Optimal Margin Distribution Clustering
Maximum margin clustering (MMC), which borrows the large margin heuristic from support vector machine (SVM), has achieved more accurate results than traditional clustering methods. The intuition is that, for a good clustering, when labels are assigned to different clusters, SVM can achieve a large minimum margin on this data. Recent studies, however, disclosed that maximizing the minimum margin does not necessarily lead to better performance, and instead, it is crucial to optimize the margin distribution. In this paper, we propose a novel approach ODMC (Optimal margin Distribution Machine for Clustering), which tries to cluster the data 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 descent method to solve the resultant minimax problem. Moreover, we prove theoretically that ODMC has the same convergence rate with state-of-the-art cutting plane based algorithms but involves much less computation cost per iteration, so our method is much more scalable than existing approaches. Extensive experiments on UCI data sets show that ODMC is significantly better than compared methods, which verifies the superiority of optimal margin distribution learning.