Multi-Class Support Vector Machine with Maximizing Minimum Margin

Support Vector Machine (SVM) stands out as a prominent machine learning technique widely applied in practical pattern recognition tasks. It achieves binary classification by maximizing the”margin”, which represents the minimum distance between instances and the decision boundary. Although many efforts have been dedicated to expanding SVM to multi-class case through strategies such as one versus one and one versus the rest, satisfactory solutions remain to be developed. In this paper, we propose a novel method for multi-class SVM that incorporates pairwise class loss considerations and maximizes the minimum margin. Adhering to this concept, we derive a formulation through a new multi-objective optimization strategy. Furthermore, the correlations between the proposed method and multiple forms of multiclass SVM are analyzed. Empirical evaluations demonstrate the effectiveness and superiority of our proposed method over existing multi-classification methods. Complete version is available at https://arxiv.org/pdf/2312.06578.pdf. Code is available at https://github.com/zz-haooo/M3SVM.