Improved conjugate gradient implementation for least squares support vector machines

As a promising method for pattern recognition and function estimation, least squares support vector machines (LS-SVM) express the training in terms of solving a linear system instead of a quadratic programming problem as for conventional support vector machines (SVM). In this paper, by using the information provided by the equality constraint, we transform the minimization problem with a single equality constraint in LS-SVM into an unconstrained minimization problem, then propose reduced formulations for LS-SVM. By introducing this transformation, the times of using conjugate gradient (CG) method, which is a greatly time-consuming step in obtaining the numerical solution, are reduced to one instead of two as proposed by Suykens et al. (1999). The comparison on computational speed of our method with the CG method proposed by Suykens et al. and the first order and second order SMO methods on several benchmark data sets shows a reduction of training time by up to 44%. (C) 2011 Elsevier B.V. All rights reserved.

Experimentally validated partial least squares model for dynamic line rating

This study presents a model based on partial least squares (PLS) regression for dynamic line rating (DLR). The model has been verified using data from field measurements, lab tests and outdoor experiments. Outdoor experimentation has been conducted both to verify the model predicted DLR and also to provide training data not available from field measurements, mainly heavily loaded conditions. The proposed model, unlike the direct measurement based DLR techniques, enables prediction of line rating for periods ahead of time whenever a reliable weather forecast is available. The PLS approach yields a very simple statistical model that accurately captures the physical performance of the conductor within a given environment without requiring a predetermination of parameters as required by many physical modelling techniques. Accuracy of the PLS model has been tested by predicting the conductor temperature for measurement sets other than those used for training. Being a linear model, it is straightforward to estimate the conductor ampacity for a set of predicted weather parameters. The PLS estimated ampacity has proven its accuracy through an outdoor experiment on a piece of the line conductor in real weather conditions.

Partial least squares model for dynamic rating of overhead line in wind intensive areas based on field measurements

This paper presents a statistical model for the thermal behaviour of the line model based on lab tests and field measurements. This model is based on Partial Least Squares (PLS) multi regression and is used for the Dynamic Line Rating (DLR) in a wind intensive area. DLR provides extra capacity to the line, over the traditional seasonal static rating, which makes it possible to defer the need for reinforcement the existing network or building new lines. The proposed PLS model has a number of appealing features; the model is linear, so it is straightforward to use for predicting the line rating for future periods using the available weather forecast. Unlike the available physical models, the proposed model does not require any physical parameters of the line, which avoids the inaccuracies resulting from the errors and/or variations in these parameters. The developed model is compared with physical model, the Cigre model, and has shown very good accuracy in predicting the conductor temperature as well as in determining the line rating for future time periods. 

Two-Stage Orthogonal Least Squares Methods for Neural Network Construction

A number of neural networks can be formulated as the linear-in-the-parameters models. Training such networks can be transformed to a model selection problem where a compact model is selected from all the candidates using subset selection algorithms. Forward selection methods are popular fast subset selection approaches. However, they may only produce suboptimal models and can be trapped into a local minimum. More recently, a two-stage fast recursive algorithm (TSFRA) combining forward selection and backward model refinement has been proposed to improve the compactness and generalization performance of the model. This paper proposes unified two-stage orthogonal least squares methods instead of the fast recursive-based methods. In contrast to the TSFRA, this paper derives a new simplified relationship between the forward and the backward stages to avoid repetitive computations using the inherent orthogonal properties of the least squares methods. Furthermore, a new term exchanging scheme for backward model refinement is introduced to reduce computational demand. Finally, given the error reduction ratio criterion, effective and efficient forward and backward subset selection procedures are proposed. Extensive examples are presented to demonstrate the improved model compactness constructed by the proposed technique in comparison with some popular methods.

The alternating least-squares algorithm for CDPCA

Clustering and Disjoint Principal Component Analysis (CDP CA) is a constrained principal component analysis recently proposed for clustering of objects and partitioning of variables, simultaneously, which we have implemented in R language. In this paper, we deal in detail with the alternating least-squares algorithm for CDPCA and highlight its algebraic features for constructing both interpretable principal components and clusters of objects. Two applications are given to illustrate the capabilities of this new methodology.

An efficient parallel implementation of a least squares problem

Least squares solutions are a very important problem, which appear in a broad range of disciplines (for instance, control systems, statistics, signal processing). Our interest in this kind of problems lies in their use of training neural network controllers.

An efficient parallel implementation of a least squares problem

Least squares solutions are a very important problem, which appear in a broad range of disciplines (for instance, control systems, statistics, signal processing). Our interest in this kind of problems lies in their use of training neural network controllers.

Face recogniton based on the optimal combination of neural networks, eigenfaces and least squares matching methods

Report of a research project of the Fachhochschule Hannover, University of Applied Sciences and Arts, Department of Information Technologies. Automatic face recognition increases the security standards at public places and border checkpoints. The picture inside the identification documents could widely differ from the face, that is scanned under random lighting conditions and for unknown poses. The paper describes an optimal combination of three key algorithms of object recognition, that are able to perform in real time. The camera scan is processed by a recurrent neural network, by a Eigenfaces (PCA) method and by a least squares matching algorithm. Several examples demonstrate the achieved robustness and high recognition rate.

Time domain design of fractional differintegrators using least-squares

In this paper we propose the use of the least-squares based methods for obtaining digital rational approximations (IIR filters) to fractional-order integrators and differentiators of type sα, α∈R. Adoption of the Padé, Prony and Shanks techniques is suggested. These techniques are usually applied in the signal modeling of deterministic signals. These methods yield suboptimal solutions to the problem which only requires finding the solution of a set of linear equations. The results reveal that the least-squares approach gives similar or superior approximations in comparison with other widely used methods. Their effectiveness is illustrated, both in the time and frequency domains, as well in the fractional differintegration of some standard time domain functions.

Non invasive classification system of scoliosis curve types using least-squares support vector machines

Objective To determine scoliosis curve types using non invasive surface acquisition, without prior knowledge from X-ray data. Methods Classification of scoliosis deformities according to curve type is used in the clinical management of scoliotic patients. In this work, we propose a robust system that can determine the scoliosis curve type from non invasive acquisition of the 3D back surface of the patients. The 3D image of the surface of the trunk is divided into patches and local geometric descriptors characterizing the back surface are computed from each patch and constitute the features. We reduce the dimensionality by using principal component analysis and retain 53 components using an overlap criterion combined with the total variance in the observed variables. In this work, a multi-class classifier is built with least-squares support vector machines (LS-SVM). The original LS-SVM formulation was modified by weighting the positive and negative samples differently and a new kernel was designed in order to achieve a robust classifier. The proposed system is validated using data from 165 patients with different scoliosis curve types. The results of our non invasive classification were compared with those obtained by an expert using X-ray images. Results The average rate of successful classification was computed using a leave-one-out cross-validation procedure. The overall accuracy of the system was 95%. As for the correct classification rates per class, we obtained 96%, 84% and 97% for the thoracic, double major and lumbar/thoracolumbar curve types, respectively. Conclusion This study shows that it is possible to find a relationship between the internal deformity and the back surface deformity in scoliosis with machine learning methods. The proposed system uses non invasive surface acquisition, which is safe for the patient as it involves no radiation. Also, the design of a specific kernel improved classification performance.

On the relationship between the Method of Least Squares and Gram-Schmidt orthogonalization

The method of Least Squares is due to Carl Friedrich Gauss. The Gram-Schmidt orthogonalization method is of much younger date. A method for solving Least Squares Problems is developed which automatically results in the appearance of the Gram-Schmidt orthogonalizers. Given these orthogonalizers an induction-proof is available for solving Least Squares Problems.