Advertisement

Merge-Based Computation of Minimal Generators

  • Céline Frambourg
  • Petko Valtchev
  • Robert Godin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3596)

Abstract

Minimal generators (mingens) of concept intents are valuable elements of the Formal Concept Analysis (FCA) landscape, which are widely used in the database field, for data mining but also for database design purposes. The volatility of many real-world datasets has motivated the study of the evolution in the concept set under various modifications of the initial context. We believe this should be extended to the evolution of mingens. In the present paper, we build up on previous work about the incremental maintenance of the mingen family of a context to investigate the case of lattice merge upon context subposition. We first recall the theory underlying the singleton increment and show how it generalizes to lattice merge. Then we present the design of an effective merge procedure for concepts and mingens together with some preliminary experimental results about its performance.

Keywords

Equivalence Class Association Rule Minimal Generator Association Rule Mining 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berge, C.: Hypergraphs: Combinatorics of Finite Sets. North Holland, Amsterdam (1989)zbMATHGoogle Scholar
  2. 2.
    Le Floc’h, A., Fisette, C., Missaoui, R., Valtchev, P., Godin, R.: Jen: un algorithme efficace de construction de générateurs pour l’identification des règles d’association. Numéro spécial de la revue des Nouvelles Technologies de l’Information 1(1), 135–146 (2003)Google Scholar
  3. 3.
    Ganter, B.: Two basic algorithms in concept analysis, preprint 831, Technische Hochschule, Darmstadt (1984)Google Scholar
  4. 4.
    Ganter, B., Wille, R.: Formal Concept Analysis. Mathematical Foundations. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  5. 5.
    Godin, R., Missaoui, R., Alaoui, H.: Incremental Concept Formation Algorithms Based on Galois (Concept) Lattices. Computational Intelligence 11(2), 246–267 (1995)CrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    Kengue, J.F.D., Valtchev, P., Djamegni, C.T.: A parallel algorithm for lattice construction. In: Ganter, B., Godin, R. (eds.) ICFCA 2005. LNCS (LNAI), vol. 3403, pp. 249–264. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Kryszkiewicz, M., Gajek, M.: Concise representation of frequent patterns based on generalized disjunction-free generators. In: Chen, M.-S., Yu, P.S., Liu, B. (eds.) PAKDD 2002. LNCS (LNAI), vol. 2336, pp. 159–171. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Maier, D.: The theory of Relational Databases. Computer Science Press (1983)Google Scholar
  10. 10.
    Mannila, H., Räihä, K.-J.: On the complexity of inferring functional dependencies. Discrete Applied Mathematics 40(2), 237–243 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Pasquier, N.: Data Mining: Algorithmes d’extraction et de réduction des règles d’association dans les bases de données. Ph. d. thesis, Université Blaise Pascal,Clermont- Ferrand II (2000)Google Scholar
  12. 12.
    Pfaltz, J., Taylor, C.: Scientific discovery through iterative transformations of concept lattices. In: Proceedings of the 1st International Workshop on Discrete Mathematics and Data Mining, Washington, DC, USA, April 2002, pp. 65–74 (2002)Google Scholar
  13. 13.
    Stumme, G., Taouil, R., Bastide, Y., Pasquier, N., Lakhal, L.: Computing Iceberg Concept Lattices with Titanic. Data and Knowledge Engineering 42(2), 189–222 (2002)zbMATHCrossRefGoogle Scholar
  14. 14.
    Valtchev, P., Duquenne, V.: Towards scalable divide-and-conquer methods for computing concepts and implications. In: SanJuan, E., Berry, A., Sigayret, A., Napoli, A. (eds.) Proceedings of the 4th Intl. Conference Journées de l’Informatique Messine (JIM 2003): Knowledge Discovery and Discrete Mathematics, Metz (FR), September 3-6, pp. 3–14. INRIA (2003)Google Scholar
  15. 15.
    Valtchev, P., Rouane Hacene, M., Missaoui, R.: A generic scheme for the design of efficient on-line algorithms for lattices. In: Ganter, B., de Moor, A., Lex, W. (eds.) ICCS 2003. LNCS, vol. 2746, pp. 282–295. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  16. 16.
    Valtchev, P., Missaoui, R.: Building concept (Galois) lattices from parts: generalizing the incremental methods. In: Delugach, H.S., Stumme, G. (eds.) ICCS 2001. LNCS (LNAI), vol. 2120, pp. 290–303. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  17. 17.
    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
  18. 18.
    Valtchev, P., Missaoui, R., Lebrun, P.: A partition-based approach towards building Galois (concept) lattices. Discrete Mathematics 256(3), 801–829 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Valtchev, P., Missaoui, R., Rouane-Hacene, M., Godin, R.: Incremental maintenance of association rule bases. In: Proceedings of the 2nd Workshop on Discrete Mathematics and Data Mining, San Francisco (CA), USA (May 2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Céline Frambourg
    • 1
  • Petko Valtchev
    • 2
  • Robert Godin
    • 1
  1. 1.Département d’informatiqueUQAMMontréalCanada
  2. 2.DIROUniversité de MontréalMontréalCanada

Personalised recommendations