Skip to main content
SpringerLink
Log in

Some Programming Optimizations for Computing Formal Concepts

  • Conference paper
  • First Online:
Ontologies and Concepts in Mind and Machine (ICCS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12277))

Included in the following conference series:

  • 406 Accesses

Abstract

This paper describes in detail some optimization approaches taken to improve the efficiency of computing formal concepts. In particular, it describes the use and manipulation of bit-arrays to represent FCA structures and carry out the typical operations undertaken in computing formal concepts, thus providing data structures that are both memory-efficient and time saving. The paper also examines the issues and compromises involved in computing and storing formal concepts, describing a number of data structures that illustrate the classical trade-off between memory footprint and code efficiency. Given that there has been limited publication of these programmatical aspects, these optimizations will be useful to programmers in this area and also to any programmers interested in optimizing software that implements Boolean data structures. The optimizations are shown to significantly increase performance by comparing an unoptimized implementation with the optimized one.

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 EPUB and 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

Notes

  1. 1.

    In-Close on SourceForge: https://sourceforge.net/projects/inclose/.

References

  1. AMD: AMD64 Architecture Programmers Manual Volume 6: 128-Bit and 256-Bit XOP, FMA4 and CVT16 Instructions, May 2009

    Google Scholar 

  2. Andrews, S.: In-Close, a fast algorithm for computing formal concepts. In: Rudolph, S., Dau, F., Kuznetsov, S.O. (eds.) ICCS 2009, vol. 483. CEUR WS (2009)

    Google Scholar 

  3. 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). https://doi.org/10.1007/978-3-642-22688-5_4

    Chapter  Google Scholar 

  4. Andrews, S.: A partial-closure canonicity test to increase the efficiency of CbO-type algorithms. In: Hernandez, N., Jäschke, R., Croitoru, M. (eds.) ICCS 2014. LNCS (LNAI), vol. 8577, pp. 37–50. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08389-6_5

    Chapter  Google Scholar 

  5. Andrews, S.: A best-of-breed approach for designing a fast algorithm for computing fixpoints of Galois connections. Inf. Sci. 295, 633–649 (2015)

    Article  MathSciNet  Google Scholar 

  6. Andrews, S.: Making use of empty intersections to improve the performance of CbO-type algorithms. In: Bertet, K., Borchmann, D., Cellier, P., Ferré, S. (eds.) ICFCA 2017. LNCS (LNAI), vol. 10308, pp. 56–71. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59271-8_4

    Chapter  Google Scholar 

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

    Book  Google Scholar 

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

  9. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1998). https://doi.org/10.1007/978-3-642-59830-2

    Book  MATH  Google Scholar 

  10. Intel: Intel Developer Zone, ISA Extensions. https://software.intel.com/en-us/isa-extensions. Accessed June 2016

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

    Google Scholar 

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

  13. Krajca, P., Vychodil, V., Outrata, J.: Advances in algorithms based on CbO. In: Kryszkiewicz, M., Obiedkov, S. (eds.) CLA 2010, pp. 325–337. University of Sevilla (2010)

    Google Scholar 

  14. Kuznetsov, S.O.: A fast algorithm for computing all intersections of objects in a finite semi-lattice. Nauchno-Tekhnicheskaya Informatsiya, ser. 2 27(5), 11–21 (1993)

    Google Scholar 

  15. Kuznetsov, S.O.: Mathematical aspects of concept analysis. Math. Sci. 80(2), 1654–1698 (1996)

    Article  MathSciNet  Google Scholar 

  16. Outrata, J., Vychodil, V.: Fast algorithm for computing fixpoints of Galois connections induced by object-attribute relational data. Inf. Sci. 185(1), 114–127 (2012)

    Article  MathSciNet  Google Scholar 

  17. Priss, U.: Formal concept analysis in information science. Ann. Rev. Inf. Sci. Technol. (ASIST) 40 (2008)

    Google Scholar 

  18. Wille, R.: Formal concept analysis as mathematical theory of concepts and concept hierarchies. In: Ganter, B., Stumme, G., Wille, R. (eds.) Formal Concept Analysis. LNCS (LNAI), vol. 3626, pp. 1–33. Springer, Heidelberg (2005). https://doi.org/10.1007/11528784_1

    Chapter  MATH  Google Scholar 

  19. Wolff, K.E.: A first course in formal concept analysis: how to understand line diagrams. Adv. Stat. Softw. 4, 429–438 (1993)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Conceptual Structures Research Group, Department of Computing, College of Business, Technology and Engineering, The Industry and Innovation Research Institute, 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. FIZ Karlsruhe – Leibniz Institute for Information Infrastructure, Karlsruhe, Germany

    Mehwish Alam

  2. Institute of Information Systems, University of Lübeck, Lübeck, Germany

    Tanya Braun

  3. Department of Computing Science, University of Aberdeen, Aberdeen, UK

    Bruno Yun

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Andrews, S. (2020). Some Programming Optimizations for Computing Formal Concepts. In: Alam, M., Braun, T., Yun, B. (eds) Ontologies and Concepts in Mind and Machine. ICCS 2020. Lecture Notes in Computer Science(), vol 12277. Springer, Cham. https://doi.org/10.1007/978-3-030-57855-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-57855-8_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-57854-1

  • Online ISBN: 978-3-030-57855-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation