Implication Strength of Classification Rules

  • Gilbert Ritschard
  • Djamel A. Zighed
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4203)

Abstract

This paper highlights the interest of implicative statistics for classification trees. We start by showing how Gras’ implication index may be defined for the rules derived from an induced decision tree. Then, we show that residuals used in the modeling of contingency tables provide interesting alternatives to Gras’ index. We then consider two main usages of these indexes. The first is purely descriptive and concerns the a posteriori individual evaluation of the classification rules. The second usage, considered for instance by [15], relies upon the intensity of implication to define the conclusion in each leaf of the induced tree.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Agresti, A.: Categorical Data Analysis. Wiley, New York (1990)MATHGoogle Scholar
  2. 2.
    Bishop, Y.M.M., Fienberg, S.E., Holland, P.W.: Discrete Multivariate Analysis. MIT Press, Cambridge (1975)MATHGoogle Scholar
  3. 3.
    Blanchard, J., Guillet, F., Gras, R., Briand, H.: Using information-theoretic measures to assess association rule interestingness. In: Proceedings of the 5th IEEE International Conference on Data Mining (ICDM 2005), pp. 66–73. IEEE Computer Society, Los Alamitos (2005)CrossRefGoogle Scholar
  4. 4.
    Breiman, L., Friedman, J.H., Olshen, R.A., Stone, C.J.: Classification And Regression Trees. Chapman and Hall, New York (1984)MATHGoogle Scholar
  5. 5.
    Briand, H., Fleury, L., Gras, R., Masson, Y., Philippe, J.: A statistical measure of rules strength for machine learning. In: Proceedings of the Second World Conference on the Fundamentals of Artificial Intelligence WOCFAI 1995, Paris, Angkor, pp. 51–62 (1995)Google Scholar
  6. 6.
    Gras, R.: Contribution á l’étude expérimentale et á l’analyse de certaines acquisitions cognitives et de certains objectifs didactiques. Thése d’état, Université de Rennes 1, France (1979)Google Scholar
  7. 7.
    Gras, R., Couturier, R., Blanchard, J., Briand, H., Kuntz, P., Peter, P.: Quelques critéres pour une mesure de qualité de régles d’association. Revue des nouvelles technologies de l’information RNTI E-1, 3–30 (2004)Google Scholar
  8. 8.
    Gras, R., Larher, A.: L’implication statistique, une nouvelle méthode d’analyse de données. Mathématique, Informatique et Sciences Humaines 120, 5–31 (1992)MATHMathSciNetGoogle Scholar
  9. 9.
    Gras, R., Ratsima-Rajohn, H.: L’implication statistique, une nouvelle méthode d’analyse de données. RAIRO Recherche Opérationnelle 30(3), 217–232 (1996)MATHGoogle Scholar
  10. 10.
    Guillaume, S., Guillet, F., Philippé, J.: Improving the discovery of association rules with intensity of implication. In: Żytkow, J.M. (ed.) PKDD 1998. LNCS, vol. 1510, pp. 318–327. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  11. 11.
    Kass, G.V.: An exploratory technique for investigating large quantities of categorical data. Applied Statistics 29(2), 119–127 (1980)CrossRefGoogle Scholar
  12. 12.
    Lerman, I.C., Gras, R., Rostam, H.: Elaboration d’un indice d’implication pour données binaires I. Mathématiques et sciences humaines (74), 5–35 (1981)Google Scholar
  13. 13.
    Raftery, A.E.: Bayesian model selection in social research. In: Marsden, P. (ed.) Sociological Methodology, pp. 111–163. The American Sociological Association, Washington (1995)Google Scholar
  14. 14.
    Suzuki, E., Kodratoff, Y.: Discovery of surprising exception rules based on intensity of implication. In: Żytkow, J.M. (ed.) PKDD 1998. LNCS, vol. 1510, pp. 10–18. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  15. 15.
    Zighed, D.A., Rakotomalala, R.: Graphes d’induction: apprentissage et data mining. Hermes Science Publications, Paris (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gilbert Ritschard
    • 1
  • Djamel A. Zighed
    • 2
  1. 1.Dept of EconometricsUniversity of GenevaGeneva 4Switzerland
  2. 2.Laboratoire ERICUniversity of Lyon 2BronFrance

Personalised recommendations