Performance evaluation of multiobjective multiclass support vector machines maximizing geometric margins

Abstract

The all-together method is one of the support vector machine (SVM) for multiclass classification by using a piece-wise linear function. Recently, we proposed a new hard-margin all-together model maximizing geometric margins in the sense of multiobjective optimization for the high generalization ability, which is called the multiobjective multiclass SVM (MMSVM). Moreover, we derived its solving techniques which can find a Pareto optimal solution for the MMSVM, and verified that classifiers with larger geometric margins were obtained by the proposed techniques through numerical experiments. However, the experiments are not enough to evaluate the classification performance of the proposed model, and the MMSVM is a hard-margin model which can be applied to only piecewise linearly separable data. Therefore, in this paper, we extend the hard-margin model into soft-margin one by introducing penalty functions for the slack margin variables, and derive a single-objective second-order cone programming (SOCP) problem to solve it. Furthermore, through numerical experiments we verify the classification performance of the hard and soft-margin MMSVMs for benchmark problems.