Resampling approach for cluster model selection

  • Authors:

  • Z. Volkovich;Z. Barzily;G. -W. Weber;D. Toledano-Kitai;R. Avros

  • Affiliations:

  • Ort Braude College of Engineering, Karmiel, Israel 21982;Ort Braude College of Engineering, Karmiel, Israel 21982;Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey 06531 and University of Siegen, Siegen, Germany and University of Aveiro, Aveiro, Portugal and Universiti Teknolo ...;Ort Braude College of Engineering, Karmiel, Israel 21982;Ort Braude College of Engineering, Karmiel, Israel 21982

  • Venue:
  • Machine Learning
  • Year:
  • 2011

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Abstract

In cluster analysis, selecting the number of clusters is an "ill-posed" problem of crucial importance. In this paper we propose a re-sampling method for assessing cluster stability. Our model suggests that samples' occurrences in clusters can be considered as realizations of the same random variable in the case of the "true" number of clusters. Thus, similarity between different cluster solutions is measured by means of compound and simple probability metrics. Compound criteria result in validation rules employing the stability content of clusters. Simple probability metrics, in particular those based on kernels, provide more flexible geometrical criteria. We analyze several applications of probability metrics combined with methods intended to simulate cluster occurrences. Numerical experiments are provided to demonstrate and compare the different metrics and simulation approaches.