Support Vector Machines with Embedded Reject Option

In this paper, the problem of implementing the reject option in 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 in terms of the achievable error-reject trade-off.