITS is an iterating computer program that adjusts the parameters of a function to fit a set of data points according to the least squares criterion and then lists and plots the results. The function can be programmed or chosen from a library that is provided. The library can be expanded to include up to 99 functions. A general plotting routine, contained in the program but useful in its own right, is described separately in an Appendix.

A Monte Carlo Library Least Square approach in the Neutron Inelastic-scattering and Thermal-capture Analysis (NISTA) process in bulk coal samples

Science.gov (United States)

Reyhancan, Iskender Atilla; Ebrahimi, Alborz; Çolak, Üner; Erduran, M. Nizamettin; Angin, Nergis

2017-01-01

A new Monte-Carlo Library Least Square (MCLLS) approach for treating non-linear radiation analysis problem in Neutron Inelastic-scattering and Thermal-capture Analysis (NISTA) was developed. 14 MeV neutrons were produced by a neutron generator via the 3H (2H , n) 4He reaction. The prompt gamma ray spectra from bulk samples of seven different materials were measured by a Bismuth Germanate (BGO) gamma detection system. Polyethylene was used as neutron moderator along with iron and lead as neutron and gamma ray shielding, respectively. The gamma detection system was equipped with a list mode data acquisition system which streams spectroscopy data directly to the computer, event-by-event. A GEANT4 simulation toolkit was used for generating the single-element libraries of all the elements of interest. These libraries were then used in a Linear Library Least Square (LLLS) approach with an unknown experimental sample spectrum to fit it with the calculated elemental libraries. GEANT4 simulation results were also used for the selection of the neutron shielding material.

Contrast improvement of continuous wave diffuse optical tomography reconstruction by hybrid approach using least square and genetic algorithm

Science.gov (United States)

Patra, Rusha; Dutta, Pranab K.

2015-07-01

Reconstruction of the absorption coefficient of tissue with good contrast is of key importance in functional diffuse optical imaging. A hybrid approach using model-based iterative image reconstruction and a genetic algorithm is proposed to enhance the contrast of the reconstructed image. The proposed method yields an observed contrast of 98.4%, mean square error of 0.638×10-3, and object centroid error of (0.001 to 0.22) mm. Experimental validation of the proposed method has also been provided with tissue-like phantoms which shows a significant improvement in image quality and thus establishes the potential of the method for functional diffuse optical tomography reconstruction with continuous wave setup. A case study of finger joint imaging is illustrated as well to show the prospect of the proposed method in clinical diagnosis. The method can also be applied to the concentration measurement of a region of interest in a turbid medium.

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)

Figure-of-merit (FOM), an improved criterion over the normalized chi-squared test for assessing goodness-of-fit of gamma-ray spectral peaks

International Nuclear Information System (INIS)

Garo Balian, H.; Eddy, N.W.

1977-01-01

A careful experimenter knows that in order to choose the best curve fits of peaks from a gamma ray spectrum for such purposes as energy or intensity calibration, half-life determination, etc., the application of the normalized chi-squared test, [chisub(N)] 2 =chi 2 /(n-m), is insufficient. One must normally verify the goodness-of-fit with plots, detailed scans of residuals, etc. Because of different techniques of application, variations in backgrounds, in peak sizes and shapes, etc., quotation of the [chisub(N)] 2 value associated with an individual peak fit conveys very little information unless accompanied by considerable ancillary data. (This is not to say that the traditional chi 2 formula should not be used as the source of the normal equations in the least squares fitting procedure. But after the fitting, it is unreliable as a criterion for comparison with other fits.) The authors present a formula designated figure-of-merit (FOM) which greatly improves on the uncertainty and fluctuations of the [chisub(N)] 2 formula. An FOM value of less than 2.5% indicates a good fit (in the authors' judgement) irrespective of background conditions and variations in peak sizes and shapes. Furthermore, the authors feel the FOM formula is less subject to fluctuations resulting from different techniques of application. (Auth.)

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

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.

Enhancing Video Games Policy Based on Least-Squares Continuous Action Policy Iteration: Case Study on StarCraft Brood War and Glest RTS Games and the 8 Queens Board Game

Directory of Open Access Journals (Sweden)

Shahenda Sarhan

2016-01-01

Full Text Available With the rapid advent of video games recently and the increasing numbers of players and gamers, only a tough game with high policy, actions, and tactics survives. How the game responds to opponent actions is the key issue of popular games. Many algorithms were proposed to solve this problem such as Least-Squares Policy Iteration (LSPI and State-Action-Reward-State-Action (SARSA but they mainly depend on discrete actions, while agents in such a setting have to learn from the consequences of their continuous actions, in order to maximize the total reward over time. So in this paper we proposed a new algorithm based on LSPI called Least-Squares Continuous Action Policy Iteration (LSCAPI. The LSCAPI was implemented and tested on three different games: one board game, the 8 Queens, and two real-time strategy (RTS games, StarCraft Brood War and Glest. The LSCAPI evaluation proved superiority over LSPI in time, policy learning ability, and effectiveness.

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.

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

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.

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.

Small-kernel, constrained least-squares restoration of sampled image data

Science.gov (United States)

Hazra, Rajeeb; Park, Stephen K.

1992-01-01

Following the work of Park (1989), who extended a derivation of the Wiener filter based on the incomplete discrete/discrete model to a more comprehensive end-to-end continuous/discrete/continuous model, it is shown that a derivation of the constrained least-squares (CLS) filter based on the discrete/discrete model can also be extended to this more comprehensive continuous/discrete/continuous model. This results in an improved CLS restoration filter, which can be efficiently implemented as a small-kernel convolution in the spatial domain.

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

Test and intercomparisons of data fitting with general least squares code GMA versus Bayesian code GLUCS

International Nuclear Information System (INIS)

Pronyaev, V.G.

2003-01-01

Data fitting with GMA and GLUCS gives consistent results. Difference in the evaluated central values obtained with different formalisms can be related to the general accuracy with which fits could be done in different formalisms. It has stochastic nature and should be accounted in the final results of the data evaluation as small SERC uncertainty. Some shift in central values of data evaluated with GLUCS and GMA relative the central values evaluated with the R-matrix model code RAC is observed for cases of fitting strongly varying data and is related to the PPP. The procedure of evaluation, free from PPP, should be elaborated. (author)

Least squares autoregressive (maximum entropy) spectral estimation for Fourier spectroscopy and its application to the electron cyclotron emission from plasma

International Nuclear Information System (INIS)

Iwama, N.; Inoue, A.; Tsukishima, T.; Sato, M.; Kawahata, K.

1981-07-01

A new procedure for the maximum entropy spectral estimation is studied for the purpose of data processing in Fourier transform spectroscopy. The autoregressive model fitting is examined under a least squares criterion based on the Yule-Walker equations. An AIC-like criterion is suggested for selecting the model order. The principal advantage of the new procedure lies in the enhanced frequency resolution particularly for small values of the maximum optical path-difference of the interferogram. The usefulness of the procedure is ascertained by some numerical simulations and further by experiments with respect to a highly coherent submillimeter wave and the electron cyclotron emission from a stellarator plasma. (author)

Automatic bounding estimation in modified NLMS algorithm

International Nuclear Information System (INIS)

Shahtalebi, K.; Doost-Hoseini, A.M.

2002-01-01

Modified Normalized Least Mean Square algorithm, which is a sign form of Nlm based on set-membership (S M) theory in the class of optimal bounding ellipsoid (OBE) algorithms, requires a priori knowledge of error bounds that is unknown in most applications. In a special but popular case of measurement noise, a simple algorithm has been proposed. With some simulation examples the performance of algorithm is compared with Modified Normalized Least Mean Square

Automatic Curve Fitting Based on Radial Basis Functions and a Hierarchical Genetic Algorithm

Directory of Open Access Journals (Sweden)

G. Trejo-Caballero

2015-01-01

Full Text Available Curve fitting is a very challenging problem that arises in a wide variety of scientific and engineering applications. Given a set of data points, possibly noisy, the goal is to build a compact representation of the curve that corresponds to the best estimate of the unknown underlying relationship between two variables. Despite the large number of methods available to tackle this problem, it remains challenging and elusive. In this paper, a new method to tackle such problem using strictly a linear combination of radial basis functions (RBFs is proposed. To be more specific, we divide the parameter search space into linear and nonlinear parameter subspaces. We use a hierarchical genetic algorithm (HGA to minimize a model selection criterion, which allows us to automatically and simultaneously determine the nonlinear parameters and then, by the least-squares method through Singular Value Decomposition method, to compute the linear parameters. The method is fully automatic and does not require subjective parameters, for example, smooth factor or centre locations, to perform the solution. In order to validate the efficacy of our approach, we perform an experimental study with several tests on benchmarks smooth functions. A comparative analysis with two successful methods based on RBF networks has been included.

