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  Limits of Spectral Clustering

von Luxburg, U., Bousquet, O., & Belkin, M. (2005). Limits of Spectral Clustering. In L. Saul, Y. Weiss, & L. Bottou (Eds.), Advances in Neural Information Processing Systems 17 (pp. 857-864). Cambridge, MA, USA: MIT Press.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-D523-C Version Permalink: http://hdl.handle.net/21.11116/0000-0005-219C-6
Genre: Conference Paper

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 Creators:
von Luxburg, U1, 2, Author              
Bousquet, O1, 2, Author              
Belkin, M, 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: An important aspect of clustering algorithms is whether the partitions constructed on finite samples converge to a useful clustering of the whole data space as the sample size increases. This paper investigates this question for normalized and unnormalized versions of the popular spectral clustering algorithm. Surprisingly, the convergence of unnormalized spectral clustering is more difficult to handle than the normalized case. Even though recently some first results on the convergence of normalized spectral clustering have been obtained, for the unnormalized case we have to develop a completely new approach combining tools from numerical integration, spectral and perturbation theory, and probability. It turns out that while in the normalized case, spectral clustering usually converges to a nice partition of the data space, in the unnormalized case the same only holds under strong additional assumptions which are not always satisfied. We conclude that our analysis gives strong evidence for the superiority of normalized spectral clustering. It also provides a basis for future exploration of other Laplacian-based methods.

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 Dates: 2005-07
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: 2775
 Degree: -

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Title: Eighteenth Annual Conference on Neural Information Processing Systems (NIPS 2004)
Place of Event: Vancouver, BC, Kanada
Start-/End Date: 2004-12-13 - 2004-12-16

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Title: Advances in Neural Information Processing Systems 17
Source Genre: Proceedings
 Creator(s):
Saul, LK, Editor
Weiss, Y, Editor
Bottou, L, Editor
Affiliations:
-
Publ. Info: Cambridge, MA, USA : MIT Press
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 857 - 864 Identifier: ISBN: 0-262-19534-8