  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.
