Maximum Margin Clustering without Nonconvex Optimization: an Equivalent Transformation

Abstract

On account of the promising performance in accuracy, maximum margin clustering (MMC) has attracted attentions from many research domains. MMC derived from the extension of support vector machine (SVM). But due to the undetermined labeling of samples in dataset, the original optimization is a nonconvex problem which is time-consuming to solve. Based on another high-quality nonlinear clustering technique— spectral clustering, this paper discusses an equivalent transformation of MMC into spectral clustering. By virtue of the establishment of equivalent relation between MMC and spectral clustering, we search for a simplified spectral clustering based method to solve the optimization problem of MMC efficiently, reducing its computational complexity. Experimental results on real world datasets show that the clustering results of MMC from the equivalent transformed spectral clustering method are better than any other baseline algorithms in comparison, and the reduced time consuming makes this advanced MMC more scalable. KEYWORD: Maximum margin clustering; Spectral clustering; Kernel machine