Two-group classification via a biobjective margin maximization model

In this paper we propose a biobjective model for two-group classification via margin maximization, in which the margins in both classes are simultaneously maximized. The set of Pareto-optimal solutions is described, yielding a set of parallel hyperplanes, one of which is just the solution of the classical SVM approach. In order to take into account different misclassification costs or a priori probabilities, the ROC curve can be used to select one out of such hyperplanes by expressing the adequate tradeoff for sensitivity and specificity. Our result gives a theoretical motivation for using the ROC approach in case misclassification costs in the two groups are not necessarily equal.