Formal Concept Analysis with Constraints by Closure Operators

  • Radim Bělohlávek
  • Vilém Vychodil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4068)


The paper presents a general method of imposing constraints in formal concept analysis of tabular data describing objects and their attributes. The constraints represent a user-defined requirements which are supplied along with the input data table. The main effect is to filter-out outputs of the analysis (conceptual clusters and if-then rules) which are not compatible with the constraint, in a computationally efficient way (polynomial time delay algorithm without the need to compute all outputs). Our approach covers several examples studied before, e.g. extraction of closed frequent itemsets in generation of non-redundant association rules. We present motivations, foundations, and examples.


Association Rule Formal Concept Closure Operator Complete Lattice Concept Lattice 
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.
    Bělohlávek, R., Sklenář, V., Zacpal, J.: Formal concept analysis with hierarchically ordered attributes. Int. J. General Systems 33(4), 283–294 (2004)Google Scholar
  2. 2.
    Bělohlávek, R., Sklenář, V.: Formal concept analysis constrained by attribute-dependency formulas. In: Ganter, B., Godin, R. (eds.) ICFCA 2005. LNCS (LNAI), vol. 3403, pp. 176–191. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Boulicaut, J.-F., Jeudy, B.: Constraint-based data mining. In: Maimon, O., Rokach, L. (eds.) The Data Mining and Knowledge Discovery Handbook, pp. 399–416. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Carpineto, C., Romano, G.: Concept Data Analysis. Theory and Applications. J.Wiley, Chichester (2004)zbMATHCrossRefGoogle Scholar
  5. 5.
    Dekel, U., Gill, Y.: Visualizing class interfaces with formal concept analysis. In: OOPSLA 2003, Anaheim, CA, pp. 288–289 (October 2003)Google Scholar
  6. 6.
    Ganter, B., Wille, R.: Formal Concept Analysis. Mathematical Foundations. Springer, Berlin (1999)zbMATHGoogle Scholar
  7. 7.
    Guigues, J.-L., Duquenne, V.: Familles minimales d’implications informatives resultant d’un tableau de données binaires. Math. Sci. Humaines 95, 5–18 (1986)MathSciNetGoogle Scholar
  8. 8.
    Maier, D.: The Theory of Relational Databases. Computer Science Press, Rockville (1983)zbMATHGoogle Scholar
  9. 9.
    Norris, E.M.: An algorithm for computing the maximal rectangles of a binary relation. Journal of ACM 21, 266–356 (1974)Google Scholar
  10. 10.
    Pasquier, N., Bastide, Y., Taouil, R., Lakhal, L.: Efficient Mining of Association Rules Using Closed Itemset Lattices. Information Systems 24(1), 25–46 (1999)CrossRefGoogle Scholar
  11. 11.
    Snelting, G., Tip, F.: Understanding class hierarchies using concept analysis. ACM Trans. Program. Lang. Syst. 22(3), 540–582 (2000)CrossRefGoogle Scholar
  12. 12.
    Zaki, M.J.: Mining non-redundant association rules. Data Mining and Knowledge Discovery 9, 223–248 (2004)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Zhang, C., Zhang, S.: Association Rule Mining. Models and Algorithms. Springer, Berlin (2002)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Radim Bělohlávek
    • 1
  • Vilém Vychodil
    • 1
  1. 1.Department of Computer SciencePalacky University, OlomoucOlomoucCzech Republic

Personalised recommendations