  Cross-manifold clustering is a hard topic and many traditional clustering
methods fail because of the cross-manifold structures. In this paper, we
propose a Multiple Flat Projections Clustering (MFPC) to deal with
cross-manifold clustering problems. In our MFPC, the given samples are
projected into multiple subspaces to discover the global structures of the
implicit manifolds. Thus, the cross-manifold clusters are distinguished from
the various projections. Further, our MFPC is extended to nonlinear manifold
clustering via kernel tricks to deal with more complex cross-manifold
clustering. A series of non-convex matrix optimization problems in MFPC are
solved by a proposed recursive algorithm. The synthetic tests show that our
MFPC works on the cross-manifold structures well. Moreover, experimental
results on the benchmark datasets show the excellent performance of our MFPC
compared with some state-of-the-art clustering methods.
