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Indexed by:Journal Papers

Date of Publication:2011-05-01

Journal:Journal of Information and Computational Science

Included Journals:EI、Scopus

Volume:8

Issue:5

Page Number:725-737

ISSN No.:15487741

Abstract:Locally Linear Embedding (LLE) is an effective method for both single manifold embedding and multiple manifolds clustering. However, LLE may fail to model data drawn from mixture of manifolds because a point and its Nearest Neighbors (NNs) cannot guaranteed to be on the same manifold, especially when the point is at the junction of different manifolds. In this paper, we propose a new method, named Low Rank Embedding (LRE), to model the geometric structure of mixture of manifolds. LRE defines the neighborhood structure as linear combination of other samples with an additional minimum rank constraint on the points that belong to the same manifold. This way, LRE removes the dependency with the number and metric of NNs, and it makes a more accurate selection of the neighbors belonging to the same manifold. Both theoretical and experimental results show that LRE is a promising tool for embedding and clustering mixture of manifolds.