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  Consistency of Spectral Clustering

von Luxburg, U., Belkin, M., & Bousquet, O. (2008). Consistency of Spectral Clustering. The Annals of Statistics, 36(2), 555-586. doi:10.1214/009053607000000640.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-C9B7-0 Version Permalink: http://hdl.handle.net/21.11116/0000-0003-30CC-1
Genre: Journal Article

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 Creators:
von Luxburg, U1, 2, Author              
Belkin, M, Author
Bousquet, O1, 2, Author              
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: Consistency is a key property of statistical algorithms when the data is drawn from some underlying probability distribution. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of the popular family of spectral clustering algorithms, which clusters the data with the help of eigenvectors of graph Laplacian matrices. We develop new methods to establish that for increasing sample size, those eigenvectors converge to the eigenvectors of certain limit operators. As a result we can prove that one of the two major classes of spectral clustering (normalized clustering) converges under very general conditions, while the other (unnormalized clustering) is only consistent under strong additional assumptions, which are not always satisfied in real data. We conclude that our analysis provides strong evidence for the superiority of normalized spectral clustering.

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 Dates: 2008-04
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Method: -
 Identifiers: BibTex Citekey: 4403
DOI: 10.1214/009053607000000640
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Title: The Annals of Statistics
Source Genre: Journal
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Publ. Info: Cleveland, Ohio [etc] : Institute of Mathematical Statistics [etc.]
Pages: - Volume / Issue: 36 (2) Sequence Number: - Start / End Page: 555 - 586 Identifier: ISSN: 0090-5364
CoNE: https://pure.mpg.de/cone/journals/resource/954925461135