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A New Criterion for Obtaining a Fuzzy Partition from a Hybrid Fuzzy/Hierarchical Clustering Method

  • Arnaud Devillez
  • Patrice Billaudel
  • Gérard Villermain Lecolier
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

Classical fuzzy clustering methods are not able to compute a partition into a set of points, when classes have non-convex shape. Furthermore, we know that in this case, the usual criteria of class validity, such as fuzzy hyper volume or compactness - separability, do not allow one to find the optimal partition.

The purpose of our paper is to provide a criterion allowing one to find the optimal fuzzy partition in a set of points including classes of any shape. To that effect we shall use the Fuzzy C Means algorithm to divide the set of points into an overspecified number of subclasses. A fuzzy relation is established between them in order to extract the structure of the set of points. The subclasses are merged according to this relation and the criterion that we propose allows one to find the optimal regrouping.

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Copyright information

© Springer-Verlag Berlin · Heidelberg 2000

Authors and Affiliations

  • Arnaud Devillez
    • 1
  • Patrice Billaudel
    • 1
  • Gérard Villermain Lecolier
    • 1
  1. 1.Laboratoire d’Automatique et de MicroélectroniqueFaculté des Sciences - Moulin de la HousseReims Cedex 2France

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