ALFA: an automated line fitting algorithm

Science.gov (United States)

Wesson, R.

2016-03-01

I present the automated line fitting algorithm, ALFA, a new code which can fit emission line spectra of arbitrary wavelength coverage and resolution, fully automatically. In contrast to traditional emission line fitting methods which require the identification of spectral features suspected to be emission lines, ALFA instead uses a list of lines which are expected to be present to construct a synthetic spectrum. The parameters used to construct the synthetic spectrum are optimized by means of a genetic algorithm. Uncertainties are estimated using the noise structure of the residuals. An emission line spectrum containing several hundred lines can be fitted in a few seconds using a single processor of a typical contemporary desktop or laptop PC. I show that the results are in excellent agreement with those measured manually for a number of spectra. Where discrepancies exist, the manually measured fluxes are found to be less accurate than those returned by ALFA. Together with the code NEAT, ALFA provides a powerful way to rapidly extract physical information from observations, an increasingly vital function in the era of highly multiplexed spectroscopy. The two codes can deliver a reliable and comprehensive analysis of very large data sets in a few hours with little or no user interaction.

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...

Least-squares resolution of gamma-ray spectra in environmental samples

International Nuclear Information System (INIS)

Kanipe, L.G.; Seale, S.K.; Liggett, W.S.

1977-08-01

The use of ALPHA-M, a least squares computer program for analyzing NaI (Tl) gamma spectra of environmental samples, is evaluated. Included is a comprehensive set of program instructions, listings, and flowcharts. Two other programs, GEN4 and SIMSPEC, are also described. GEN4 is used to create standard libraries for ALPHA-M, and SIMSPEC is used to simulate spectra for ALPHA-M analysis. Tests to evaluate the standard libraries selected for use in analyzing environmental samples are provided. An evaluation of the results of sample analyses is discussed

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)

Influence of the least-squares phase on optical vortices in strongly scintillated beams

CSIR Research Space (South Africa)

Chen, M

2009-06-01

Full Text Available , the average total number of vortices is reduced further. However, the reduction becomes smaller for each succes- sive step. This indicates that the ability of getting rid of optical vortices by removing the least-squares phase becomes progressively less...

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

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

Developing a local least-squares support vector machines-based neuro-fuzzy model for nonlinear and chaotic time series prediction.

Science.gov (United States)

Miranian, A; Abdollahzade, M

2013-02-01

Local modeling approaches, owing to their ability to model different operating regimes of nonlinear systems and processes by independent local models, seem appealing for modeling, identification, and prediction applications. In this paper, we propose a local neuro-fuzzy (LNF) approach based on the least-squares support vector machines (LSSVMs). The proposed LNF approach employs LSSVMs, which are powerful in modeling and predicting time series, as local models and uses hierarchical binary tree (HBT) learning algorithm for fast and efficient estimation of its parameters. The HBT algorithm heuristically partitions the input space into smaller subdomains by axis-orthogonal splits. In each partitioning, the validity functions automatically form a unity partition and therefore normalization side effects, e.g., reactivation, are prevented. Integration of LSSVMs into the LNF network as local models, along with the HBT learning algorithm, yield a high-performance approach for modeling and prediction of complex nonlinear time series. The proposed approach is applied to modeling and predictions of different nonlinear and chaotic real-world and hand-designed systems and time series. Analysis of the prediction results and comparisons with recent and old studies demonstrate the promising performance of the proposed LNF approach with the HBT learning algorithm for modeling and prediction of nonlinear and chaotic systems and time series.

