A Multi-class Support Vector Machine Based on Geometric Margin Maximization

Abstract

Support vector machines (SVMs) are popular supervised learning methods. The original SVM was developed for binary classification. It selects a linear classifier by maximizing the geometric margin between the boundary hyperplane and sample examples. There are several extensions of the SVM for multi-class classification problems. However, they do not maximize geometric margins exactly. Recently, Tatsumi and Tanino have proposed multi-objective multi-class SVM, which simultaneously maximizes the margins for all class pairs. In this paper, we propose another multi-class SVM based on the geometric margin maximization. The SVM is formulated as minimization of the sum of inverse-squared margins for all class pairs. Since this is a nonconvex optimization problem, we propose an approximate solution. By numerical experiments, we show that the propose SVM has better performance in generalization capability than one of the conventional multi-class SVMs.