Spectral clustering based on matrix perturbation theory

	Spectral clustering based on matrix perturbation theory
	Zheng, Tian ; Li XiaoBin ; Ju YanWei
刊名	SCIENCE IN CHINA SERIES F-INFORMATION SCIENCES
	2007-02-01
卷号	50 期号:1 页码:63-81
关键词	spectral clustering weight matrix spectrum of weight matrix number of the clusters unsupervised spectral clustering algorithm based on weight matrix
英文摘要	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.
WOS标题词	Science & Technology ; Technology
类目[WOS]	Computer Science, Information Systems
研究领域[WOS]	Computer Science
收录类别	SCI
语种	英语
WOS记录号	WOS:000245639600006
公开日期	2015-12-24
内容类型	期刊论文
源URL	[http://ir.ia.ac.cn/handle/173211/9425]
专题	自动化研究所_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
推荐引用方式 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.