Globalized distributionally robust chance-constrained support vector machine based on core sets

Abstract

Support vector machine (SVM) is a well known binary linear classification model in supervised learning. This paper proposes a globalized distributionally robust chance-constrained (GDRC) SVM model based on core sets to address uncertainties in the dataset and provide a robust classifier. The globalization means that we focus on the uncertainty in the sample population rather than the small perturbations around each sample point. The uncertainty is mainly specified by the confidence region of the first- and second-order moments. The core sets are constructed to capture some small regions near the potential classification hyperplane, which helps improve the classification quality via the expected distance constraint of the random vector to core sets. We obtain the equivalent semi-definite programming reformulation of the GDRC SVM model under some appropriate assumptions. To deal with the large-scale problem, an approximation approach based on principal component analysis is applied to the GDRC SVM. The numerical experiments are presented to illustrate the effectiveness and advantage of our model.