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

International Nuclear Information System (INIS)

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

2007-01-01

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

DE and NLP Based QPLS Algorithm

Science.gov (United States)

Yu, Xiaodong; Huang, Dexian; Wang, Xiong; Liu, Bo

As a novel evolutionary computing technique, Differential Evolution (DE) has been considered to be an effective optimization method for complex optimization problems, and achieved many successful applications in engineering. In this paper, a new algorithm of Quadratic Partial Least Squares (QPLS) based on Nonlinear Programming (NLP) is presented. And DE is used to solve the NLP so as to calculate the optimal input weights and the parameters of inner relationship. The simulation results based on the soft measurement of diesel oil solidifying point on a real crude distillation unit demonstrate that the superiority of the proposed algorithm to linear PLS and QPLS which is based on Sequential Quadratic Programming (SQP) in terms of fitting accuracy and computational costs.

Efficient Constrained Local Model Fitting for Non-Rigid Face Alignment.

Science.gov (United States)

Lucey, Simon; Wang, Yang; Cox, Mark; Sridharan, Sridha; Cohn, Jeffery F

2009-11-01

Active appearance models (AAMs) have demonstrated great utility when being employed for non-rigid face alignment/tracking. The "simultaneous" algorithm for fitting an AAM achieves good non-rigid face registration performance, but has poor real time performance (2-3 fps). The "project-out" algorithm for fitting an AAM achieves faster than real time performance (> 200 fps) but suffers from poor generic alignment performance. In this paper we introduce an extension to a discriminative method for non-rigid face registration/tracking referred to as a constrained local model (CLM). Our proposed method is able to achieve superior performance to the "simultaneous" AAM algorithm along with real time fitting speeds (35 fps). We improve upon the canonical CLM formulation, to gain this performance, in a number of ways by employing: (i) linear SVMs as patch-experts, (ii) a simplified optimization criteria, and (iii) a composite rather than additive warp update step. Most notably, our simplified optimization criteria for fitting the CLM divides the problem of finding a single complex registration/warp displacement into that of finding N simple warp displacements. From these N simple warp displacements, a single complex warp displacement is estimated using a weighted least-squares constraint. Another major advantage of this simplified optimization lends from its ability to be parallelized, a step which we also theoretically explore in this paper. We refer to our approach for fitting the CLM as the "exhaustive local search" (ELS) algorithm. Experiments were conducted on the CMU Multi-PIE database.

The IAEA neutron coincidence counting (INCC) and the DEMING least-squares fitting programs

International Nuclear Information System (INIS)

Krick, M.S.; Harker, W.C.; Rinard, P.M.; Wenz, T.R.; Lewis, W.; Pham, P.; Ridder, P. de

1998-01-01

Two computer programs are described: (1) the INCC (IAEA or International Neutron Coincidence Counting) program and (2) the DEMING curve-fitting program. The INCC program is an IAEA version of the Los Alamos NCC (Neutron Coincidence Counting) code. The DEMING program is an upgrade of earlier Windows reg-sign and DOS codes with the same name. The versions described are INCC 3.00 and DEMING 1.11. The INCC and DEMING codes provide inspectors with the software support needed to perform calibration and verification measurements with all of the neutron coincidence counting systems used in IAEA inspections for the nondestructive assay of plutonium and uranium

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

Science.gov (United States)

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

2017-06-01

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

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...

Fast Algorithms for Fitting Active Appearance Models to Unconstrained Images

NARCIS (Netherlands)

Tzimiropoulos, Georgios; Pantic, Maja

2016-01-01

Fitting algorithms for Active Appearance Models (AAMs) are usually considered to be robust but slow or fast but less able to generalize well to unseen variations. In this paper, we look into AAM fitting algorithms and make the following orthogonal contributions: We present a simple “project-out‿

Credit Risk Evaluation Using a C-Variable Least Squares Support Vector Classification Model

Science.gov (United States)

Yu, Lean; Wang, Shouyang; Lai, K. K.

