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Discovering R-rules with a directed hierarchy

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Abstract

In this paper, we extend the classical notion of quasi-implication (“when a i is present then usually a j is also present”) to R-rules (rules of rules), the premisses and the conclusions of which can be rules themselves. A new statistical measure, based on the implicative intensity defined by Gras for quasi-implications, is defined to assess the significance of R-rules on a data set. We show how to organize R-rules in a new combinatorial structure, the directed hierarchy, which is inspired by the classical hierarchical classification. An incremental algorithm is developed to find the most significant R-rule “amalgamation”. An illustration is presented on a real data set stemming from a recent survey of the French Public Education Mathematical Teacher Society on the level in mathematics of pupils in the final year of secondary education and the perception of this subject.

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References

  1. Agrawal R, Imielinsky T, Swami A (1993) Mining association rules between sets of items in large databases. In: Proceeding of the ACM SIGMOD'93, pp 207–216

  2. Bailleul M (2001) Implicative networks for highlighting representations (in french). Mathématiques et Sciences Humaines, 154:31–46

  3. Benzécri JP (1973) L'analyse des données (vol. 1): Taxonomie. Dunod, Paris

  4. Blanchard J, Kuntz P, Guillet G, Gras R (2003) Implication intensity: from the basic definition to the entropic version – chapter 28. In: Chapman et al. (ed) Statistical data mining and knowledge discovery. CRC Press, Boca Raton, pp 475–493

  5. Buntine W (1996) Graphical models for knowledge discovery. In: Fayyad UM, Piatetsky-Shapiro G, Smyth P (eds) Advances in knowledge discovery and data mining, pp 59–82

  6. Gordon AD(1999) Classification. Chapman and Hall CRC, Londen/Boca Raton

  7. Gras R (1996) L'implication statistique - Nouvelle méthode exploratoire de données. La Pensee Sauvage editions, France

  8. Gras R, Briand H, Peter P (1996) Structuration sets with implication intensity. In: Proceedings of the international conference on ordinal and symbolic data analysis Springer, Berlin Heidelberg New York, pp 147–156

  9. Gras R, Kuntz P, 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

  10. Greenacre JM (1984) Theory and applications of correspondence analysis. Academic, New York

  11. Hilderman RJ, Hamilton HJ (2000) Heuristics measures of interestingness. In: Proceedings of the 4th European conference of principles of data mining and knowledge discovery, L.N.A.I. 1910, pp 232–241

  12. Horschka P, Klösgen W (1991) A support system for interpreting statistical data. In: Piatetsky-Shapiro G, Frawley W-J (eds), Knowledge discovery in databases, pp 325–345. AAAI Press, Menlo Park

  13. Johnson SC (1967) Hierarchical clustering scheme. Psychometrika 32:241–254

    Google Scholar 

  14. Klementtinen M, Mannila H, Ronkainen P, Toivonen H, Verkamo AI (1994) Finding interesting rules from large sets of discovered association rules. In: Proceedings of the 3rd international conference on information and knowledge management. ACM, New York, pp 401–407

  15. Kuntz P, Lehn R, Guillet F, Briand H (2000) A user-driven process for mining association rules. In: Proceedings of principles of data mining and knowledge discovery, Springer, Berlin Heidelberg New York, pp 483–489

  16. Lent B, Swami AN, Widom J (1997) Clustering association rules. In: Proceedings of the 13th international conference on data engineering. IEEE Computer Society, pp 220–231

  17. Lerman IC (1981) Classification et analyse ordinale des données. Dunod, Paris

  18. Lerman IC (1993) Likelihood linkage analysis classification method. Biochimie 75:379–397

    Google Scholar 

  19. Silberschatz A, Tuzhilin A (1996) What makes patterns interesting in knowledge discovery systems. IEEE Trans on Knowl Data Eng 8(6):970–974

    Google Scholar 

  20. Skowron A, Stepaniuk J (2004) Information granules and rough-neuro computing. In: Pal SK, Polkowski L, Skowron A (eds) Rough-neural computing: Techniques for computing with words, Springer, Berlin Heidelberg New York, pp 43–84

  21. Toivonen H, Klementtinen M, Ronkainen P, Hätönen K, Mannila H (1995) Pruning and grouping of discovered association rules. In: Workshop notes of the ECML workshop on statistics, machine learning, and knowledge discovery in databases. MLnet, Heraklion, pp 47–52

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  1. Ecole Polytechnique de l'Université de Nantes, La Chantrerie, BP 50610, 44306, Nantes cedex 3, France

    R. Gras & P. Kuntz

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  1. R. Gras
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  2. P. Kuntz
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Correspondence to P. Kuntz.

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Gras, R., Kuntz, P. Discovering R-rules with a directed hierarchy. Soft Comput 10, 453–460 (2006). https://doi.org/10.1007/s00500-005-0506-8

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  • DOI: https://doi.org/10.1007/s00500-005-0506-8

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