Cost-sensitive learning in Support Vector Machines

In this paper, a cost-sensitive learning method for support vector machine (SVM) classifiers is proposed. We focus on a particular case of cost-sensitive problems, namely, classification with reject option. Standard learning algorithms, the one for SVMs included, are not cost-sensitive. In particular, they can not handle the reject option. However, we show that, under the framework of the structural risk minimisation induction principle, on which standard SVMs are based, the rejection region should be determined during the training phase of a classifier, by the learning algorithm. We apply this approach to develop a cost-sensitive SVM classifier, by following Vapnik’s maximum margin method to the derivation of standard SVMs. This lead us to a SVM with embedded reject option. To implement such a SVM, we develop a novel formulation of the training problem, and a specific algorithm to solve it. Preliminary results on a character recognition problem seem to show the advantages of the proposed cost-sensitive SVM, in terms of the achievable errorreject trade-off.