Multi-manifold Clustering

Manifold clustering, which regards clusters as groups of points around compact manifolds, has been realized as a promising generalization of traditional clustering. A number of linear or nonlinear manifold clustering approaches have been developed recently. Although they have attained better performances than traditional clustering methods in many scenarios, most of these approaches suffer from two weaknesses. First, when the data are drawn from hybrid modeling, i.e., some data manifolds are separated but some are intersected, existing approaches could not work well although hybrid modeling often appears in real data. Second, many approaches require to know the number of clusters and the intrinsic dimensions of the manifolds in advance, while it is hard for the user to provide such information in practice. In this paper, we propose a new manifold clustering approach, mumCluster, to address these issues. Experimental results show that the performance of the proposed mumCluster approach is encouraging.