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Axiomatization of Frequent Sets

  • Toon Calders
  • Jan Paredaens
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1973)

Abstract

In data mining association rules are very popular. Most of the algorithms in the literature for finding association rules start by searching for frequent itemsets. The itemset mining algorithms typically interleave brute force counting of frequencies with a meta-phase for pruning parts of the search space. The knowledge acquired in the counting phases can be represented by frequent set expressions. A frequent set expression is a pair containing an itemset and a frequency indicating that the frequency of that itemset is greater than or equal to the given fre-quency. A system of frequent sets is a collection of such expressions. We give an axiomatization for these systems. This axiomatization characterizes complete systems. A system is complete when it explicitly contains all information that it logically implies. Every system of frequent sets has a unique completion. The completion of a system actually represents the knowledge that maximally can be derived in the meta-phase.

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References

  1. 1.
    R. Agrawal, T. Imilienski, and A. Swami. Mining association rules between sets of items in large databases. In Proc. ACM SIGMOD, 1993Google Scholar
  2. 2.
    R. Agrawal, R. Srikant. Fast Algorithms for Mining Association Rules. In Proc. VLDB, 1994Google Scholar
  3. 3.
    T. Calders, and J. Paredaens. A Theoretical Framework for Reasoning about Frequent Itemsets. Technical Report 006, Universiteit Antwerpen, Belgium, http://win-www.uia.ac.be/u/calders/download/axiom.ps, June 2000.Google Scholar
  4. 4.
    R. Fagin, J. Halpern, and N. Megiddo. A Logic for Reasoning about Probabilities. In Information and Computation 87(1,2): 78–128, 1990.CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    R. Fagin, M. Y. Vardi. Armstrong Databases for Functional and Inclusion Dependencies. In IPL 16(1): 13–19, 1983.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    A. M. Frisch, P. Haddawy. Anytime Deduction for Probabilistic Logic. In Artificial Intelligence 69(1-2): 93–122, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    G. Georgakopoulos, D. Kavvadias, and C. H. Papadimitriou. Probabilistic Satisfiability. In Journal of Complexity 4:1–11, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    J. Han, J. Pei, and Y. Yin. Mining frequent patterns without candidate generation. In Proc. ACM SIGMOD, 2000Google Scholar
  9. 9.
    P. Hansen, B. Jaumard, G.-B. D. Nguetsé, M. P. de Aragäo. Models and Algorithms for Probabilistic and Bayesian Logic. In Proc. IJCAI, 1995Google Scholar
  10. 10.
    P. Hansen, B. Jaumard. Probabilistic Satisfiability. Les Cahiers du GERAD G-96-31, 1996Google Scholar
  11. 11.
    L. V.S. Laksmanan, R.T. Ng, J. Han, and A. Pang. Optimization of Constrained Frequent Set Queries with 2-variable Constraints. Proc. ACM SIGMOD, 1999Google Scholar
  12. 12.
    N. Nilsson. Probabilistic Logic. In Artificial Intelligence 28: 71–87, 1986zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Toon Calders
    • 1
  • Jan Paredaens
    • 1
  1. 1.Departement Wiskunde-InformaticaUniversiteit AntwerpenWilrijkBelgium

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