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Cluster Identification in Nearest-Neighbor Graphs


Technical Report


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.
Number (issue): 163
Year: 2007
Month: May
Day: 0

Department(s): Empirical Inference
Bibtex Type: Technical Report (techreport)

Institution: Max-Planck-Institute for Biological Cybernetics, Tübingen, Germany

Digital: 0
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF


  title = {Cluster Identification in Nearest-Neighbor Graphs},
  author = {Maier, M. and Hein, M. and von Luxburg, U.},
  number = {163},
  organization = {Max-Planck-Gesellschaft},
  institution = {Max-Planck-Institute for Biological Cybernetics, Tübingen, Germany},
  school = {Biologische Kybernetik},
  month = may,
  year = {2007},
  month_numeric = {5}