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This book focuses on Least Squares Support Vector Machines (LSSVMs) which are reformulations to standard SVMs. LSSVMs are closely related to regularization networks and Gaussian processes but additionally emphasize and exploit primaldual interpretations from optimization theory. The authors explain the natural links between LSSVM classifiers and kernel Fisher discriminant analysis. Bayesian inference of LSSVM models is discussed, together with methods for imposing sparseness and employing robust statistics.The framework is further extended towards unsupervised learning by considering PCA analysis and its kernel version as a oneclass modelling problem. This leads to new primaldual support vector machine formulations for kernel PCA and kernel CCA analysis. Furthermore, LSSVM formulations are given for recurrent networks and control. In general, support vector machines may pose heavy computational challenges for large data sets. For this purpose, a method of fixed size LSSVM is proposed where the estimation is done in the primal space in relation to a Nystrm sampling with active selection of support vectors. The methods are illustrated with several examples.
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