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Reduction of Redundant Rules in Statistical Implicative Analysis

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Abstract

Quasi-implications, also called association rules in data mining, have become the major concept to represent implicative trends between itemset patterns. To make their interpretation easier, two problems have become crucial: filtering the most interestingness rules and structuring them to highlight their relationships. In this paper, we put ourselves in the Statistical Implicative Analysis framework, and we propose a new methodology for reducing rule sets by detecting redundant rules. We define two new measures based on the Shannon’s entropy and the Gini’s coefficient.

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References

  • AGRAWAL, R., IMIELINSKY, T., and SWANI, A. (1993): Mining association rules between sets of items in large databases. In: Proc. of the ACM SIGMOD’93. AAAI Press, 679–696.

    Google Scholar 

  • BERNARD, J.-M. and POITRENAUD, S. (1999): L’analyse implicative bayesienne d’un questionnaire binaire: quasi-implications et treillis de Galois simplifié. Mathématiques, Informatique et Sciences Humaines, 147, 25–46.

    Google Scholar 

  • BLANCHARD, J., GUILLET, F., and BRIAND, H. (2007): Interactive visual exploration of association rules with the rule focusing methodology. Knowledge and Information Systems (to appear).

    Google Scholar 

  • GRAS, R. (1979): Contribution à l’étude expérimentale et à l’analyse de certaines acquisitions cognitives et de certains objectifs didactiques en mathématiques. PhD thesis, Université de Rennes I, France.

    Google Scholar 

  • GRAS, R., ALMOULOUD, S.A., BAILLEUL, M., LARHER, A., POLO, M., RATSIMBA-RAJOHN, H., and TOTOHASINA, A. (1996): L’implication statistique — Nouvelle méthode exploratoire de données. La Pensée Sauvage editions, France.

    Google Scholar 

  • GRAS, R. and KUNTZ, P. (2005): Discovering r-rules with a directed hierarchy. Soft Computing, 1, 46–58.

    Google Scholar 

  • GRAS, R., KUNTZ, P., and BRIAND, H. (2001): The foundations of the implicative statistical analysis and some extensions for data mining (in french). Mathématiques et Sciences Humaines, 154, 9–29.

    Google Scholar 

  • HAVRDA, J.-H. and CHARVAT, F. (1967): Quantification methods of classification processes. Concepts of structural entropy — Kybernetica, 3, 30–37.

    Google Scholar 

  • HILDERMAN, R. and HAMILTON, H. (1999): Knowledge discovery and interestingness measures: a survey. Technical Report 99-04, University of Regina.

    Google Scholar 

  • KLEMENTTINEN, M., MANNILA, H., RONKAINEN, P., TOIVONEN, H., and VERKAMO, A. (1994): Finding interesting rules from large sets of discovered association rules. In: Proc. of the 3 rd Int. Conf. on Information and Knowledge Management. ACM, 401–407.

    Google Scholar 

  • KUNTZ, P., LEHN, R., GUILLET, F., and BRIAND, H. (2000): A user-driven process for mining association rules. In: Proc. of Principles of Data Mining and Knowledge Discovery. Springer Verlag, 483–489.

    Google Scholar 

  • LENT, B., SWANI, A., and WIDOM, J. (1997): Clustering association rules. In: Proc. of the 13 th Int. Conf. on Data Engineering. 220–231.

    Google Scholar 

  • LOEVINGER, J. (1947): A systemic approach to the construction and evaluation of tests of ability. Psychological Monographs, 61(4).

    Google Scholar 

  • SIMOVICI, D. and JAROSZEWICZ, S. (2003): Generalized conditional entropy and decision trees. Revue d’Intelligence Artificielle, 17(3), 369–380.

    Google Scholar 

  • VAILLANT, B. (2006): Mesurer la qualité des règles d’association — Études formelles et expérimentales. PhD thesis, Université de Bretagne Sud.

    Google Scholar 

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Gras, R., Kuntz, P. (2007). Reduction of Redundant Rules in Statistical Implicative Analysis. In: Brito, P., Cucumel, G., Bertrand, P., de Carvalho, F. (eds) Selected Contributions in Data Analysis and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73560-1_34

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