Multi-class support vector machine based on minimization of reciprocal-geometric-margin norms

In this paper, we propose a Support Vector Machine (SVM) method 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 ${\ell }_p$-norm scalarization and convex approximation to MMSVM. Additionally, we develop the margin theory for multi-class linear classification, in order to justify minimization of reciprocal class-pair geometric margins. Experimental results on synthetic datasets explain situations where the proposed RGMNSVM successfully works, while conventional multi-class SVMs fail to fit underlying distributions. Results of classification performance evaluation using benchmark data sets show that RGMNSVM is generally comparable with conventional multi-class SVMs. However, we observe that the proposed approach to geometric margin maximization actually performs better classification accuracy for certain real-world data sets.