Efficient Maximum Margin Clustering via Cutting Plane Algorithm

Maximum margin clustering (MMC) is a recently proposed clustering method, which extends the theory of support vector machine to the unsupervised scenario and aims at finding the maximum margin hyperplane which separates the data from different classes. Traditionally, MMC is formulated as a non-convex integer programming problem and is thus difficult to solve. Several methods have been proposed in the literature to solve the MMC problem based on either semidefinite programming or alternative optimization. However, these methods are time demanding while handling large scale datasets and therefore unsuitable for real world applications. In this paper, we propose the cutting plane maximum margin clustering (CPMMC) algorithm, to solve the MMC problem. Specifically, we construct a nested sequence of successively tighter relaxations of the original MMC problem, and each optimization problem in this sequence could be efficiently solved using the constrained concave-convex procedure (CCCP). Moreover, we prove theoretically that the CPMMC algorithm takes time O(sn) to converge with guaranteed accuracy, where n is the total number of samples in the dataset and s is the average number of non-zero features, i.e. the sparsity. Experimental evaluations on several real world datasets show that CPMMC performs better than existing MMC methods, both in efficiency and accuracy.