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Alternative Normalization Schemas for Bayesian Confirmation Measures

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6178))

Abstract

Analysis of rule interestingness measures with respect to their properties is an important research area helping to identify groups of measures that are truly meaningful. In this article, we analyze property Ex 1, of preservation of extremes, in a group of confirmation measures. We consider normalization as a mean to transform them so that they would obtain property Ex 1 and we introduce three alternative approaches to the problem: an approach inspired by Nicod, Bayesian, and likelihoodist approach. We analyze the results of the normalizations of seven measures with respect to property Ex 1 and show which approaches lead to the desirable results. Moreover, we extend the group of ordinally non-equivalent measures possessing valuable property Ex 1.

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References

  1. Bramer, M.: Principles of Data Mining. Springer, New York (2007)

    MATH  Google Scholar 

  2. Carnap, R.: Logical Foundations of Probability, 2nd edn. University of Chicago Press, Chicago (1962)

    Google Scholar 

  3. Christensen, D.: Measuring confirmation. Journal of Philosophy 96, 437–461 (1999)

    Article  MathSciNet  Google Scholar 

  4. Crupi, V., Tentori, K., Gonzalez, M.: On Bayesian measures of evidential support: Theoretical and empirical issues. Philosophy of Science (2007)

    Google Scholar 

  5. Eells, E., Fitelson, B.: Symmetries and asymmetries in evidential support. Philosophical Studies 107(2), 129–142 (2002)

    Article  Google Scholar 

  6. Fayyad, U., Piatetsky-Shapiro, G., Smyth, P.: From data mining to knowledge discovery: an overview. In: Fayyad, U., Piatetsky-Shapiro, G., Smyth, P., Uthursamy, R. (eds.) Advances in Knowledge Discov. and Data Mining, pp. 1–34. AAAI Press, Menlo Park (1996)

    Google Scholar 

  7. Finch, H.A.: Confirming Power of Observations Metricized for Decisions among Hypotheses. Philosophy of Science 27, 293–307, 391–404 (1999)

    Article  MathSciNet  Google Scholar 

  8. Fitelson, B.: Studies in Bayesian Confirmation Theory. Ph.D. Thesis, University of Wisconsin, Madison (2001)

    Google Scholar 

  9. Geng, L., Hamilton, H.J.: Interestingness Measures for Data Mining: A Survey. ACM Computing Surveys, article 9 38(3) (2006)

    Google Scholar 

  10. Greco, S., Pawlak, Z., Słowiński, R.: Can Bayesian confirmation measures be useful for rough set decision rules? Eng. Application of Artif. Intelligence 17, 345–361 (2004)

    Article  Google Scholar 

  11. Greco, S., Sowiski, R., Szczch, I.: Assessing the quality of rules with a new monotonic interestingness measure Z. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS (LNAI), vol. 5097, pp. 556–565. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  12. Hempel, C.G.: Studies in the logic of confirmation (I). Mind 54, 1–26 (1945)

    Article  MathSciNet  Google Scholar 

  13. McGarry, K.: A survey of interestingness measures for knowledge discovery. The Knowledge Engineering Review 20(1), 39–61 (2005)

    Article  Google Scholar 

  14. Mortimer, H.: The Logic of Induction. Paramus/Prentice Hall (1988)

    Google Scholar 

  15. Nicod, J.: Le probleme de la logique de l’induction. Alcan, Paris (1923)

    Google Scholar 

  16. Nozick, R.: Philosophical Explanations. Clarendon Press, Oxford (1981)

    Google Scholar 

  17. Rips, L.J.: Two Kinds of Reasoning. Psychological Science 12, 129–134 (2001)

    Article  Google Scholar 

  18. Szczȩch, I.: Multicriteria Attractiveness Evaluation of Decision and Association Rules. In: Peters, J.F., Skowron, A., Wolski, M., Chakraborty, M.K., Wu, W.-Z. (eds.) Transactions on Rough Sets X. LNCS, vol. 5656, pp. 197–274. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  19. Tan, P.-N., Kumar, V., Srivastava, J.: Selecting the right interestingness measure for association patterns. In: Proc. of the 8th international Conf. on Knowledge Discovery and Data Mining (KDD 2002), Edmonton, Canada, pp. 32–41 (2002)

    Google Scholar 

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Greco, S., Słowiński, R., Szczȩch, I. (2010). Alternative Normalization Schemas for Bayesian Confirmation Measures. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Computational Intelligence for Knowledge-Based Systems Design. IPMU 2010. Lecture Notes in Computer Science(), vol 6178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14049-5_24

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  • DOI: https://doi.org/10.1007/978-3-642-14049-5_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14048-8

  • Online ISBN: 978-3-642-14049-5

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