Improving the generalization performance of multi-class SVM via angular regularization

In multi-class support vector machine (MSVM) for classification, one core issue is to regularize the coefficient vectors to reduce overfitting. Various regularizes have been proposed such as l₂, l₁, and trace norm. In this paper, we introduce a new type of regularization approach - angular regularization, that encourages the coefficient vectors to have larger angles such that class regions can be widen to flexibly accommodate unseen samples. We propose a novel angular regularizer based on the singular values of the coefficient matrix, where the uniformity of singular values reduces the correlation among different classes and drives the angles between coefficient vectors to increase. In generalization error analysis, we show that decreasing this regularizer effectively reduces generalization error bound. On various datasets, we demonstrate the efficacy of the regularizer in reducing overfitting.