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Mining frequent conjunctive queries using functional and inclusion dependencies

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Abstract

We address the issue of mining frequent conjunctive queries in a relational database, a problem known to be intractable even for conjunctive queries over a single table. In this article, we show that mining frequent projection-selection-join queries becomes tractable if joins are performed along keys and foreign keys, in a database satisfying functional and inclusion dependencies, under certain restrictions. We note that these restrictions cover most practical cases, including databases operating over star schemas, snow-flake schemas and constellation schemas. In our approach, we define an equivalence relation over queries using a pre-ordering with respect to which the support is shown to be anti-monotonic. We propose a level-wise algorithm for computing all frequent queries by exploiting the fact that equivalent queries have the same support. We report on experiments showing that, in our context, mining frequent projection-selection-join queries is indeed tractable, even for large data sets.

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References

  1. Agrawal R., Mannila H., Srikant R., Toivonen H., Verkamo A.: Fast discovery of association rules. In: Fayyad, U.M., Piatetsky-Shapiro, G., Smyth, P., Uthurusamy, R. (Eds.) Advances in Knowledge Discovery and Data Mining., pp. 309–328. AAAI-MIT Press, Manlo Park, CA (1996)

    Google Scholar 

  2. Armstrong, W.: Dependency structures of data base relationships. In: IFIP Congress, pp. 580–583. North Holland (1974)

  3. Bohannon, P., Fan, W., Geerts, F., Jia, X., Kementsietsidis, A.: Conditional functional dependencies for data cleaning. In: ICDE, pp. 746–755 (2007)

  4. Casanova M.A., Fagin R., Papadimitriou C.H.: Inclusion dependencies and their interaction with functional dependencies. J. Comput. Syst. Sci. 28(1), 29–59 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  5. De Marchi F., Lopes S., Petit J.-M.: Unary and n-ary inclusion dependency discovery in relational databases. J. Intell. Inf. Syst. 32(1), 53–73 (2009)

    Article  Google Scholar 

  6. Dehaspe, L., Raedt, L.D.: Mining association rules in multiple relations. In: 7th International Workshop on Inductive Logic Programming, vol. 1297 of LNCS, pp. 125–132. Springer (1997)

  7. Dieng, C.-T., Jen, T.-Y., Laurent, D.: An efficient computation of frequent queries in a star schema. In: DEXA 2010, vol. 6262(II) of LNCS, pp. 225–239. Springer (2010)

  8. Diop, C., Giacometti, A., Laurent, D., Spyratos, N. Composition of mining contexts for efficient extraction of association rules. In: EDBT’02, vol. 2287 of LNCS, pp. 106–123. Springer (2002)

  9. Fan W., Geerts F., Li J., Xiong M.: Discovering conditional functional dependencies. IEEE Trans. Knowl. Data Eng. 23(5), 683–698 (2011)

    Article  Google Scholar 

  10. Faye, A., Giacometti, A., Laurent, D., Spyratos, N.: Mining rules in databases with multiple tables: problems and perspectives. In: Proceedings of the 3rd International Conference on Computing Anticipatory Systems (CASYS) (1999)

  11. Goethals, B., den Bussche, J.V.: Relational association rules: getting warmer. In: ESF Exploratory Workshop on Pattern Detection and Discovery in Data Mining, vol. 2447 of LNCS, pp. 125–139. Springer (2002)

  12. Goethals, B., Hoekx, E., den Bussche, J.V.: Mining tree queries in a graph. In: Proceedings of 11th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pp. 61–69 (2005)

  13. Goethals, B., Laurent, D., Page, W.L.: Discovery and application of functional dependencies in conjunctive query mining. In: DAWAK 2010, vol. 6263 of LNCS, pp. 142–156. Springer (2010)

  14. Goethals, B., Page, W.L., Mapaey, M.: Mining interesting sets and rules in relational databases. In: ACM SAC, pp. 997–1001. ACM Press (2010)

  15. Goethals, B., Page, W.L., Mannila, H.: Mining association rules of simple conjunctive queries. In: SIAM-SDM, pp. 96–107 (2008)

