In this paper, the problem of implementing the reject option i n support vector machines (SVMs) is addressed. We started by observing that methods proposed so far simply apply a reject threshold to the outputs of a trained SVM. We then showed that, under the framework of the structural risk minimisation principle, the rejection region must be determined during the training phase of a classifier. By applying this concept, and by following Vapnik's approach, we developed a maximum margin classifier with reject option. This led us to a SVM whose rejection region is determined during the training phase, that is, a SVM with embedded reject option. To implement such a SVM, we devised a novel formulation of the SVM training problem and developed a specific algorithm to solve it. Preliminary results on a character recognition problem show the advantages of the proposed SVM i n terms of the achievable error-reject trade-off.

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.