Skip to main content
SpringerLink
Log in

Approximating Concept Stability

  • Conference paper
Formal Concept Analysis (ICFCA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7278))

Included in the following conference series:

Abstract

Concept stability was used in numerous applications for selecting concepts as biclusters of similar objects. However, scalability remains a challenge for computing stability. The best algorithms known so far have algorithmic complexity quadratic in the size of the lattice. In this paper the problem of approximate stability computation is analyzed. An approximate algorithm for computing stability is proposed. Its computational complexity and results of computer experiments in comparing stability index and its approximations are discussed.

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. Kuznetsov, S.O.: Stability as an estimate of the degree of substantiation of hypotheses derived on the basis of operational similarity. Autom. Document. Math. Ling. (Nauchn. Tekh. Inf., Ser. 2) (12), 21–29 (1990)

    Google Scholar 

  2. Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press (1995)

    Google Scholar 

  3. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Berlin (1999)

    Book  MATH  Google Scholar 

  4. Dyer, M., Goldberg, L.A., Greenhill, C., Jerrum, M.: On the Relative Complexity of Approximate Counting Problems. In: Jansen, K., Khuller, S. (eds.) APPROX 2000. LNCS, vol. 1913, pp. 108–119. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  5. Kuznetsov, S.O.: On Computing the Size of a Lattice and Related Decision Problems. Order 18(4), 313–321 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kuznetsov, S.O.: Stability of a Formal Concept. In: San-Juan, E. (ed.) Proc. 4th Journee d’Informatique Messine (JIM 2003), Metz (2003)

    Google Scholar 

  7. Roth, C., Obiedkov, S., Kourie, D.: Towards Concise Representation for Taxonomies of Epistemic Communities. In: Yahia, S.B., Nguifo, E.M., Belohlavek, R. (eds.) CLA 2006. LNCS (LNAI), vol. 4923, pp. 240–255. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  8. Kuznetsov, S.O.: On Stability of a Formal Concept. Annals of Mathematics and Artificial Intelligence 49, 101–115 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kuznetsov, S.O., Obiedkov, S., Roth, C.: Reducing the Representation Complexity of Lattice-Based Taxonomies. In: Priss, U., Polovina, S., Hill, R. (eds.) ICCS 2007. LNCS (LNAI), vol. 4604, pp. 241–254. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  10. Roth, C., Obiedkov, S., Kourie, D.: Towards Concise Representation for Taxonomies of Epistemic Communities. In: Yahia, S.B., Nguifo, E.M., Belohlavek, R. (eds.) CLA 2006. LNCS (LNAI), vol. 4923, pp. 240–255. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. Obiedkov, S.A., Roth, C., Kourie, D.G.: On Succinct Representation of Knowledge Community Taxonomies with Formal Concept Analysis. Int. J. Found. Comput. Sci. 19(2), 383–404 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Jay, N., Kohler, F., Napoli, A.: Analysis of Social Communities with Iceberg and Stability-Based Concept Lattices. In: Medina, R., Obiedkov, S. (eds.) ICFCA 2008. LNCS (LNAI), vol. 4933, pp. 258–272. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  13. Klimushkin, M., Obiedkov, S., Roth, C.: Approaches to the Selection of Relevant Concepts in the Case of Noisy Data. In: Kwuida, L., Sertkaya, B. (eds.) ICFCA 2010. LNCS, vol. 5986, pp. 255–266. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  14. Falk, I., Gardent, C., Lorenzo, A.: Using Formal Concept Analysis to Acquire Knowledge about Verbs. In: Proc. 7th of the International Conference on Concept Lattices and Their Applications (CLA 2010), pp. 151–162 (2010)

    Google Scholar 

  15. Falk, I., Gardent, C.: Bootstrapping a Classification of French Verbs Using Formal Concept Analysis. In: Interdisciplinary Workshop on Verbs, Pisa, Italy (2011)

    Google Scholar 

  16. Falk, I., Gardent, C.: Combining Formal Concept Analysis and Translation to Assign Frames and Thematic Role Sets to French Verbs. In: Proc. International Conference Concept Lattices and Their Applications (CLA 2011), Nancy, France (2011)

    Google Scholar 

  17. Egho, E., Jay, N., Raissi, C., Napoli, A.: A FCA-based Analysis of Sequential Care Trajectories. In: Proc. 8th of the International Conference on Concept Lattices and Their Applications (CLA 2011), Nancy, France, pp. 362–376 (2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Higher School of Economics, National Research University, Pokrovskii bd. 11, 109028, Moscow, Russia

    Mikhail A. Babin & Sergei O. Kuznetsov

Authors
  1. Mikhail A. Babin
    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

Editor information

Editors and Affiliations

  1. Computer Science Department, University of Nicosia, 46 Makedonitissas Ave., 1700, Nicosia, Cyprus

    Florent Domenach

  2. Higher School of Economics, National Research University, Pokrovsky Boulevard, 109028, Moscow, Russia

    Dmitry I. Ignatov

  3. Faculty of Business and Economics, Katholieke Universiteit Leuven, Naamsestraat 69, 3000, Leuven, Belgium

    Jonas Poelmans

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Babin, M.A., Kuznetsov, S.O. (2012). Approximating Concept Stability. In: Domenach, F., Ignatov, D.I., Poelmans, J. (eds) Formal Concept Analysis. ICFCA 2012. Lecture Notes in Computer Science(), vol 7278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29892-9_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29892-9_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29891-2

  • Online ISBN: 978-3-642-29892-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation