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Cluster Identification in Nearest-Neighbor Graphs

2007

Conference Paper

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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.

Author(s): Maier, M. and Hein, M. and von Luxburg, U.
Book Title: ALT 2007
Journal: Algorithmic Learning Theory: Proceedings of the 18th International Confererence (ALT 2007)
Pages: 196-210
Year: 2007
Month: October
Day: 0
Editors: Hutter, M. , R. A. Servedio, E. Takimoto
Publisher: Springer

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

DOI: 10.1007/978-3-540-75225-7_18
Event Name: 18th International Conference on Algorithmic Learning Theory
Event Place: Sendai, Japan

Address: Berlin, Germany
Digital: 0
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{4590,
  title = {Cluster Identification in Nearest-Neighbor Graphs},
  author = {Maier, M. and Hein, M. and von Luxburg, U.},
  journal = {Algorithmic Learning Theory: Proceedings of the 18th International Confererence (ALT 2007)},
  booktitle = {ALT 2007},
  pages = {196-210},
  editors = {Hutter, M. , R. A. Servedio, E. Takimoto},
  publisher = {Springer},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Berlin, Germany},
  month = oct,
  year = {2007},
  month_numeric = {10}
}