Credit risk evaluation is one of the most important issues in financial risk management. In this paper, a C-variable least squares support vector classification (C-VLSSVC) model is proposed for credit risk analysis. The main idea of this model is based on the prior knowledge that different classes may have different importance for modeling and more weights should be given to those classes with more importance. The C-VLSSVC model can be constructed by a simple modification of the regularization parameter in LSSVC, whereby more weights are given to the lease squares classification errors with important classes than the lease squares classification errors with unimportant classes while keeping the regularized terms in its original form. For illustration purpose, a real-world credit dataset is used to test the effectiveness of the C-VLSSVC model.

Non-linear HVAC computations using least square support vector machines

International Nuclear Information System (INIS)

Kumar, Mahendra; Kar, I.N.

2009-01-01

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

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

Attenuation compensation in least-squares reverse time migration using the visco-acoustic wave equation

KAUST Repository

Dutta, Gaurav; Lu, Kai; Wang, Xin; Schuster, Gerard T.

2013-01-01

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

FITS: a function-fitting program

Energy Technology Data Exchange (ETDEWEB)

Balestrini, S.J.; Chezem, C.G.

1982-08-01

FITS is an iterating computer program that adjusts the parameters of a function to fit a set of data points according to the least squares criterion and then lists and plots the results. The function can be programmed or chosen from a library that is provided. The library can be expanded to include up to 99 functions. A general plotting routine, contained in the program but useful in its own right, is described separately in Appendix A. An example problem file and its solution is given in Appendix B.

Computing ordinary least-squares parameter estimates for the National Descriptive Model of Mercury in Fish

Science.gov (United States)

Donato, David I.

2013-01-01

A specialized technique is used to compute weighted ordinary least-squares (OLS) estimates of the parameters of the National Descriptive Model of Mercury in Fish (NDMMF) in less time using less computer memory than general methods. The characteristics of the NDMMF allow the two products X'X and X'y in the normal equations to be filled out in a second or two of computer time during a single pass through the N data observations. As a result, the matrix X does not have to be stored in computer memory and the computationally expensive matrix multiplications generally required to produce X'X and X'y do not have to be carried out. The normal equations may then be solved to determine the best-fit parameters in the OLS sense. The computational solution based on this specialized technique requires O(8p2+16p) bytes of computer memory for p parameters on a machine with 8-byte double-precision numbers. This publication includes a reference implementation of this technique and a Gaussian-elimination solver in preliminary custom software.

Speed control of induction motor using fuzzy recursive least squares technique

OpenAIRE

Santiago Sánchez; Eduardo Giraldo

2008-01-01

A simple adaptive controller design is presented in this paper, the control system uses the adaptive fuzzy logic, sliding modes and is trained with the recursive least squares technique. The problem of parameter variation is solved with the adaptive controller; the use of an internal PI regulator produces that the speed control of the induction motor be achieved by the stator currents instead the input voltage. The rotor-flux oriented coordinated system model is used to develop and test the c...

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...

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.

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.

Consistent Partial Least Squares Path Modeling via Regularization.

Science.gov (United States)

Jung, Sunho; Park, JaeHong

2018-01-01

Partial least squares (PLS) path modeling is a component-based structural equation modeling that has been adopted in social and psychological research due to its data-analytic capability and flexibility. A recent methodological advance is consistent PLS (PLSc), designed to produce consistent estimates of path coefficients in structural models involving common factors. In practice, however, PLSc may frequently encounter multicollinearity in part because it takes a strategy of estimating path coefficients based on consistent correlations among independent latent variables. PLSc has yet no remedy for this multicollinearity problem, which can cause loss of statistical power and accuracy in parameter estimation. Thus, a ridge type of regularization is incorporated into PLSc, creating a new technique called regularized PLSc. A comprehensive simulation study is conducted to evaluate the performance of regularized PLSc as compared to its non-regularized counterpart in terms of power and accuracy. The results show that our regularized PLSc is recommended for use when serious multicollinearity is present.

Consistent Partial Least Squares Path Modeling via Regularization

Directory of Open Access Journals (Sweden)

Sunho Jung

2018-02-01

Full Text Available Partial least squares (PLS path modeling is a component-based structural equation modeling that has been adopted in social and psychological research due to its data-analytic capability and flexibility. A recent methodological advance is consistent PLS (PLSc, designed to produce consistent estimates of path coefficients in structural models involving common factors. In practice, however, PLSc may frequently encounter multicollinearity in part because it takes a strategy of estimating path coefficients based on consistent correlations among independent latent variables. PLSc has yet no remedy for this multicollinearity problem, which can cause loss of statistical power and accuracy in parameter estimation. Thus, a ridge type of regularization is incorporated into PLSc, creating a new technique called regularized PLSc. A comprehensive simulation study is conducted to evaluate the performance of regularized PLSc as compared to its non-regularized counterpart in terms of power and accuracy. The results show that our regularized PLSc is recommended for use when serious multicollinearity is present.

Least-squares reverse time migration with radon preconditioning

KAUST Repository

Dutta, Gaurav

2016-09-06

We present a least-squares reverse time migration (LSRTM) method using Radon preconditioning to regularize noisy or severely undersampled data. A high resolution local radon transform is used as a change of basis for the reflectivity and sparseness constraints are applied to the inverted reflectivity in the transform domain. This reflects the prior that for each location of the subsurface the number of geological dips is limited. The forward and the adjoint mapping of the reflectivity to the local Radon domain and back are done through 3D Fourier-based discrete Radon transform operators. The sparseness is enforced by applying weights to the Radon domain components which either vary with the amplitudes of the local dips or are thresholded at given quantiles. Numerical tests on synthetic and field data validate the effectiveness of the proposed approach in producing images with improved SNR and reduced aliasing artifacts when compared with standard RTM or LSRTM.

Comparing implementations of penalized weighted least-squares sinogram restoration

International Nuclear Information System (INIS)

Forthmann, Peter; Koehler, Thomas; Defrise, Michel; La Riviere, Patrick

2010-01-01

Purpose: A CT scanner measures the energy that is deposited in each channel of a detector array by x rays that have been partially absorbed on their way through the object. The measurement process is complex and quantitative measurements are always and inevitably associated with errors, so CT data must be preprocessed prior to reconstruction. In recent years, the authors have formulated CT sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. The authors have explored both penalized Poisson likelihood (PL) and penalized weighted least-squares (PWLS) objective functions. At low doses, the authors found that the PL approach outperforms PWLS in terms of resolution-noise tradeoffs, but at standard doses they perform similarly. The PWLS objective function, being quadratic, is more amenable to computational acceleration than the PL objective. In this work, the authors develop and compare two different methods for implementing PWLS sinogram restoration with the hope of improving computational performance relative to PL in the standard-dose regime. Sinogram restoration is still significant in the standard-dose regime since it can still outperform standard approaches and it allows for correction of effects that are not usually modeled in standard CT preprocessing. Methods: The authors have explored and compared two implementation strategies for PWLS sinogram restoration: (1) A direct matrix-inversion strategy based on the closed-form solution to the PWLS optimization problem and (2) an iterative approach based on the conjugate-gradient algorithm. Obtaining optimal performance from each strategy required modifying the naive off-the-shelf implementations of the algorithms to exploit the particular symmetry and sparseness of the sinogram-restoration problem. For the closed-form approach, the authors subdivided the large matrix

Discrete least squares polynomial approximation with random evaluations - application to PDEs with Random parameters

KAUST Repository

Nobile, Fabio

2015-01-01

the parameter-to-solution map u(y) from random noise-free or noisy observations in random points by discrete least squares on polynomial spaces. The noise-free case is relevant whenever the technique is used to construct metamodels, based on polynomial

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...

A novel line segment detection algorithm based on graph search

Science.gov (United States)

Zhao, Hong-dan; Liu, Guo-ying; Song, Xu

2018-02-01

To overcome the problem of extracting line segment from an image, a method of line segment detection was proposed based on the graph search algorithm. After obtaining the edge detection result of the image, the candidate straight line segments are obtained in four directions. For the candidate straight line segments, their adjacency relationships are depicted by a graph model, based on which the depth-first search algorithm is employed to determine how many adjacent line segments need to be merged. Finally we use the least squares method to fit the detected straight lines. The comparative experimental results verify that the proposed algorithm has achieved better results than the line segment detector (LSD).

Flow-Injection Solid Phase Partial Least-Squares Spectrophotometric Simultaneous Determination of Iron, Nickel and Zinc

Directory of Open Access Journals (Sweden)

Teixeira Leonardo S. G.

