1. Multiple Flat Projections for Cross-Manifold Clustering
- Author
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Yuan-Hai Shao, Lan Bai, Nai-Yang Deng, Zhen Wang, and Wei-Jie Chen
- Subjects
FOS: Computer and information sciences ,Computer Science - Machine Learning ,Computer science ,Machine Learning (stat.ML) ,02 engineering and technology ,Machine Learning (cs.LG) ,Statistics - Machine Learning ,020204 information systems ,0202 electrical engineering, electronic engineering, information engineering ,Electrical and Electronic Engineering ,Cluster analysis ,Projection (set theory) ,Mathematics::Symplectic Geometry ,Series (mathematics) ,Manifold ,Computer Science Applications ,Human-Computer Interaction ,Nonlinear system ,ComputingMethodologies_PATTERNRECOGNITION ,Kernel (image processing) ,Control and Systems Engineering ,Video tracking ,Benchmark (computing) ,020201 artificial intelligence & image processing ,Mathematics::Differential Geometry ,Algorithm ,Software ,Information Systems - 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., Comment: 12 pages, 58 figures
- Published
- 2022
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