Characterization of Database Dependencies with FCA and Pattern Structures

  • Jaume BaixeriesEmail author
  • Mehdi Kaytoue
  • Amedeo Napoli
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 436)


In this review paper, we present some recent results on the characterization of Functional Dependencies and variations with the formalism of Pattern Structures and Formal Concept Analysis.

Although these dependencies have been paramount in database theory, they have been used in different fields: artificial intelligence and knowledge discovery, among others.


Attribute implications Data dependencies Pattern structures Formal concept analysis Data analysis 



This research work has been supported by the Spanish Ministry of Education and Science (project TIN2008-06582-C03-01), EU PASCAL2 Network of Excellence, and by the Generalitat de Catalunya (2009-SGR-980 and 2009-SGR-1428) and AGAUR (grant 2010PIV00057).


  1. 1.
    Baixeries, J.: Lattice Characterization of Armstrong and Symmetric Dependencies (Ph.D. Thesis). Universitat Politècnica de Catalunya, (2007)Google Scholar
  2. 2.
    Baixeries, J., Balcázar, J.L.: Discrete deterministic data mining as knowledge compilation. In: Proceedings of Workshop on Discrete Mathematics and Data Mining - SIAM (2003)Google Scholar
  3. 3.
    Baixeries, J., Balcázar, J.L.: A lattice representation of relations, multivalued dependencies and armstrong relations. In: ICCS, pp. 13–26 (2005)Google Scholar
  4. 4.
    Baixeries, J., Kaytoue, M., Napoli, A.: Computing functional dependencies with pattern structures. In: Szathmary, L., Priss, U., (eds.) CLA. CEUR Workshop Proceedings, vol. 972, pp. 175–186. (2012)Google Scholar
  5. 5.
    Baixeries, J., Kaytoue, M., Napoli, A.: Computing similarity dependencies with pattern structures. In: CLA, pp. 33–44 (2013)Google Scholar
  6. 6.
    Baixeries, J., Kaytoue, M., Napoli, A.: Characterizing functional dependencies in formal concept analysis with pattern structures. Ann. Math. Artif. Intell. 72, 1–21 (2014)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Baudinet, M., Chomicki, J., Wolper, P.: Constraint-generating dependencies. J. Comput. Syst. Sci. 59(1), 94–115 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Bělohlávek, R., Vychodil, V.: Data tables with similarity relations: functional dependencies, complete rules and non-redundant bases. In: Li Lee, M., Tan, K.-L., Wuwongse, V. (eds.) DASFAA 2006. LNCS, vol. 3882, pp. 644–658. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Bertossi, L., Kolahi, S., Lakshmanan, L.V.S.: Data cleaning and query answering with matching dependencies and matching functions. In: Proceedings of the 14th International Conference on Database Theory, ICDT ’11, pp. 268–279. ACM, New York (2011)Google Scholar
  10. 10.
    Fan, W., Gao, H., Jia, X., Li, J., Ma, S.: Dynamic constraints for record matching. The VLDB J. 20(4), 495–520 (2011)CrossRefGoogle Scholar
  11. 11.
    Ganter, B., Kuznetsov, S.O.: Pattern structures and their projections. In: Delugach, H.S., Stumme, G. (eds.) ICCS 2001. LNCS (LNAI), vol. 2120, pp. 129–142. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Ganter, B., Wille, R.: Formal Concept Analysis. Springer, Berlin (1999)CrossRefzbMATHGoogle Scholar
  13. 13.
    Graetzer, G., Davey, B., Freese, R., Ganter, B., Greferath, M., Jipsen, P., Priestley, H., Rose, H., Schmidt, E., Schmidt, S., Wehrung, F., Wille, R.: General Lattice Theory. Freeman, San Francisco (1971)Google Scholar
  14. 14.
    Guigues, J.-L., Duquenne, V.: Familles minimales d’implications informatives résultant d’un tableau de données binaires. Mathématiques et Sciences Humaines 95, 5–18 (1986)MathSciNetGoogle Scholar
  15. 15.
    Huhtala, Y., Kärkkäinen, J., Porkka, P., Toivonen, H.: Tane: an efficient algorithm for discovering functional and approximate dependencies. Comput. J. 42(2), 100–111 (1999)CrossRefzbMATHGoogle Scholar
  16. 16.
    Kaytoue, M., Kuznetsov, S.O., Napoli, A.: Revisiting numerical pattern mining with formal concept analysis. In: IJCAI, pp. 1342–1347 (2011)Google Scholar
  17. 17.