2002-01-01

Full Text Available A PLS-2 multivariate calibration method has been developed for the simultaneous determination of iron, nickel and zinc in ternary mixtures by solid phase spectrophotometry associated with flow injection analysis. Fe(II, Ni(II and Zn(II form color complexes with 1-(2-thiazolylazo-2-naphthol (TAN, immobilized on a C18 bonded silica support, at pH 6.4. The proposed procedure is based on the different reaction/retention ratios of the studied ions on the solid support. Bilinear spectrophotometric data of the analytes, fixed in the solid support, were recorded in the 400-800 nm wavelength range as a function of time and a partial least squares (PLS-2 algorithm was used to predict results of synthetic samples. The calibration set employed was integrated by 8 ternary mixture standards and a blank solution. Mixtures containing 0.040 to 0.20 mg L-1, of each species, were successfully resolved, using 3 factors for each analyte and a restricted number of absorbance data obtained in the wavelength range from 560 to 650 nm.

Conjugate gradient and cross-correlation based least-square reverse time migration and its application

Science.gov (United States)

Sun, Xiao-Dong; Ge, Zhong-Hui; Li, Zhen-Chun

2017-09-01

Although conventional reverse time migration can be perfectly applied to structural imaging it lacks the capability of enabling detailed delineation of a lithological reservoir due to irregular illumination. To obtain reliable reflectivity of the subsurface it is necessary to solve the imaging problem using inversion. The least-square reverse time migration (LSRTM) (also known as linearized reflectivity inversion) aims to obtain relatively high-resolution amplitude preserving imaging by including the inverse of the Hessian matrix. In practice, the conjugate gradient algorithm is proven to be an efficient iterative method for enabling use of LSRTM. The velocity gradient can be derived from a cross-correlation between observed data and simulated data, making LSRTM independent of wavelet signature and thus more robust in practice. Tests on synthetic and marine data show that LSRTM has good potential for use in reservoir description and four-dimensional (4D) seismic images compared to traditional RTM and Fourier finite difference (FFD) migration. This paper investigates the first order approximation of LSRTM, which is also known as the linear Born approximation. However, for more complex geological structures a higher order approximation should be considered to improve imaging quality.

Speed control of induction motor using fuzzy recursive least squares technique

Directory of Open Access Journals (Sweden)

Santiago Sánchez

2008-12-01

Full Text Available A simple adaptive controller design is presented in this paper, the control system uses the adaptive fuzzy logic, sliding modes and is trained with the recursive least squares technique. The problem of parameter variation is solved with the adaptive controller; the use of an internal PI regulator produces that the speed control of the induction motor be achieved by the stator currents instead the input voltage. The rotor-flux oriented coordinated system model is used to develop and test the control system.

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

Energy Technology Data Exchange (ETDEWEB)

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

2006-02-15

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

Fast and exact Newton and Bidirectional fitting of Active Appearance Models.

Science.gov (United States)

Kossaifi, Jean; Tzimiropoulos, Yorgos; Pantic, Maja

2016-12-21

Active Appearance Models (AAMs) are generative models of shape and appearance that have proven very attractive for their ability to handle wide changes in illumination, pose and occlusion when trained in the wild, while not requiring large training dataset like regression-based or deep learning methods. The problem of fitting an AAM is usually formulated as a non-linear least squares one and the main way of solving it is a standard Gauss-Newton algorithm. In this paper we extend Active Appearance Models in two ways: we first extend the Gauss-Newton framework by formulating a bidirectional fitting method that deforms both the image and the template to fit a new instance. We then formulate a second order method by deriving an efficient Newton method for AAMs fitting. We derive both methods in a unified framework for two types of Active Appearance Models, holistic and part-based, and additionally show how to exploit the structure in the problem to derive fast yet exact solutions. We perform a thorough evaluation of all algorithms on three challenging and recently annotated inthe- wild datasets, and investigate fitting accuracy, convergence properties and the influence of noise in the initialisation. We compare our proposed methods to other algorithms and show that they yield state-of-the-art results, out-performing other methods while having superior convergence properties.

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

Science.gov (United States)