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Comparison of Proximity Measures: A Topological Approach

  • Djamel Abdelkader ZighedEmail author
  • Rafik Abdesselam
  • Ahmed Bounekkar
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Part of the Studies in Computational Intelligence book series (SCI, volume 471)

Abstract

In many application domains, the choice of a proximity measure affect directly the result of classification, comparison or the structuring of a set of objects. For any given problem, the user is obliged to choose one proximity measure between many existing ones. However, this choice depend on many characteristics. Indeed, according to the notion of equivalence, like the one based on pre-ordering, some of the proximity measures are more or less equivalent. In this paper, we propose a new approach to compare the proximity measures. This approach is based on the topological equivalence which exploits the concept of local neighbors and defines an equivalence between two proximity measures by having the same neighborhood structure on the objects.We compare the two approaches, the pre-ordering and our approach, to thirty five proximity measures using the continuous and binary attributes of empirical data sets.

Keywords

Adjacency Matrix Minimal Span Tree Appendix Table Neighborhood Structure Dissimilarity Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Djamel Abdelkader Zighed
    • 1
    Email author
  • Rafik Abdesselam
    • 1
  • Ahmed Bounekkar
    • 2
  1. 1.Laboratoire ERICUniversity Lumière of Lyon 2Bron CedexFrance
  2. 2.Laboratoire ERICUniversity Claude Bernard of Lyon 1Villeurbanne CedexFrance

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