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Spectral clustering based on matrix perturbation theory
Zheng, Tian; Li XiaoBin; Ju YanWei
Source PublicationSCIENCE IN CHINA SERIES F-INFORMATION SCIENCES
2007-02-01
Volume50Issue:1Pages:63-81
SubtypeArticle
AbstractThis 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.
KeywordSpectral Clustering Weight Matrix Spectrum Of Weight Matrix Number Of The Clusters Unsupervised Spectral Clustering Algorithm Based On Weight Matrix
WOS HeadingsScience & Technology ; Technology
Indexed BySCI
Language英语
WOS Research AreaComputer Science
WOS SubjectComputer Science, Information Systems
WOS IDWOS:000245639600006
Citation statistics
Cited Times:15[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.ia.ac.cn/handle/173211/9425
Collection09年以前成果
Affiliation1.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
Recommended Citation
GB/T 7714
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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