Chapter 13. Validation of Clustering Structure: Determination of the Number of Clusters

  1. Edwin Diday2 and
  2. Monique Noirhomme-Fraiture3
  1. André Hardy

Published Online: 28 JAN 2008

DOI: 10.1002/9780470723562.ch13

Symbolic Data Analysis and the SODAS Software

Symbolic Data Analysis and the SODAS Software

How to Cite

Hardy, A. (2008) Validation of Clustering Structure: Determination of the Number of Clusters, in Symbolic Data Analysis and the SODAS Software (eds E. Diday and M. Noirhomme-Fraiture), John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470723562.ch13

Editor Information

  1. 2

    Université Paris IX-Dauphine, LISE-CEREMADE, Place du Marechal de Lattre de Tassigny, Paris Cedex 16, France F-75775

  2. 3

    Facultés Universitaires Notre-Dame de la Paix, Faculté d'Informatique, Rue Grandgagnage, 21, Namur, Belgium, B-5000

Author Information

  1. Facultés Universitaires Notre-Dame de la Paix, Départment de Mathématique, Rempart de la Vièrge, 8, Namur, Belgium, B-5000

Publication History

  1. Published Online: 28 JAN 2008
  2. Published Print: 18 JAN 2007

ISBN Information

Print ISBN: 9780470018835

Online ISBN: 9780470723562

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Keywords:

  • hypervolumes clustering criterion;
  • interval-valued, multi-valued and modal variables;
  • within-cluster pairwise dissimilarities and between-clusters pairwise dissimilarities;
  • categorical multi-valued, quantitative multi-valued and interval-valued;
  • dynamical clustering method;
  • single linkage method;
  • complete linkage method;
  • centroid method and Ward method;
  • hypervolumes clustering method;
  • multidimensional Lebesgue measure

Summary

This chapter contains sections titled:

  • Introduction

  • The clustering problem

  • Classical criteria for the number of clusters

  • Symbolic variables

  • Dissimilarity measures for symbolic objects

  • Symbolic clustering procedures

  • Determination of the number of clusters for symbolic objects

  • Statistical models based on the Poisson processes

  • Statistical tests for the number of clusters based on the homogeneous Poisson point process

  • Examples

  • Conclusion

  • References