research 2009.08.31 20:40
Support Vector Machines is a powerful methodology for solving problems in nonlinear classification, function estimation and density estimation which has also led to many other recent developments in kernel based methods in general. Originally, it has been introduced within the context of statistical learning theory and structural risk minimization. In the methods one solves convex optimization problems, typically quadratic programs. Least Squares Support Vector Machines (LS-SVM) are reformulations to the standard SVMs which lead to solving linear KKT systems. LS-SVMs are closely related to regularization networks and Gaussian processes but additionally emphasize and exploit primal-dual interpretations. Links between kernel versions of classical pattern recognition algorithms such as kernel Fisher discriminant analysis and extensions to unsupervised learning, recurrent networks and control are available. Robustness, sparseness and weightings can be imposed to LS-SVMs where needed and a Bayesian framework with three levels of inference has been developed. LS-SVM alike primal-dual formulations have been given to kernel PCA, kernel CCA and kernel PLS. For ultra large scale problems and on-line learning a method of Fixed Size LS-SVM is proposed. The present LS-SVMlab toolbox contains Matlab/C implementations for a number of LS-SVM algorithms.

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