Clustering Quality Evaluation Based on Fuzzy FCA

  • Minyar Sassi
  • Amel Grissa Touzi
  • Habib Ounelli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4653)


Because clustering is an unsupervised procedure, clustering results need be judged by external criteria called validity indices. These indices play an important role in determining the number of clusters in a given dataset. A general approach for determining this number is to select the optimal value of a certain cluster validity index. Most existing indices give good results for data sets with well separated clusters, but usually fail for complex data sets, for example, data sets with overlapping clusters. In this paper, we propose a new approach for clustering quality evaluation while combining fuzzy logic with Formal Concept Analysis based on concept lattice. We define a formal quality index including the separation degree and the overlapping rate.


Clustering Quality Overlapping Rate Separation Degree Validity Index Formal Concept Analyis Fuzzy Concept Lattice 


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  1. 1.
    Menard, M., Eboueya, M.: Extreme physical information and objective function in fuzzy clustering. Fuzzy Sets and Systems 128, 285–303 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bezdek, J.C.: Pattern Recognition in Handbook of Fuzzy Computation. ch. F6. IOP Publishing Ltd, Bristol (1998)Google Scholar
  3. 3.
    Sun, H.: A theory on distinguishing overlapping components in mixture models, Research Report, DMI, University of Sherbrooke, No 345 (Novenber 2003)Google Scholar
  4. 4.
    Sassi, M., Grissa Touzi, A., Ounelli, H.: Two Levels of Extensions of Validity Function Based Fuzzy Clustering. In: The 4th International Multiconference on Computer Science & Information Technology (CSIT 2006), Amman-Jordan (April 5-7, 2006)Google Scholar
  5. 5.
    Priss, U.: Formal Concept Analysis in Information Science, Annual Review of Information Science and Technology (ARIST), Preview, vol. 40 (2006)Google Scholar
  6. 6.
    Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  7. 7.
    Valtxhev, P., Missaoui, P., Godin, R.: Formal Concept analysis for Knowledge Discovery and Data Mining: The New Challenges. In: Eklund, P.W. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, Springer, Heidelberg (2004)Google Scholar
  8. 8.
    Ganter, B., Wille, R.: Formal Concept Analysis: mathematical foundations. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  9. 9.
    Vogt, F., Wille, R.: TOSCANA - a graphical tool for analyzing and exploring data. In: Tamassia, R., Tollis, I.G. (eds.) Graph Drawing, pp. 193–205. Springer, Heidelberg (1994)Google Scholar
  10. 10.
    Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Minyar Sassi
    • 1
  • Amel Grissa Touzi
    • 1
  • Habib Ounelli
    • 2
  1. 1.Ecole Nationale d’Ingénieurs de Tunis, Bp. 37, Le Belvédère 1002 TunisTunisia
  2. 2.Faculté des Sciences de Tunis, Campus Universitaire -1060 TunisTunisia

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