Robust Classification via Support Vector Machines

The loss function choice for any Support Vector Machine classifier has raised great interest in the literature due to the lack of robustness of the Hinge loss, which is the standard loss choice. In this paper, we plan to robustify the binary classifier by maintaining the overall advantages of the Hinge loss, rather than modifying this standard choice. We propose two robust classifiers under data uncertainty. The first is called Single Perturbation SVM (SP-SVM) and provides a constructive method by allowing a controlled perturbation to one feature of the data. The second method is called Extreme Empirical Loss SVM (EEL-SVM) and is based on a new empirical loss estimate, namely, the Extreme Empirical Loss (EEL), that puts more emphasis on extreme violations of the classification hyper-plane, rather than taking the usual sample average with equal importance for all hyper-plane violations. Extensive numerical investigation reveals the advantages of the two robust classifiers on simulated data and well-known real datasets.