Skip to main content

Tree Based Reduction of Concept Lattices Based on Conceptual Indexes

  • Conference paper
  • First Online:

Part of the book series: Advances in Intelligent Systems and Computing ((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.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
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

Learn about institutional subscriptions

References

  1. Wille, R.: Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts. Springer, Netherlands (1982)

    MATH  Google Scholar 

  2. Birkhoff, G.: Lattice Theory. American Mathematical Soc. (1940)

    Google Scholar 

  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. Keim, D.A.: Information visualization and visual data mining. IEEE Trans. Vis. Comput. Graph. 8(1), 1–8 (2002)

    Google Scholar 

  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. 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. Belohlavek, R.: Introduction to Formal Concept Analysis. Palacky University, Department of Computer Science, Olomouc (2008)

    Google Scholar 

  8. Borchmann, D.: A Generalized Next-Closure Algorithm–Enumerating Semilattice Elements from a Generating Set. arXiv (2011)

    Google Scholar 

  9. Butka, P., Pocs, J.: Generalization of one-sided concept lattices. Comput. Informat. 32(2), 355–370 (2013)

    MathSciNet  Google Scholar 

  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. Pocs, J., Pocsova, J.: Basic theorem as representation of heterogeneous concept lattices. Front. Comput. Sci. 9(4), 636–642 (2015)

    Article  Google Scholar 

  12. Pocs, J., Pocsova, J.: Bipolarized extension of heterogeneous concept lattices. Appl. Math. Sci. 8(125–128), 6359–6365 (2014)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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. Gajdos, P., Moravec, P., Snasel, V.: Concept lattice generation by singular value decomposition. In: Proceedings of CLA (2004)

    Google Scholar 

  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. Ganter, B. Stumme, G. Wille, R.: Formal Concept Analysis: Foundations and Applications. Springer (2005)

    Google Scholar 

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

    Google Scholar 

Download references

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Miroslav Smatana .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Smatana, M., Butka, P., Cöveková, L. (2017). Tree Based Reduction of Concept Lattices Based on Conceptual Indexes. In: Borzemski, L., Grzech, A., Świątek, J., Wilimowska, Z. (eds) Information Systems Architecture and Technology: Proceedings of 37th International Conference on Information Systems Architecture and Technology – ISAT 2016 – Part I. Advances in Intelligent Systems and Computing, vol 521. Springer, Cham. https://doi.org/10.1007/978-3-319-46583-8_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-46583-8_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46582-1

  • Online ISBN: 978-3-319-46583-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics