Skip to main content
SpringerLink
Log in

A Partial-Closure Canonicity Test to Increase the Efficiency of CbO-Type Algorithms

  • Conference paper
Graph-Based Representation and Reasoning (ICCS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8577))

Included in the following conference series:

Abstract

Computing formal concepts is a fundamental part of Formal Concept Analysis and the design of increasingly efficient algorithms to carry out this task is a continuing strand of FCA research. Most approaches suffer from the repeated computation of the same formal concepts and, initially, algorithms concentrated on efficient searches through already computed results to detect these repeats, until the so-called canonicity test was introduced. The canonicity test meant that it was sufficient to examine the attributes of a computed concept to determine its newness: searching through previously computed concepts was no longer necessary. The employment of this test in Close-by-One type algorithms has proved to be highly effective. The typical CbO approach is to compute a concept and then test its canonicity. This paper describes a more efficient approach, whereby a concept need only be partially computed in order to carry out the test. Only if it passes the test does the computation of the concept need to be completed. This paper presents this ‘partial-closure’ canonicity test in the In-Close algorithm and compares it to a traditional CbO algorithm to demonstrate the increase in efficiency.

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. Andrews, S., Orphanides, C.: Analysis of large data sets using formal concept lattices. In: [31], pp. 104–115

    Google Scholar 

  2. Tanabata, T., Sawase, K., Nobuhara, H., Bede, B.: Interactive data mining for image databases based on fca. Journal of Advanced Computational Intelligence and Intelligent Informatics 14, 303–308 (2010)

    Google Scholar 

  3. Kaytoue, M., Duplessis, S., Kuznetsov, S.O., Napoli, A.: Two FCA-based methods for mining gene expression data. In: Ferré, S., Rudolph, S. (eds.) ICFCA 2009. LNCS (LNAI), vol. 5548, pp. 251–266. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  6. Kuznetsov, S.O.: Mathematical aspects of concept analysis. Mathematical Science 80, 1654–1698 (1996)

    Article  MATH  Google Scholar 

  7. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer (1998)

    Google Scholar 

  8. Lindig, C.: Fast concept analysis. In: Working with Conceptual Structures: Contributions to ICCS 2000, pp. 152–161. Shaker Verlag, Aachen (2000)

    Google Scholar 

  9. Godin, R., Missaoui, R., Alaoui, H.: Incremental concept formation algorithms based on Galois lattices. Computational Intelligence 11, 246–267 (1995)

    Article  Google Scholar 

  10. Kuznetsov, S.O.: Learning of simple conceptual graphs from positive and negative examples. In: Żytkow, J.M., Rauch, J. (eds.) PKDD 1999. LNCS (LNAI), vol. 1704, pp. 384–391. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  11. Kuznetsov, S., Obiedkov, S.: Comparing performance of algorithms for generating concept lattices. Journal of Experimental and Theoretical Artificial Intelligence 14, 189–216 (2002)

    Article  MATH  Google Scholar 

  12. Krajca, P., Outrata, J., Vychodil, V.: Parallel recursive algorithm for FCA. In: Belohavlek, R., Kuznetsov, S. (eds.) Proceedings of Concept Lattices and their Applications (2008)

    Google Scholar 

  13. Andrews, S.: In-close, a fast algorithm for computing formal concepts. In: Rudolph, S., Dau, F., Kuznetsov, S.O. (eds.) ICCS 2009. CEUR WS, vol. 483 (2009), http://sunsite.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-483/

  14. Andrews, S.: In-close2, a high performance formal concept miner. In: Andrews, S., Polovina, S., Hill, R., Akhgar, B. (eds.) ICCS 2011. LNCS (LNAI), vol. 6828, pp. 50–62. Springer, Heidelberg (2011)

    Google Scholar 

  15. Krajca, P., Vychodil, V., Outrata, J.: Advances in algorithms based on CbO. In: [31], pp. 325–337

    Google Scholar 

  16. Outrata, J., Vychodil, V.: Fast algorithm for computing fixpoints of Galois connections induced by object-attribute relational data. Inf. Sci. 185, 114–127 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  17. Strok, F., Neznanov, A.: Comparing and analyzing the computational complexity of fca algorithms. In: Proceedings of the 2010 Annual Research Conference of the South African Institute of Computer Scientists and Information Technologists, pp. 417–420 (2010)

