ABSTRACT:

Support vector machines (SVM's), as recently introduced by Vapnik, is a new method for solving classification and static nonlinear function estimation problems. A typical property of SVM's is that, up to a small number of hyperparameters, the solution is characterized by a convex optimization problem, more specifically a quadratic programming (QP) problem. Moreover, the model complexity (e.g.~number of hidden units) also follows from this QP problem. Recently, we have introduced a modified version of SVM's, so-called least squares SVM's (LS-SVM's). In LS-SVM's the solution is given by a linear system instead of a QP problem. The aim of this paper is to give an introduction to the theory and methods of LS-SVM's for classification and nonlinear function estimation. The LS-SVM formulation turns out to be surprisingly simple and at the same time very powerful.