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  On the Convergence of Spectral Clustering on Random Samples: The Normalized Case

von Luxburg, U., Bousquet, O., & Belkin, M. (2004). On the Convergence of Spectral Clustering on Random Samples: The Normalized Case. In J. Shawe-Taylor, & Y. Singer (Eds.), Learning Theory: 17th Annual Conference on Learning Theory, COLT 2004, Banff, Canada, July 1-4 (pp. 457-471). Berlin, Germany: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-F382-8 Version Permalink: https://hdl.handle.net/21.11116/0000-0005-5339-E
Genre: Conference Paper

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https://link.springer.com/content/pdf/10.1007%2F978-3-540-27819-1_32.pdf (Publisher version)
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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: Given a set of n randomly drawn sample points, spectral clustering in its simplest form uses the second eigenvector of the graph Laplacian matrix, constructed on the similarity graph between the sample points, to obtain a partition of the sample. We are interested in the question how spectral clustering behaves for growing sample size n. In case one uses the normalized graph Laplacian, we show that spectral clustering usually converges to an intuitively appealing limit partition of the data space. We argue that in case of the unnormalized graph Laplacian, equally strong convergence results are difficult to obtain.

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 Dates: 2004-07
 Publication Status: Issued
 Pages: -
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 Rev. Type: -
 Identifiers: BibTex Citekey: 2623
DOI: 10.1007/978-3-540-27819-1_32
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Title: 17th Annual Conference on Learning Theory (COLT 2004)
Place of Event: Banff, Canada
Start-/End Date: 2004-07-01 - 2004-07-04

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Title: Learning Theory: 17th Annual Conference on Learning Theory, COLT 2004, Banff, Canada, July 1-4
Source Genre: Proceedings
 Creator(s):
Shawe-Taylor, J, Editor
Singer, Y, Editor
Affiliations:
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Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 457 - 471 Identifier: ISBN: 978-3-540-22282-8

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Title: Lecture Notes in Computer Science
Source Genre: Series
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Pages: - Volume / Issue: 3120 Sequence Number: - Start / End Page: - Identifier: -