Benchmarking Least Squares Support Vector Machine Classifiers
van Gestel, Tony Suykens, Johan AK Baesens, Bart Viaene, Stijn Vanthienen, Jan Dedene, Guido de Moor, Bart Vandewalle, Joos
van Gestel, Tony
Suykens, Johan AK
Baesens, Bart
Viaene, Stijn
Vanthienen, Jan
Dedene, Guido
de Moor, Bart
Vandewalle, Joos
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Journal article with impact factor
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Supervisor
Publication Year
2004-01
Journal
Machine Learning
Book
Publication Volume
54
Publication Issue
1
Publication Begin page
5
Publication End page
32
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Abstract
In Support Vector Machines (SVMs), the solution of the classification problem is characterized by a (convex) quadratic programming (QP) problem. In a modified version of SVMs, called Least Squares SVM classifiers (LS-SVMs), a least squares cost function is proposed so as to obtain a linear set of equations in the dual space. While the SVM classifier has a large margin interpretation, the LS-SVM formulation is related in this paper to a ridge regression approach for classification with binary targets and to Fisher's linear discriminant analysis in the feature space. Multiclass categorization problems are represented by a set of binary classifiers using different output coding schemes. While regularization is used to control the effective number of parameters of the LS-SVM classifier, the sparseness property of SVMs is lost due to the choice of the 2-norm. Sparseness can be imposed in a second stage by gradually pruning the support value spectrum and optimizing the hyperparameters during the sparse approximation procedure. In this paper, twenty public domain benchmark datasets are used to evaluate the test set performance of LS-SVM classifiers with linear, polynomial and radial basis function (RBF) kernels. Both the SVM and LS-SVM classifier with RBF kernel in combination with standard cross-validation procedures for hyperparameter selection achieve comparable test set performances. These SVM and LS-SVM performances are consistently very good when compared to a variety of methods described in the literature including decision tree based algorithms, statistical algorithms and instance based learning methods. We show on ten UCI datasets that the LS-SVM sparse approximation procedure can be successfully applied.
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Keywords
4603 Computer Vision and Multimedia Computation, 46 Information and Computing Sciences, 4611 Machine Learning