  16. Han, J., Fu, Y., Wang, W., Koperski, K., Zaiane, O.: Dmql : a data mining query language for relational databases. In:SIGMOD-DMKD’96, pp. 27–34 (1996)

  17. Jen, T.-Y., Laurent, D., Spyratos, N.: Mining all frequent selection-projection queries from a relational table. In: EDBT’08, pp. 368–379. ACM Press (2008)

  18. Jen, T.-Y., Laurent, D., Spyratos, N.: Mining frequent conjunctive queries in star schemas. In: Proceedings of the International Database Engineering and Applications Symposium (IDEAS), pp. 97–108. ACM Press (2009)

  19. Jen T.-Y., Laurent D., Spyratos N.: Computing supports of conjunctive queries on relational tables with functional dependencies. Fundamenta Informaticae 99(3), 263–292 (2010)

    MathSciNet  MATH  Google Scholar 

  20. Jen, T.-Y., Laurent, D., Spyratos, N., Sy, O.: Towards mining frequent queries in star schemes. In: International Workshop on Knowledge Discovery in Databases (KDID), vol. 3933 of LNCS, pp. 104–123. Springer (2005)

  21. Jen, T.-Y., Taouil, R., Laurent, D.: A dichotomous algorithm for association rule mining. In: International workshop Grid and Peer-to-Peer Computing Impacts on Large Scale Heterogeneous Distributed Database Systems (GLOBE), in conjunction with International conference on DEXA, pp. 567–571. IEEE Press (2004)

  22. Kimball R.: The Data Warehouse Toolkit. Wiley, New York (1996)

    Google Scholar 

  23. Levene M., Loizou G.: Guaranteeing no interaction between functional dependencies and tree-like inclusion dependencies. Theor. Comput. Sci. 254, 683–690 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  24. Levene M., Loizou G.: Why is the snowflake schema a good data warehouse design?. Inf. Syst. 28(3), 225–240 (2003)

    Article  Google Scholar 

  25. Lopes S., Petit J.-M., Lakhal L.: Functional and approximative dependency mining: database and FCA points of view. J. Exp. Theor. Artif. Intell. 14(2–3), 93–114 (2002)

    Article  MATH  Google Scholar 

  26. Meo R., Psaila G., Ceri S.: An extension to sql for mining association rules. Data Min. Knowl. Discov. 9, 275–300 (1997)

    Google Scholar 

  27. Mitchell J.C.: The implication problem for functional dependencies and inclusion dependencies. Inf. Control 56, 154–173 (1983)

    Article  MATH  Google Scholar 

  28. Turmeaux, T., Salleb, A., Vrain, C., Cassard, D.: Learning characteristic rules relying on quantified paths. In: PKDD, vol. 2838 of LNCS, pp. 471–482. Springer (2003)

  29. Ullman J.: Principles of Databases and Knowledge-Base Systems, vol. 1. Computer Science Press, Rockville, MD (1988)

    Google Scholar 

  30. Yao H., Hamilton H.J.: Mining functional dependencies from data. Data Min. Knowl. Discov. 16(2), 197–219 (2008)

    Article  MathSciNet  Google Scholar 

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Author notes

  1. Cheikh Tidiane Dieng

    Present address: Laboratoire d’Analyse Numérique et Informatique, Université Gaston-Berger, Saint-Louis, Senegal

Authors and Affiliations

  1. ETIS, CNRS, ENSEA, Université de Cergy Pontoise, 95000, Cergy-Pontoise, France

    Cheikh Tidiane Dieng, Tao-Yuan Jen & Dominique Laurent

  2. LRI, CNRS, Université de Paris Sud, 91405, Orsay Cedex, France

    Nicolas Spyratos

Authors
  1. Cheikh Tidiane Dieng
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  2. Tao-Yuan Jen
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  3. Dominique Laurent
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  4. Nicolas Spyratos
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Corresponding author

Correspondence to Dominique Laurent.

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Dieng, C.T., Jen, TY., Laurent, D. et al. Mining frequent conjunctive queries using functional and inclusion dependencies. The VLDB Journal 22, 125–150 (2013). https://doi.org/10.1007/s00778-012-0277-7

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  • DOI: https://doi.org/10.1007/s00778-012-0277-7

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