  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 for 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 embrace a new formulation that imparts
heightened flexibility to multi-class SVM. Furthermore, the correlations
between the proposed method and multiple forms of multi-class SVM are analyzed.
The proposed regularizer, akin to the concept of "margin", can serve as a
seamless enhancement over the softmax in deep learning, providing guidance for
network parameter learning. Empirical evaluations demonstrate the effectiveness
and superiority of our proposed method over existing multi-classification
methods.Code is available at https://github.com/zz-haooo/M3SVM.
