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Tree Based Reduction of Concept Lattices Based on Conceptual Indexes

  • Miroslav SmatanaEmail author
  • Peter Butka
  • Lenka Cöveková
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 521)

Abstract

There are many approaches and tools which deal with conceptual structures in datasets and their main goal is to support user in understanding of data and structure. One of methods is formal concept analysis (FCA) which is suitable for processing and analyzing input data of object-attributes models based on their relationship. One from FCA family is model of generalized one-sided concept lattice (GOSCL). It is suitable to work with different type of attributes. While generating one-sided concept lattices in FCA improved understanding and interpretation of analysis, one of the lasting problem is to provide the users a result of FCA in appropriate form, if there is large number of concept lattices and generated structure is complex. This is one of the main topics in the FCA and solution can be reached with the reduction methods. In this paper we propose some of the reduction techniques and their combinations.

Keywords

Formal concept analysis One-sided concept lattices Reductions Conceptual indexes 

Notes

Acknowledgments

The work presented in this paper was partially supported by the Slovak Cultural and Educational Grant Agency of Ministry of Education, Science, Research and Sport of the Slovak Republic (KEGA) under grant No. 025TUKE-4/2015 and also by the Slovak Grant Agency of Ministry of Education and Academy of Science of Slovak Republic (VEGA) under grant No. 1/0493/16.

References

  1. 1.
    Wille, R.: Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts. Springer, Netherlands (1982)zbMATHGoogle Scholar
  2. 2.
    Birkhoff, G.: Lattice Theory. American Mathematical Soc. (1940)Google Scholar
  3. 3.
    Thomas, J., Cook, K.: Illuminating the path: research and development agenda for visual analytics. In: National Visualization and Analytics Ctr. (2005)Google Scholar
  4. 4.
    Keim, D.A.: Information visualization and visual data mining. IEEE Trans. Vis. Comput. Graph. 8(1), 1–8 (2002) Google Scholar
  5. 5.
    Hamrouni, T., Yahia, S.B., Slimani, Y.: Avoiding the itemser clousure computation pitfall. In: Belohlavek, R., Snasel, V. (eds.) CLA (2005) Google Scholar
  6. 6.
    Hermann, M., Sertkaya, B.: On the complexity of computing generators of closed sets. In: ICFCA, LNAI 4933, pp. 158–168, Springer, Berlin (2008)Google Scholar
  7. 7.
    Belohlavek, R.: Introduction to Formal Concept Analysis. Palacky University, Department of Computer Science, Olomouc (2008)Google Scholar
  8. 8.
    Borchmann, D.: A Generalized Next-Closure Algorithm–Enumerating Semilattice Elements from a Generating Set. arXiv (2011)Google Scholar
  9. 9.
    Butka, P., Pocs, J.: Generalization of one-sided concept lattices. Comput. Informat. 32(2), 355–370 (2013)MathSciNetGoogle Scholar
  10. 10.
    Butka, P., Pocs, J., Pocsova, J.: On equivalence of conceptual scaling and generalized one-sided concept lattices. Inform. Sci. 259, 57–70 (2014)Google Scholar
  11. 11.
    Pocs, J., Pocsova, J.: Basic theorem as representation of heterogeneous concept lattices. Front. Comput. Sci. 9(4), 636–642 (2015)CrossRefGoogle Scholar
  12. 12.
    Pocs, J., Pocsova, J.: Bipolarized extension of heterogeneous concept lattices. Appl. Math. Sci. 8(125–128), 6359–6365 (2014)CrossRefGoogle Scholar
  13. 13.
    Butka, P., Pocs, J., Pocsová, J.: Reduction of concepts from generalized one-sided concept lattice based on subsets quality measure. Adv. Intell. Syst. Comput. 314, 101–111 (2015)CrossRefGoogle Scholar
  14. 14.
    Antoni, L., Krajci, S., Kridlo, O.: Randomized fuzzy formal contexts and relevance of one-sided concepts. In: LNAI (Subseries of LNCS) 9113, pp. 183–199 (2014)Google Scholar
  15. 15.
    Melo, C., Le-Grand, B., Aufaure, A.: Browsing large concept lattices through tree extraction and reduction methods. Int. J. Intell. Inf. Technol. (IJIIT) 9(4), 16–34 (2013)CrossRefGoogle Scholar
  16. 16.
    Pensa, R., Boulicaut, J.-F.: Towards fault-tolerant formal concept analysis. In: Proceedings of 9th Congress of the Italian Association for Artificial Intelligence, LNAI, pp. 212–223, Springer (2005)Google Scholar
  17. 17.
    Gajdos, P., Moravec, P., Snasel, V.: Concept lattice generation by singular value decomposition. In: Proceedings of CLA (2004)Google Scholar
  18. 18.
    Snasel, V., Polovincak, M., Abdulla, H.: Concept lattice reduction by singular value decomposition. In: Proceedings of the SYRCoDIS, Moscow, Russia (2007)Google Scholar
  19. 19.
    Ganter, B. Stumme, G. Wille, R.: Formal Concept Analysis: Foundations and Applications. Springer (2005)Google Scholar
  20. 20.
    Kuznetsov, S.O.: Stability as an estimate of the degree of substantiation of hypotheses derived on the basis of operational similarity. In: Automatic Documentation and Mathematical Linguistics (1990)Google Scholar
  21. 21.
    Ganter, B. Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer Science & Business Media (2012)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Miroslav Smatana
    • 1
    Email author
  • Peter Butka
    • 1
  • Lenka Cöveková
    • 1
  1. 1.Faculty of Electrical Engineering and Informatics, Department of Cybernetics and Artificial IntelligenceTechnical University of KošiceKošiceSlovakia

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