ROC-based cost-sensitive classification with a reject option

In many real-world classification tasks, it is crucial to take into account misclassification costs for designing an accurate classification system. Nevertheless, begin able to reject a sample is also often needed in order to avoid a very risky prediction error. In that case, a cost-sensitive classifier must embed a rejection mechanism, that takes into account the rejection costs as well as the misclassification costs. In binary classification, the ROC space has shown to be very powerful for designing cost-sensitive classifiers, but it has been poorly exploited for designing classifiers able to reject. The purpose of this work is to extend a ROC-based ensemble method recently proposed, called the ROC Front method, with a cost-sensitive rejection mechanism. This approach compares favorably to the state-of-the-art ROC-based rejection rule recently proposed for binary cost-sensitive classification. It is also more robust as it allows to design an accurate classifier for all cost- sensitive situations contrary to the state-of-the-art method that fails in many cases, as for example with small datasets.