From Triconcepts to Triclusters

  • Dmitry I. Ignatov
  • Sergei O. Kuznetsov
  • Ruslan A. Magizov
  • Leonid E. Zhukov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6743)


A novel approach to triclustering of a three-way binary data is proposed. Tricluster is defined in terms of Triadic Formal Concept Analysis as a dense triset of a binary relation Y, describing relationship between objects, attributes and conditions. This definition is a relaxation of a triconcept notion and makes it possible to find all triclusters and triconcepts contained in triclusters of large datasets. This approach generalizes the similar study of concept-based biclustering.


formal concept analysis data mining triclustering three-way data folksonomy 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Belohlavek, R., Vychodil, V.: Factor analysis of incidence data via novel decomposition of matrices. In: Ferré, S., Rudolph, S. (eds.) ICFCA 2009. LNCS, vol. 5548, pp. 83–97. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  2. 2.
    Belohlavek, R., Vychodil, V.: Factorizing three-way binary data with triadic formal concepts. In: Setchi, R., Jordanov, I., Howlett, R., Jain, L. (eds.) KES 2010. LNCS, vol. 6276, pp. 471–480. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Besson, J., Robardet, C., Boulicaut, J.F.: Mining a new fault-tolerant pattern type as an alternative to formal concept discovery. In: Schärfe, H., Hitzler, P., Øhrstrøm, P. (eds.) ICCS 2006. LNCS (LNAI), vol. 4068, pp. 144–157. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
  5. 5.
    Cerf, L., Besson, J., Robardet, C., Boulicaut, J.F.: Data peeler: Contraint-based closed pattern mining in n-ary relations. In: SDM, pp. 37–48. SIAM, Philadelphia (2008)Google Scholar
  6. 6.
    Cerf, L., Besson, J., Robardet, C., Boulicaut, J.F.: Closed patterns meet -ary relations. TKDD 3(1) (2009)Google Scholar
  7. 7.
    Clauset, A., Shalizi, C.R., Newman, M.E.J.: Power-law distributions in empirical data. SIAM Review 51(4), 661–703 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Ganter, B., Obiedkov, S.: Implications in triadic formal contexts. In: Wolff, K., Pfeiffer, H., Delugach, H. (eds.) ICCS 2004. LNCS (LNAI), vol. 3127, pp. 186–195. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Ganter, B., Wille, R.: Formal concept analysis: Mathematical foundations. Springer, Heidelberg (1999)CrossRefzbMATHGoogle Scholar
  10. 10.
    Hartigan, J.A.: Direct clustering of a data matrix. Journal of the American Statistical Association 67(337), 123–129 (1972)CrossRefGoogle Scholar
  11. 11.
    Ignatov, D.I., Kaminskaya, A.Y., Kuznetsov, S.O., Magizov, R.A.: A concept-based biclustering algorithm. In: Proceedings of the Eight International conference on Intelligent Information Processing (IIP-8), pp. 140–143. MAKS Press (2010) (in russian) Google Scholar
  12. 12.
    Jäschke, R., Hotho, A., Schmitz, C., Ganter, B., Stumme, G.: Trias - an algorithm for mining iceberg tri-lattices. In: ICDM, pp. 907–911. IEEE Computer Society, Los Alamitos (2006)Google Scholar
  13. 13.
    Ji, L., Tan, K.L., Tung, A.K.H.: Mining frequent closed cubes in 3d datasets. In: Dayal, U., Whang, K.Y., Lomet, D.B., Alonso, G., Lohman, G.M., Kersten, M.L., Cha, S.K., Kim, Y.K. (eds.) VLDB, pp. 811–822. ACM, New York (2006)Google Scholar
  14. 14.
    Lehmann, F., Wille, R.: A triadic approach to formal concept analysis. In: Ellis, G., Levinson, R., Rich, W., Sowa, J. (eds.) ICCS 1995. LNCS, vol. 954, pp. 32–43. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  15. 15.
    Mirkin, B.: Mathematical Classification and Clustering. Kluwer, Dordrecht (1996)CrossRefzbMATHGoogle Scholar
  16. 16.
    Newman, M.E.J.: Power laws, pareto distributions and zipf’s law. Contemporary Physics 46(5), 323–351 (2005)CrossRefGoogle Scholar
  17. 17.
    Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, Boston, pp. 445–470 (1982)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dmitry I. Ignatov
    • 1
  • Sergei O. Kuznetsov
    • 1
  • Ruslan A. Magizov
    • 1
  • Leonid E. Zhukov
    • 1
  1. 1.National Research University Higher School of EconomicsMoscowRussia

Personalised recommendations