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  Consistency of Spectral Clustering

von Luxburg, U., Belkin, M., & Bousquet, O.(2004). Consistency of Spectral Clustering (134). Tübingen, Germany: Max Planck Institute for Biological Cybernetics.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-D74B-6 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-8B2A-3
Genre: Report

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MPIK-TR-134.pdf (Publisher version), 327KB
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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 a popular family of spectral clustering algorithms, which cluster the data with the help of eigenvectors of graph Laplacian matrices. We show that one of the two of major classes of spectral clustering (normalized clustering) converges under some very general conditions, while the other (unnormalized), is only consistent under strong additional assumptions, which, as we demonstrate, are not always satisfied in real data. We conclude that our analysis provides strong evidence for the superiority of normalized spectral clustering in practical applications. We believe that methods used in our analysis will provide a basis for future exploration of Laplacian-based methods in a statistical setting.

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 Dates: 2004-12
 Publication Status: Published in print
 Pages: 34
 Publishing info: Tübingen, Germany : Max Planck Institute for Biological Cybernetics
 Table of Contents: -
 Rev. Type: -
 Identifiers: Report Nr.: 134
BibTex Citekey: 3199
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Title: Technical Report of the Max Planck Institute for Biological Cybernetics
Source Genre: Series
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Pages: - Volume / Issue: 134 Sequence Number: - Start / End Page: - Identifier: -