    Google Scholar 

  18. Kirchberg, M., Leonardi, E., Tan, Y.S., Link, S., Ko, R.K.L., Lee, B.S.: Formal concept discovery in semantic web data. In: Domenach, F., Ignatov, D.I., Poelmans, J. (eds.) ICFCA 2012. LNCS (LNAI), vol. 7278, pp. 164–179. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  19. Borchman, D.: A generalized next-closure algorithm - enumerating semilattice elements from a generating set. In: Szathmary, L., Priss, U. (eds.) Proceedings of Concept Lattices and thie Applications (CLA 2012), pp. 9–20. Universidad de Malaga (2012)

    Google Scholar 

  20. Chein, M.: Algorithme de recherche des sous-matrices premires dune matrice. Bull. Math. Soc. Sci. Math. R.S. Roumanie 13, 21–25 (1969)

    MathSciNet  Google Scholar 

  21. Norris, E.M.: Maximal rectangular relations. In: Karpinski, M. (ed.) FCT 1977. LNCS, vol. 56, pp. 476–481. Springer, Heidelberg (1977)

    Chapter  Google Scholar 

  22. Ganter, B.: Two basic algorithms in concept analysis. FB4-Preprint 831. TH Darmstadt (1984)

    Google Scholar 

  23. Bordat, J.P.: Calcul pratique du treillis de Galois dune correspondance. Math. Sci. Hum. 96, 31–47 (1986)

    MATH  MathSciNet  Google Scholar 

  24. Nourine, L., Raynaud, O.: A fast algorithm for building lattices. Information Procesing Letters 71, 199–204 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  25. van der Merwe, D., Obiedkov, S., Kourie, D.: Addintent: A new incremental algorithm for constructing concept lattices. In: Eklund, P. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, pp. 372–385. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  26. Andrews, S.: Appendix to a partial-closure canonicity test to increase the efficiency of CbO-type algorithms (2013), https://dl.dropboxusercontent.com/u/3318140/partialclosureappendix.pdf

  27. Frank, A., Asuncion, A.: UCI machine learning repository (2010), http://archive.ics.uci.edu/ml

  28. Uno, T., Kiyomi, M., Arimura, H.: Lcm ver. 3: Collaboration of array, bitmap and prefix tree for frequent itemset mining. In: Proceedings of the 1st International Workshop on Open Source Data Mining: Frequent Pattern Mining Implementations, pp. 77–86. ACM (2005)

    Google Scholar 

  29. Andrews, S.: In-Close program (2013), http://sourceforge.net/projects/inclose/

  30. Krajca, P., Outrata, J., Vychodil, V.: FCbO program (2012), http://fcalgs.sourceforge.net/

  31. Kryszkiewicz, M., Obiedkov, S. (eds.): Proceeding of 7th International Conference on Concept Lattices and Their Applications, CLA 2010. University of Sevilla, Seville (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Conceptual Structures Research Group Communication and Computing Research Centre Faculty of Arts, Computing, Engineering and Sciences, Sheffield Hallam University, Sheffield, UK

    Simon Andrews

Authors
  1. Simon Andrews
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Simon Andrews .

Editor information

Editors and Affiliations

  1. Université Toulouse le Mirail, Toulouse, France

    Nathalie Hernandez

  2. L3S Research Center, Hannover, Germany

    Robert Jäschke

  3. LIRMM, Montpellier, France

    Madalina Croitoru

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Andrews, S. (2014). A Partial-Closure Canonicity Test to Increase the Efficiency of CbO-Type Algorithms. In: Hernandez, N., Jäschke, R., Croitoru, M. (eds) Graph-Based Representation and Reasoning. ICCS 2014. Lecture Notes in Computer Science(), vol 8577. Springer, Cham. https://doi.org/10.1007/978-3-319-08389-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08389-6_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08388-9

  • Online ISBN: 978-3-319-08389-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation