Skip to main content
SpringerLink
Log in

From Triconcepts to Triclusters

  • Conference paper
Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6743))

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  4. http://bibsonomy.org

  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. Cerf, L., Besson, J., Robardet, C., Boulicaut, J.F.: Closed patterns meet -ary relations. TKDD 3(1) (2009)

    Google Scholar 

  7. Clauset, A., Shalizi, C.R., Newman, M.E.J.: Power-law distributions in empirical data. SIAM Review 51(4), 661–703 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  9. Ganter, B., Wille, R.: Formal concept analysis: Mathematical foundations. Springer, Heidelberg (1999)

    Book  MATH  Google Scholar 

  10. Hartigan, J.A.: Direct clustering of a data matrix. Journal of the American Statistical Association 67(337), 123–129 (1972)

    Article  Google Scholar 

  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. 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. 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. 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)

    Chapter  Google Scholar 

  15. Mirkin, B.: Mathematical Classification and Clustering. Kluwer, Dordrecht (1996)

    Book  MATH  Google Scholar 

  16. Newman, M.E.J.: Power laws, pareto distributions and zipf’s law. Contemporary Physics 46(5), 323–351 (2005)

    Article  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    Dmitry I. Ignatov, Sergei O. Kuznetsov, Ruslan A. Magizov & Leonid E. Zhukov

Authors
  1. Dmitry I. Ignatov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sergei O. Kuznetsov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ruslan A. Magizov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Leonid E. Zhukov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. State University Higher School of Economics, Pokrovskiy Bd. 11, 109028, Moscow, Russia

    Sergei O. Kuznetsov

  2. Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland

    Dominik Ślęzak

  3. Department of Computer Science, University of Regina, 3737 Wascana Parkway, S4S 0A2, Regina, SK, Canada

    Daryl H. Hepting

  4. Birbeck University of London, Malet Street, WC1E 7HX, London, UK

    Boris G. Mirkin

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ignatov, D.I., Kuznetsov, S.O., Magizov, R.A., Zhukov, L.E. (2011). From Triconcepts to Triclusters. In: Kuznetsov, S.O., Ślęzak, D., Hepting, D.H., Mirkin, B.G. (eds) Rough Sets, Fuzzy Sets, Data Mining and Granular Computing. RSFDGrC 2011. Lecture Notes in Computer Science(), vol 6743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21881-1_41

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21881-1_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21880-4

  • Online ISBN: 978-3-642-21881-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation