Expert Constrained Clustering: A Symbolic Approach

  • Fabrice Rossi
  • Frédérick Vautrain
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1910)

Abstract

A new constrained model is discussed as a way of incorporating efficiently a priori expert knowledge into a clustering problem of a given individual set. The first innovation is the combination of fusion constraints, which request some individuals to belong to one cluster, with exclusion constraints, which separate some individuals in different clusters. This situation implies to check the existence of a solution (ie if no pair of individuals are connected by fusion and exclusion constraints). The second novelty is that the constraints are expressed in a symbolic language that allows compact description of group of individuals according to a given interpretation. This paper studies the coherence of such constraints at individual and symbolic levels. A mathematical framework, close to the Symbolic Data Analysis[3], is built in order to define how a symbolic description space may be interpreted on a given individual set. A partial order on symbolic descriptions (which is an usual assumption of Artificial Intelligence), allows a symbolic analysis of the constraints. Our results provide an individual but also a symbolic clustering.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hans-Hermann Bock and Edwin Diday, editors. Analysis of Symbolic Data. Exploratory methods for extracting statistical information from complex data. Springer Verlag, 2000.Google Scholar
  2. 2.
    Roland De Guio, Thierry Erbeja, and Vincent Laget. A clustering approach for GT family formation problems. In 1st international conference on Engineering Design and Automation, pages 18–21, March 1997.Google Scholar
  3. 3.
    Edwin Diday. L’analyse des données symboliques: un cadre théorique et des outils. Technical Report 9821, LISE/CEREMADE (CNRS UMR 7534), Université Paris-IX/Dauphine Mars 1998.Google Scholar
  4. 4.
    A. D. Gordon. A survey of constrained classiffication. Computational Statistics & Data Analysis, 21:17–29, 1996.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Amedeo Napoli. Une introduction aux logiques de descriptions. Technical Report 3314, Projet SYCO, INRIA Lorraine, 1997.Google Scholar
  6. 6.
    Fabrice Rossi and Frédérick Vautrain. Constrained classiffication. Technical report, LISE/CEREMADE (CNRS UMR 7534), Université Paris-IX/Dauphine, April 2000.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Fabrice Rossi
    • 1
  • Frédérick Vautrain
    • 1
  1. 1.LISE/CEREMADE (CNRS UMR 7534)Université Paris-IX/DauphineParis Cedex 16France

Personalised recommendations