Improved Maximum Margin Clustering via the Bundle Method

Abstract

Maximum margin clustering (MMC) is an effective clustering algorithm, which first extends a large margin principle into unsupervised learning. This paper revisits the MMC problem and points out the potential problems encountered by a cutting plane approach. We propose an improved MMC algorithm via the bundle method (BMMC). Specifically, the constrained convex-concave procedure algorithm is first applied to decompose the MMC problem into a series of convex sub-problems, and then, the bundle method is adopted to efficiently solve each sub-problem. Moreover, a simpler formulation for the multi-class MMC is presented. In addition to clustering problems, the BMMC is also extended to the semi-supervised case by incorporating the pairwise constraints, which reveals its high scalability. Compared with the previous works, the proposed solution is much simpler and faster. The experiments on several data sets are conducted to demonstrate the effectiveness of our proposed algorithm.