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A new geometrical hypothesis for clustering and discriminant analysis

  • Jean-Paul Rasson
  • Didier Jacquemin
  • Vincent Bertholet
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

In this paper, we propose a new clustering method and a new discriminant rule valid on the basic spaced ℜ2. These procedures make use of a new concept in clustering: the concept of closed and connex forms. This hypothesis generalizes the convex hypothesis and is very useful to find non convex natural clusters. Finally, we examine the admissibility of our procedure, in the sense of Fisher and Van Ness [4].

Keywords

Cluster Analysis Discriminant Analysis Lebesgue Measure Stationary Poisson Point Process Hypervolume Method Replacing the convexity Non Convex case Connex and Closed domains Optimal Closing Admissibility Conditions 

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1998

Authors and Affiliations

  • Jean-Paul Rasson
    • 1
  • Didier Jacquemin
    • 1
  • Vincent Bertholet
    • 1
  1. 1.Department of MathematicsFacultés Universitaires Notre-Dame de la PaixNamurBelgium

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