Many data mining algorithms make use of the well-known Inclusion-Exclusion principle. As a consequence, using this principle efficiently is crucial for the success of all these algorithms. Especially in the context of condensed representations, such as NDI, and in computing interesting measures, a quick inclusion-exclusion algorithm can be crucial for the performance. In this paper, we give an overview of several algorithms that depend on the inclusion-exclusion principle and propose an efficient algorithm to use it and evaluate its complexity. The theoretically obtained results are supported by experimental evaluation of the quick IE technique in isolation, and of an example application.


Contingency Table Association Rule Frequent Itemsets Data Mining Algorithm Transaction Database 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Agrawal, R., Srikant, R.: Fast algorithms for mining association rules. In: Bocca, J.B., Jarke, M., Zaniolo, C. (eds.) Proceedings 20th International Conference on Very Large Data Bases, pp. 487–499. Morgan Kaufmann, San Francisco (1994)Google Scholar
  2. 2.
    Borgelt, C., Kruse, R.: Induction of association rules: Apriori implementation. In: Härdle, W., Rönz, B. (eds.) Proceedings of the 15th Conference on Computational Statistics, pp. 395–400. Physica-Verlag (2002),
  3. 3.
    Boulicaut, J.-F., Bykowski, A., Rigotti, C.: Approximation of frequency queries by means of free-sets. In: Zighed, D.A., Komorowski, J., Żytkow, J.M. (eds.) PKDD 2000. LNCS (LNAI), vol. 1910, pp. 75–85. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. 4.
    Bykowski, A., Rigotti, C.: A condensed representation to find frequent patterns. In: Proc. PODS Int. Conf. Principles of Database Systems (2001)Google Scholar
  5. 5.
    Calders, T., Goethals, B.: Minimal k-free representations of frequent sets. In: Proc. PKDD Int. Conf. Principles of Data Mining and Knowledge Discovery, pp. 71–82 (2002)Google Scholar
  6. 6.
    Calders, T., Goethals, B.: Mining all non-derivable frequent itemsets. In: Elomaa, T., Mannila, H., Toivonen, H. (eds.) PKDD 2002. LNCS (LNAI), vol. 2431, pp. 74–85. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Jaroszewicz, S., Simovici, D.A.: Support approximations using bonferroni-type inequalities. In: Elomaa, T., Mannila, H., Toivonen, H. (eds.) PKDD 2002. LNCS (LNAI), vol. 2431, pp. 212–224. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Knuth, D.E.: Fundamental Algorithms. Addison-Wesley, Reading (1997)MATHGoogle Scholar
  9. 9.
    Kryszkiewicz, M., Gajek, M.: Why to apply generalized disjunction-free generators representation of frequent patterns? In: Proc. International Syposium on Methodologies for Intelligent Systems, pp. 382–392 (2002)Google Scholar
  10. 10.
    Mannila, H.: Local and global methods in data mining: Basic techniques and open problems. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, p. 57. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Mannila, H., Toivonen, H.: Multiple uses of frequent sets and condensed representations. In: Proc. KDD Int. Conf. Knowledge Discovery in Databases (1996)Google Scholar
  12. 12.
    Meo, R.: Theory of dependence values. ACM Trans. on Database Systems 25(3), 380–406 (2000)CrossRefGoogle Scholar
  13. 13.
    Moore, A., Lee, M.S.: Cached sufficient statistics for efficient machine learning with large datasets. Journal of Artificial Intelligence Research 8, 67–91 (1998)MathSciNetMATHGoogle Scholar
  14. 14.
    Pavlov, D., Mannila, H., Smyth, P.: Beyond independence: Probabilistic models for query approximation on binary transaction data. IEEE Trans. on Knowledge and Data Engineering 15(6), 1409–1421 (2003)CrossRefGoogle Scholar
  15. 15.
    Savinov, A.: Mining dependence rules by finding largest support quota. In: ACM Symposium on Applied Computing, pp. 525–529 (2004)Google Scholar
  16. 16.
    Silverstein, C., Brin, S., Motwani, R.: Beyond market baskets: Generalizing association rules to dependence rules. Data Mining and Knowledge Discovery 2(1), 39–68 (1998)CrossRefGoogle Scholar
  17. 17.
    Zheng, Z., Kohavi, R., Mason, L.: Real world performance of association rule algorithms. In: Proc. KDD Int. Conf. Knowledge Discovery in Databases, pp. 401–406. ACM Press, New York (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Toon Calders
    • 1
  • Bart Goethals
    • 1
  1. 1.University of AntwerpBelgium

Personalised recommendations