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Cluster Identification in Nearest-Neighbor Graphs

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Algorithmic Learning Theory (ALT 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4754))

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Abstract

Assume we are given a sample of points from some underlying distribution which contains several distinct clusters. Our goal is to construct a neighborhood graph on the sample points such that clusters are “identified”: that is, the subgraph induced by points from the same cluster is connected, while subgraphs corresponding to different clusters are not connected to each other. We derive bounds on the probability that cluster identification is successful, and use them to predict “optimal” values of k for the mutual and symmetric k-nearest-neighbor graphs. We point out different properties of the mutual and symmetric nearest-neighbor graphs related to the cluster identification problem.

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Author information

Authors and Affiliations

  1. Max Planck Institute for Biological Cybernetics, Tübingen, Germany

    Markus Maier, Matthias Hein & Ulrike von Luxburg

Authors
  1. Markus Maier
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  2. Matthias Hein
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  3. Ulrike von Luxburg
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Editor information

Editors and Affiliations

  1. RSISE @ ANU and SML @ NICTA, Canberra,, ACT, 0200, Australia

    Marcus Hutter

  2. Columbia University, NY, P.O. Box, New York, USA

    Rocco A. Servedio

  3. Graduate School of Information Sciences, Tohoku University,, Sendai 980-8579, Japan

    Eiji Takimoto

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© 2007 Springer-Verlag Berlin Heidelberg

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Maier, M., Hein, M., von Luxburg, U. (2007). Cluster Identification in Nearest-Neighbor Graphs. In: Hutter, M., Servedio, R.A., Takimoto, E. (eds) Algorithmic Learning Theory. ALT 2007. Lecture Notes in Computer Science(), vol 4754. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75225-7_18

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  • DOI: https://doi.org/10.1007/978-3-540-75225-7_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75224-0

  • Online ISBN: 978-3-540-75225-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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