Skip to main content

Bounding Stability in Formal Concept Analysis

  • Conference paper
  • First Online:
Advanced Computational and Communication Paradigms

Abstract

In Formal Concept Analysis, stability is an important utility measure to rank concepts. However, computation of stability is considered to be a hard problem. Efficient algorithms having good bounds to estimate stability holds promise. In this paper, an effective graph-based technique is proposed to estimate stability. Our estimation algorithm has a polynomial time complexity of \(O({|A|^2})\) where |A| is the number of vertices.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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

References

  1. Belohlavek, R., Trnecka, M.: Basic Level in Formal Concept Analysis: Interesting Concepts and Psychological Ramifications. In IJCAI, pp. 1233–1239, June, 2013

    Google Scholar 

  2. Wille, R.: Formal concept analysis as mathematical theory of concepts and concept hierarchies. Formal Concept Anal. 3626, 1–33 (2005)

    MATH  Google Scholar 

  3. Carpineto, C., Romano, G.: Concept Data Analysis: Theory and Applications. Wiley (2004)

    Book  Google Scholar 

  4. Kuznetsov, S.O.: On computing the size of a lattice and related decision problems. Order 18(4), 313–321 (2001)

    Article  MathSciNet  Google Scholar 

  5. Kuzuetsov, S.O.: Stability as an Estimate of thie Degree of Substantiation of Hypotheses Derived on the Basis of Operational, Similarity (1990)

    Google Scholar 

  6. Kuznetsov, S.O.: On stability of a formal concept. Ann. Math. Artif. Intell. 49(1), 101–115 (2007)

    Article  MathSciNet  Google Scholar 

  7. Roth, C., Obiedkov, S., Kourie, D.G.: On succinct representation of knowledge community taxonomies with formal concept analysis. Int. J. Found. Comput. Sci. 19(02), 383–404 (2008)

    Article  MathSciNet  Google Scholar 

  8. Buzmakov, A., Kuznetsov, S.O., Napoli, A.: Is concept stability a measure for pattern selection? Procedia Comput. Sci. 31, 918–927 (2014)

    Article  Google Scholar 

  9. Babin, M., Kuznetsov, S.: Approximating concept stability. Form. Concept Anal. 7–15 (2012)

    Google Scholar 

  10. Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Ordered Sets, pp. 445–470. Springer, Netherlands (1982)

    Chapter  Google Scholar 

  11. Wolff, K.E.: A first course in formal concept analysis. StatSoft 93, 429–438 (1993)

    Google Scholar 

  12. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer Science & Business Media (2012)

    Google Scholar 

  13. Roth, C., Obiedkov, S., Kourie, D.: Towards concise representation for taxonomies of epistemic communities. Lect. Notes Comput. Sci. 4923, 240–255 (2008)

    Article  Google Scholar 

  14. Zhi, H.L.: On the calculation of formal concept stability. J. Appl. Math. (2014)

    Google Scholar 

  15. Moon, J.W., Moser, L.: On cliques in graphs. Israel J. Math. 3(1), 23–28 (1965)

    Article  MathSciNet  Google Scholar 

  16. Hopcroft, J., Tarjan, R.: Efficient algorithms for graph manipulation (No. STAN-CS-71-207). Department of Computer Science, Stanford University, California (1971)

    Google Scholar 

  17. Bollobs, B., Nikiforov, V.: Cliques and the spectral radius. J. Comb. Theory Ser. B 97(5), 859–865 (2007)

    Article  MathSciNet  Google Scholar 

  18. Nikiforov, V.: Some inequalities for the largest eigenvalue of a graph. Comb. Probab. Comput. 11(2), 179–189 (2002)

    Article  MathSciNet  Google Scholar 

  19. Kuznetsov, S.O., Obiedkov, S.A.: Comparing performance of algorithms for generating concept lattices. J. Exp. Theor. Artif. Intell. 14(2–3), 189–216 (2002)

    Article  Google Scholar 

  20. Wille, R.: Concept lattices and conceptual knowledge systems. Comput. Math. Appl. 23(6–9), 493–515 (1992)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bikram P. Bhuyan .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bhuyan, B.P., Karmakar, A., Hazarika, S.M. (2018). Bounding Stability in Formal Concept Analysis. In: Bhattacharyya, S., Chaki, N., Konar, D., Chakraborty, U., Singh, C. (eds) Advanced Computational and Communication Paradigms. Advances in Intelligent Systems and Computing, vol 706. Springer, Singapore. https://doi.org/10.1007/978-981-10-8237-5_53

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-8237-5_53

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-8236-8

  • Online ISBN: 978-981-10-8237-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics