Influence of graph construction on graph-based clustering measures

2009

Conference Paper

ei


Graph clustering methods such as spectral clustering are defined for general weighted graphs. In machine learning, however, data often is not given in form of a graph, but in terms of similarity (or distance) values between points. In this case, first a neighborhood graph is constructed using the similarities between the points and then a graph clustering algorithm is applied to this graph. In this paper we investigate the influence of the construction of the similarity graph on the clustering results. We first study the convergence of graph clustering criteria such as the normalized cut (Ncut) as the sample size tends to infinity. We find that the limit expressions are different for different types of graph, for example the r-neighborhood graph or the k-nearest neighbor graph. In plain words: Ncut on a kNN graph does something systematically different than Ncut on an r-neighborhood graph! This finding shows that graph clustering criteria cannot be studied independently of the kind of graph they are applied to. We also provide examples which show that these differences can be observed for toy and real data already for rather small sample sizes.

Author(s): Maier, M. and von Luxburg, U. and Hein, M.
Book Title: Advances in neural information processing systems 21
Journal: Advances in neural information processing systems 21 : 22nd Annual Conference on Neural Information Processing Systems 2008
Pages: 1025-1032
Year: 2009
Month: June
Day: 0
Editors: Koller, D. , D. Schuurmans, Y. Bengio, L. Bottou
Publisher: Curran

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

Address: Red Hook, NY, USA
Digital: 0
Event Name: Twenty-Second Annual Conference on Neural Information Processing Systems (NIPS 2008)
Event Place: Vancouver, BC, Canada
ISBN: 978-1-605-60949-2
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{5393,
  title = {Influence of graph construction on graph-based clustering measures},
  author = {Maier, M. and von Luxburg, U. and Hein, M.},
  journal = {Advances in neural information processing systems 21 : 22nd Annual Conference on Neural Information Processing Systems 2008},
  booktitle = {Advances in neural information processing systems 21},
  pages = {1025-1032},
  editors = {Koller, D. , D. Schuurmans, Y. Bengio, L. Bottou},
  publisher = {Curran},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Red Hook, NY, USA},
  month = jun,
  year = {2009},
  month_numeric = {6}
}