Mining a New Fault-Tolerant Pattern Type as an Alternative to Formal Concept Discovery

  • Jérémy Besson
  • Céline Robardet
  • Jean-François Boulicaut
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4068)


Formal concept analysis has been proved to be useful to support knowledge discovery from boolean matrices. In many applications, such 0/1 data have to be computed from experimental data and it is common to miss some one values. Therefore, we extend formal concepts towards fault-tolerance. We define the DR-bi-set pattern domain by allowing some zero values to be inside the pattern. Crucial properties of formal concepts are preserved (number of zero values bounded on objects and attributes, maximality and availability of functions which “connect” the set components). DR-bi-sets are defined by constraints which are actively used by our correct and complete algorithm. Experimentation on both synthetic and real data validates the added-value of the DR-bi-sets.


Formal Concept Concept Lattice Formal Context Formal Concept Analysis Strong Density 


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  1. 1.
    Besson, J., Robardet, C., Boulicaut, J.-F.: Mining formal concepts with a bounded number of exceptions from transactional data. In: Goethals, B., Siebes, A. (eds.) KDID 2004. LNCS, vol. 3377, pp. 33–45. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    Besson, J., Robardet, C., Boulicaut, J.-F., Rome, S.: Constraint-based bi-set mining for biologically relevant pattern discovery in microarray data. IDA journal 9(1), 59–82 (2005)Google Scholar
  3. 3.
    Blake, C., Merz, C.: UCI repository of machine learning databases (1998)Google Scholar
  4. 4.
    Bucila, C., Gehrke, J.E., Kifer, D., White, W.: Dualminer: A dual-pruning algorithm for itemsets with constraints. In: ACM SIGKDD, pp. 42–51 (2002)Google Scholar
  5. 5.
    François, P., Robert, C., Cremilleux, B., Bucharles, C., Demongeot, J.: Variables processing in expert system building: application to the aetiological diagnosis of infantile meningitis. Med. Inf. 15(2), 115–124 (1990)CrossRefGoogle Scholar
  6. 6.
    Ganter, B., Stumme, G., Wille, R. (eds.): Formal Concept Analysis, Foundations and Applications. LNCS (LNAI), vol. 3626. Springer, Heidelberg (2005)MATHGoogle Scholar
  7. 7.
    Gionis, A., Mannila, H., Seppänen, J.K.: Geometric and combinatorial tiles in 0-1 data. In: Boulicaut, J.-F., Esposito, F., Giannotti, F., Pedreschi, D. (eds.) PKDD 2004. LNCS (LNAI), vol. 3202, pp. 173–184. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Guenoche, A., Mechelen, I.V.: Galois approach to the induction of concepts. Categories and concepts: Theorical views and inductive data analysis, 287–308 (1993)Google Scholar
  9. 9.
    Hereth, J., Stumme, G., Wille, R., Wille, U.: Conceptual knowledge discovery and data analysis. In: ICCS 2000, pp. 421–437 (2000)Google Scholar
  10. 10.
    Kuznetsov, S.O., Obiedkov, S.A.: Comparing performance of algorithms for generating concept lattices. JETAI 14 (2-3), 189–216 (2002)MATHCrossRefGoogle Scholar
  11. 11.
    Nguifo, E.M., Duquenne, V., Liquiere, M.: Concept lattice-based knowledge discovery in databases. JETAI 14(2-3), 75–79 (2002)CrossRefGoogle Scholar
  12. 12.
    Pei, J., Tung, A.K.H., Han, J.: Fault-tolerant frequent pattern mining: Problems and challenges. In: DMKD, Workshop (2001)Google Scholar
  13. 13.
    Pensa, R.G., Boulicaut, J.-F.: Towards fault-tolerant formal concept analysis. In: Bandini, S., Manzoni, S. (eds.) AI*IA 2005. LNCS (LNAI), vol. 3673, pp. 212–223. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Seppänen, J.K., Mannila, H.: Dense itemsets. In: ACM SIGKDD 2004, pp. 683–688 (2004)Google Scholar
  15. 15.
    Stumme, G., Taouil, R., Bastide, Y., Pasqier, N., Lakhal, L.: Computing iceberg concept lattices with TITANIC. DKE 42, 189–222 (2002)MATHCrossRefGoogle Scholar
  16. 16.
    Ventos, V., Soldano, H., Lamadon, T.: Alpha galois lattices. In: ICDM IEEE, pp. 555–558 (2004)Google Scholar
  17. 17.
    Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered sets, pp. 445–470. Reidel (1982)Google Scholar
  18. 18.
    Yang, C., Fayyad, U., Bradley, P.S.: Efficient discovery of error-tolerant frequent itemsets in high dimensions. In: ACM SIGKDD, pp. 194–203. ACM Press, New York (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jérémy Besson
    • 1
    • 2
  • Céline Robardet
    • 3
  • Jean-François Boulicaut
    • 1
  1. 1.INSA Lyon, LIRIS CNRS UMR 5205VilleurbanneFrance
  2. 2.UMR INRA/INSERM 1235LyonFrance
  3. 3.INSA Lyon, PRISMaVilleurbanneFrance

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