Recent studies disclose that maximizing the minimum margin like support vector machines does not necessarily lead to better generalization performances, and instead, it is crucial to optimize the margin distribution. Although it has been shown that for binary classification, characterizing the margin distribution by the first- and second-order statistics can achieve superior performance... It still remains open for multi-class classification, and due to the complexity of margin for multi-class classification, optimizing its distribution by mean and variance can also be difficult. In this paper, we propose mcODM (multi-class Optimal margin Distribution Machine), which can solve this problem efficiently. We also give a theoretical analysis for our method, which verifies the significance of margin distribution for multi-class classification. Empirical study further shows that mcODM always outperforms all four versions of multi-class SVMs on all experimental data sets. (read more)