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Spectral Clustering by Recursive Partitioning

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Algorithms – ESA 2006 (ESA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4168))

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Abstract

In this paper, we analyze the second eigenvector technique of spectral partitioning on the planted partition random graph model, by constructing a recursive algorithm using the second eigenvectors in order to learn the planted partitions. The correctness of our algorithm is not based on the ratio-cut interpretation of the second eigenvector, but exploits instead the stability of the eigenvector subspace. As a result, we get an improved cluster separation bound in terms of dependence on the maximum variance. We also extend our results for a clustering problem in the case of sparse graphs.

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Author information

Authors and Affiliations

  1. Yahoo! Research Labs,  

    Anirban Dasgupta

  2. Department of Computer Science, Cornell University,  

    John Hopcroft

  3. Department of Computer Science, Yale University,  

    Ravi Kannan & Pradipta Mitra

Authors
  1. Anirban Dasgupta
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  2. John Hopcroft
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  3. Ravi Kannan
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  4. Pradipta Mitra
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Editor information

Editors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA and School of Computer Science, Tel-Aviv University, 69978, Tel-Aviv, Israel

    Yossi Azar

  2. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Thomas Erlebach

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© 2006 Springer-Verlag Berlin Heidelberg

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Dasgupta, A., Hopcroft, J., Kannan, R., Mitra, P. (2006). Spectral Clustering by Recursive Partitioning. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_25

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  • DOI: https://doi.org/10.1007/11841036_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38875-3

  • Online ISBN: 978-3-540-38876-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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