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.

翻译：支持向量机（SVM）作为一种突出的机器学习技术，广泛应用于实际模式识别任务。它通过最大化“间隔”（即样本与决策边界之间的最小距离）实现二分类。尽管已有很多研究致力于通过“一对一”和“一对余”等策略将SVM扩展到多类情况，但仍有待开发令人满意的解决方案。本文提出了一种新颖的多类SVM方法，该方法融入了成对类别损失考量，并最大化最小间隔。基于这一概念，我们采用了一种新公式，赋予多类SVM更高的灵活性。此外，我们还分析了所提方法与多种形式的多类SVM之间的关联。所提出的正则化项类似于“间隔”的概念，可作为深度学习中的Softmax函数的无缝增强，为网络参数学习提供指导。实验评估表明，我们提出的方法相较于现有多分类方法具有有效性和优越性。代码可在 https://github.com/zz-haooo/M3SVM 获取。