Multiple Flat Projections for Cross-Manifold Clustering

Cross-manifold clustering is an extreme challenge learning problem. Since the low-density hypothesis is not satisfied in cross-manifold problems, many traditional clustering methods failed to discover the cross-manifold structures. In this article, we propose multiple flat projections clustering (MFPC) for cross-manifold clustering. In our MFPC, the given samples are projected into multiple localized flats to discover the global structures of implicit manifolds. Thus, the intersected clusters are distinguished in various projection flats. In MFPC, a series of nonconvex matrix optimization problems is solved by a proposed recursive algorithm. Furthermore, a nonlinear version of MFPC is extended via kernel tricks to deal with a more complex cross-manifold learning situation. The synthetic tests show that our MFPC works on the cross-manifold structures well. Moreover, experimental results on the benchmark datasets and object tracking videos show excellent performance of our MFPC compared with some state-of-the-art manifold clustering methods.

Automated summary

Cross-manifold clustering is a challenging learning problem, and traditional clustering methods often fail in this scenario. The proposed multiple flat projections clustering (MFPC) effectively discovers global structures of implicit manifolds by projecting samples into localized flats and solving nonconvex matrix optimization problems through a recursive algorithm. The nonlinear version of MFPC, extended via kernel tricks, shows promising results in dealing with complex cross-manifold learning situations.