Multi-Class Support Vector Machine Based on Minimization of Reciprocal-Geometric-Margin Norms

Abstract In this paper, we propose a SVM algorithm for multi-class classification. It follows multi-objective multi-class SVM (MMSVM), which maximizes class-pair margins on a multi-class linear classifier. The proposed method, called reciprocal-geometric-margin-norm SVM (RGMNSVM) is derived by applying the ℓp-norm scalarization and convex approximation to MMSVM. Additionally, we develop the margin theory for multi-class linear classification, in order to justify maximization of class-pair geometric margins. Experimental results on artificial datasets explain situations where the proposed RGMNSVM successfully works, while conventional multi-class SVMs fail in generalization. Results of classification performance evaluation using benchmark data sets show that RGMNSVM is generally comparable with one of the best multi-class SVMs proposed by Weston and Watkins (1999). However, we observe that the proposed approach to geometric margin maximization actually has better generalization capability for certain real-world data sets.