Multiple Flat Projections for Cross-manifold Clustering
Abstract
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.
Cite
@article{arxiv.2002.06739,
title = {Multiple Flat Projections for Cross-manifold Clustering},
author = {Lan Bai and Yuan-Hai Shao and Wei-Jie Chen and Zhen Wang and Nai-Yang Deng},
journal= {arXiv preprint arXiv:2002.06739},
year = {2021}
}
Comments
12 pages, 58 figures