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Spectral clustering based on matrix perturbation theory
Zheng, Tian; Li XiaoBin; Ju YanWei
2007-02-01
发表期刊SCIENCE IN CHINA SERIES F-INFORMATION SCIENCES
卷号50期号:1页码:63-81
文章类型Article
摘要This paper exposes some intrinsic characteristics of the spectral clustering method by using the tools from the matrix perturbation theory. We construct a weight matrix of a graph and study its eigenvalues and eigenvectors. It shows that the number of clusters is equal to the number of eigenvalues that are larger than 1, and the number of points in each of the clusters can be approximated by the associated eigenvalue. It also shows that the eigenvector of the weight matrix can be used directly to perform clustering; that is, the directional angle between the two-row vectors of the matrix derived from the eigenvectors is a suitable distance measure for clustering. As a result, an unsupervised spectral clustering algorithm based on weight matrix (USCAWM) is developed. The experimental results on a number of artificial and real-world data sets show the correctness of the theoretical analysis.
关键词Spectral Clustering Weight Matrix Spectrum Of Weight Matrix Number Of The Clusters Unsupervised Spectral Clustering Algorithm Based On Weight Matrix
WOS标题词Science & Technology ; Technology
收录类别SCI
语种英语
WOS研究方向Computer Science
WOS类目Computer Science, Information Systems
WOS记录号WOS:000245639600006
引用统计
被引频次:14[WOS]   [WOS记录]     [WOS相关记录]
文献类型期刊论文
条目标识符http://ir.ia.ac.cn/handle/173211/9425
专题09年以前成果
作者单位1.Northwestern Polytech Univ, Dept Math Appl, Xian 710072, Peoples R China
2.Chinese Acad Sci, Natl Lab Pattern Recognit, Inst Automat, Beijing 100080, Peoples R China
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Zheng, Tian,Li XiaoBin,Ju YanWei. Spectral clustering based on matrix perturbation theory[J]. SCIENCE IN CHINA SERIES F-INFORMATION SCIENCES,2007,50(1):63-81.
APA Zheng, Tian,Li XiaoBin,&Ju YanWei.(2007).Spectral clustering based on matrix perturbation theory.SCIENCE IN CHINA SERIES F-INFORMATION SCIENCES,50(1),63-81.
MLA Zheng, Tian,et al."Spectral clustering based on matrix perturbation theory".SCIENCE IN CHINA SERIES F-INFORMATION SCIENCES 50.1(2007):63-81.
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