Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS
Volume 22, Issue 7, Pages 1149-1161Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNN.2011.2147798
Keywords
Clustering; local tangent space; manifold clustering; spectral clustering
Categories
Funding
- National Fundamental Research Program of China [2010CB327903]
- National Science Foundation of China [60975043, 60975038]
- Jiangsu 333 High-Level Talent Cultivation Program
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Spectral clustering (SC) is a large family of grouping methods that partition data using eigenvectors of an affinity matrix derived from the data. Though SC methods have been successfully applied to a large number of challenging clustering scenarios, it is noteworthy that they will fail when there are significant intersections among different clusters. In this paper, based on the analysis that SC methods are able to work well when the affinity values of the points belonging to different clusters are relatively low, we propose a new method, called spectral multi-manifold clustering (SMMC), which is able to handle intersections. In our model, the data are assumed to lie on or close to multiple smooth low-dimensional manifolds, where some data manifolds are separated but some are intersecting. Then, local geometric information of the sampled data is incorporated to construct a suitable affinity matrix. Finally, spectral method is applied to this affinity matrix to group the data. Extensive experiments on synthetic as well as real datasets demonstrate the promising performance of SMMC.
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