Semi-Supervised Optimal Margin Distribution Machines

Abstract

Semi-supervised support vector machines is an extension of standard support vector machines with unlabeled instances, and the goal is to find a label assignment of the unlabeled instances, so that the decision boundary has the maximal \textit{minimum margin} on both the original labeled instances and unlabeled instances. Recent studies, however, disclosed that maximizing the minimum margin does not necessarily lead to better performance, and instead, it is crucial to optimize the \textit{margin distribution}. In this paper, we propose a novel approach SODM (Semi-supervised Optimal margin Distribution Machine), which tries to assign the label to unlabeled instances and achieve optimal margin distribution simultaneously. Specifically, we characterize the margin distribution by the first- and second-order statistics, i.e., the margin mean and variance, and extend a stochastic mirror prox method to solve the resultant minimax problem. Extensive experiments on UCI data sets show that SODM is significantly better than compared methods, which verifies the superiority of optimal margin distribution learning.