    Kaytoue, M., Kuznetsov, S.O., Napoli, A., Duplessis, S.: Mining gene expression data with pattern structures in formal concept analysis. Inf. Sci. 181(10), 1989–2001 (2011)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Kuznetsov, S.: Mathematical aspects of concept analysis. J. Math. Sci. 80(2), 1654–1698 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Kuznetsov, S.O.: Fitting pattern structures to knowledge discovery in big data. In: Cellier, P., Distel, F., Ganter, B. (eds.) ICFCA 2013. LNCS, vol. 7880, pp. 254–266. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  20. 20.
    Kuznetsov, S.O., Poelmans, J.: Knowledge representation and processing with formal concept analysis. Wiley Interdisc. Rew: Data Min. Knowl. Discov. 3(3), 200–215 (2013)Google Scholar
  21. 21.
    Lopes, S., Petit, J.-M., Lakhal, L.: Functional and approximate dependency mining: database and fca points of view. J. Exp. Theor. Artif. Intell. 14(2–3), 93–114 (2002)CrossRefzbMATHGoogle Scholar
  22. 22.
    Medina, R., Nourine, L.: A unified hierarchy for functional dependencies, conditional functional dependencies and association rules. In: Ferré, S., Rudolph, S. (eds.) ICFCA 2009. LNCS, vol. 5548, pp. 98–113. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  23. 23.
    Nedjar, S., Pesci, F., Lakhal, L., Cicchetti, R.: The agree concept lattice for multidimensional database analysis. In: Jäschke, R. (ed.) ICFCA 2011. LNCS, vol. 6628, pp. 219–234. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  24. 24.
    Poelmans, J., Ignatov, D.I., Kuznetsov, S.O., Dedene, G.: Formal concept analysis in knowledge processing: a survey on applications. Expert Syst. Appl. 40(16), 6538–6560 (2013)CrossRefGoogle Scholar
  25. 25.
    Poelmans, J., Kuznetsov, S.O., Ignatov, D.I., Dedene, G.: Formal concept analysis in knowledge processing: aD survey on models and techniques. Expert Syst. Appl. 40(16), 6601–6623 (2013)CrossRefGoogle Scholar
  26. 26.
    Simovici, D., Jaroszewicz, S.: An axiomatization of partition entropy. IEEE Trans. Inf. Theory 48(7), 2138–2142 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  27. 27.
    Simovici, D.A., Cristofor, D., Cristofor, L.: Impurity measures in databases. Acta Inf. 38(5), 307–324 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    Song, S., Chen, L.: Differential dependencies: reasoning and discovery. ACM Trans. Database Syst. 36(3), 16:1–16:41 (2011)CrossRefGoogle Scholar
  29. 29.
    Song, S., Chen, L.: Efficient discovery of similarity constraints for matching dependencies. Data Knowl. Eng. 87, 146–166 (2013)CrossRefMathSciNetGoogle Scholar
  30. 30.
    Song, S., Chen, L., Yu, P.S.: Comparable dependencies over heterogeneous data. The VLDB J. 22(2), 253–274 (2013)CrossRefGoogle Scholar
  31. 31.
    Ullman, J.: Principles of Database Systems and Knowledge-Based Systems, vol. 1–2. Computer Science Press, Rockville (MD) (1989)Google Scholar
  32. 32.
    Valtchev, P., Missaoui, R., Godin, R.: Formal concept analysis for knowledge discovery and data mining: the new challenges. In: Eklund, P. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, pp. 352–371. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  33. 33.
    Wille, R.: Why can concept lattices support knowledge discovery in databases? J. Exp. Theor. Artif. Intell. 14(2–3), 81–92 (2002)CrossRefzbMATHGoogle Scholar
  34. 34.
    Wyss, C.M., Giannella, C.M., Robertson, E.L.: FastFDs: a heuristic-driven, depth-first algorithm for mining functional dependencies from relation instances - extended abstract. In: Kambayashi, Y., Winiwarter, W., Arikawa, M. (eds.) DaWaK 2001. LNCS, vol. 2114, pp. 101–110. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  35. 35.
    Yao, H., Hamilton, H.J.: Mining functional dependencies from data. Data Min. Knowl. Discov. 16(2), 197–219 (2008)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Universitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Université de Lyon, CNRS, INSA-Lyon, LIRIS, UMR5205LyonFrance
  3. 3.LORIA (CNRS - Inria Nancy Grand Est - Université de Lorraine)Vandœuvre-lès-NancyFrance

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