Self-Organizing Map Based on City-Block Distance for Interval-Valued Data

  • Chantal Hajjar
  • Hani Hamdan
Conference paper


The Self-Organizing Maps have been widely used as multidimensional unsupervised classifiers. The aim of this paper is to develop a self-organizing map for interval data. Due to the increasing use of such data in Data Mining, many clustering methods for interval data have been proposed this last decade. In this paper, we propose an algorithm to train the self-organizing map for interval data. We use the city-block distance to compare two vectors of intervals. In order to show the usefulness of our approach, we apply the self-organizing map on real interval data issued from meteorological stations in France.


Input Vector Interval Data Symbolic Data Neighborhood Function Pattern Recognition Letter 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cazes, P., Chouakria, A., Diday, E., Schektman, Y.: Revue de Statistique Appliquée XIV(3), 5 (1997)Google Scholar
  2. 2.
    Chouakria, A.: Extension des méthodes d’analyse factorielle à des données de type intervalle. Ph.D. thesis, Université Paris 9 Dauphine (1998)Google Scholar
  3. 3.
    Billard, L., Diday, E.: In: Kiers, H., Groenen, P., Rasson, J.P., Schader, M. (eds.) Data Analysis, Classification, and Related Methods, Proc. IFCS 2000, Namur, Belgium. Springer, Heidelberg (2000)Google Scholar
  4. 4.
    Denœux, T., Masson, M.: Pattern Recognition Letters 21(1), 83 (2000), doi: Scholar
  5. 5.
    Rossi, F., Conan-Guez, B.: Classification, Clustering, and Data Analysis. In: Jajuga, K., Sokolowski, A., Bock, H.H. (eds.) pp. 427–436. Springer, Berlin (2002)Google Scholar
  6. 6.
    Chavent, M., Lechevallier, Y.: Classification, Clustering and Data Analysis. In: Jajuga, K., Sokolowski, A., Bock, H.H. (eds.) pp. 53–60. Springer, Berlin (2002); Also in the Proceedings of IFCS 2002, PolandGoogle Scholar
  7. 7.
    Barnsley, M.: Fractals Everywhere, 2nd edn. Academic Press (1993)Google Scholar
  8. 8.
    Chavent, M.: Analyse des données symboliques. une méthode divisive de classification. Ph.D. thesis, Université de PARIS-IX Dauphine (1997)Google Scholar
  9. 9.
    Bock, H.H.: Journal of the Japanese Society of Computational Statistics 15(2), 217 (2003)Google Scholar
  10. 10.
    Hamdan, H., Govaert, G.: XXXVeme Journées de Statistique, SFdS, Lyon, France, pp. 549–552 (2003)Google Scholar
  11. 11.
    Hamdan, H., Govaert, G.: CIMNA 2003, premier congrès international sur les modélisations numériques appliquées, Beyrouth, Liban, pp. 16–19 (2003)Google Scholar
  12. 12.
    Hamdan, H., Govaert, G.: IEEE International Conference on Fuzzy Systems, Reno, Nevada, USA, pp. 879–884 (2005)Google Scholar
  13. 13.
    Hamdan, H., Govaert, G.: IEEE International Conference on Systems, Man and Cybernetics, The Hague, The Netherlands, pp. 4774–4779 (2004)Google Scholar
  14. 14.
    Hamdan, H., Govaert, G.: IEEE International Conference on Cybernetics and Intelligent Systems, Singapore, pp. 410–415 (2004)Google Scholar
  15. 15.
    Chavent, M.: Classification, Clustering and Data Mining Applications. In: Banks, D., House, L., McMorris, F.R., Arabie, P., Gaul, W. (eds.) pp. 333–340. Springer, Heidelberg (2004)Google Scholar
  16. 16.
    De Souza, R.M.C.R., De Carvalho, F.A.T.: Pattern Recognition Letters 25(3), 353 (2004)Google Scholar
  17. 17.
    De Souza, R.M.C.R., De Carvalho, F.A.T., Tenório, C.P., Lechevallier, Y.: Proceedings of the 9th Conference of the International Federation of Classification Societies, pp. 351–360. Springer, Chicago (2004)Google Scholar
  18. 18.
    El Golli, A., Conan-Guez, B., Rossi, F.: JSDA Electronic Journal of Symbolic Data Analysis 2(1) (2004)Google Scholar
  19. 19.
    Kohonen, T.: Self Organization and Associative Memory, 2nd edn. Springer, Heidelberg (1984)Google Scholar
  20. 20.
    Kohonen, T.: Self-Organizing Maps, 3rd edn. Springer, Heidelberg (2001)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Signal Processing and Electronic Systems DepartmentSUPELEC Systems Sciences (E3S)Gif-sur-Yvette cedexFrance
  2. 2.Université LibanaiseBeirutLebanon

Personalised recommendations