Support vector machines for signal processing

The chapter deals with the use of the support vector machine (SVM) algorithm as a possible design method in the signal processing applications. It critically discusses the main difficulties related with its application to such a general set of problems. Moreover, the problem of digital channel equalization is also discussed in details since it is an important example of the use of the SVM algorithm in the signal processing. In the classical problem of learning a function belonging to a certain class of parametric functions (which linearly depend on their parameters), the adoption of the cost function used in the classical SVM method for classification is suggested. Since the adoption of such a cost function (almost peculiar to the basic SVM kernel-based method) is one of the most important achievements of the learning theory, this extension allows one to define new variants of the classical (batch and iterative) minimum-mean square error (MMSE) procedure. Such variants, which are more suited to the classification problem, are determined by solving a strictly convex optimization problem (not sensitive, therefore, to the presence of local minima). Improvements in terms of the achieved probability of error with respect to the classical MMSE equalization methods are obtained. The use of such a procedure together with a method for subset selection provides an important alternative to the classical SVM algorithm