Skip to main content
SpringerLink
Log in
Book cover

International Conference on Formal Concept Analysis

ICFCA 2019: Formal Concept Analysis pp 208–222Cite as

Parallelization of the GreConD Algorithm for Boolean Matrix Factorization

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11511))

Abstract

Boolean matrix factorization (BMF) is a well established and widely used tool for data analysis. Vast majority of existing algorithms for BMF is based on some greedy strategy which makes them highly sequential, thus unsuited for parallel execution. We propose a parallel variant of well-known BMF algorithm—GreConD, which is able to distribute workload among multiple parallel threads, hence can benefit from modern multicore CPUs. The proposed algorithm is based on formal concept analysis, intended for shared memory computers, and significantly reducing computation time of BMF via parallel execution.

Petr Krajča was supported by the grant JG 2019 of Palacký University Olomouc, No. JG_2019_008.

This is a preview of subscription content, 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   59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   74.99
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

Notes

  1. 1.

    GreConD is abbreviation for Greedy Concepts on Demand.

  2. 2.

    This operation atomically increments value of the variable and returns the original value, i.e., its meaning is equivalent to i++.

  3. 3.

    Documented but not a part of the language specification.

References

  1. Andrews, G.R.: Foundations of Multithreaded, Parallel, and Distributed Programming. Addison-Wesley, Reading (2002)

    Google Scholar 

  2. Belohlavek, R., Outrata, J., Trnecka, M.: Toward quality assessment of Boolean matrix factorizations. Inf. Sci. 459, 71–85 (2018). https://doi.org/10.1016/j.ins.2018.05.016

    Article  MathSciNet  Google Scholar 

  3. Belohlavek, R., Trnecka, M.: From-below approximations in Boolean matrix factorization: geometry and new algorithm. J. Comput. Syst. Sci. 81(8), 1678–1697 (2015). https://doi.org/10.1016/j.jcss.2015.06.002

    Article  MathSciNet  MATH  Google Scholar 

  4. Belohlavek, R., Vychodil, V.: Discovery of optimal factors in binary data via a novel method of matrix decomposition. J. Comput. Syst. Sci. 76(1), 3–20 (2010). https://doi.org/10.1016/j.jcss.2009.05.002

    Article  MathSciNet  MATH  Google Scholar 

  5. Ene, A., Horne, W.G., Milosavljevic, N., Rao, P., Schreiber, R., Tarjan, R.E.: Fast exact and heuristic methods for role minimization problems. In: Ray, I., Li, N. (eds.) 13th ACM Symposium on Access Control Models and Technologies, SACMAT 2008, Estes Park, CO, USA, 11–13 June 2008, Proceedings, pp. 1–10. ACM (2008). https://doi.org/10.1145/1377836.1377838

  6. Ganter, B., Wille, R.: Formal Concept Analysis Mathematical Foundations. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-642-59830-2

    Book  MATH  Google Scholar 

  7. Kannan, R., Ballard, G., Park, H.: A high-performance parallel algorithm for nonnegative matrix factorization. SIGPLAN Not. 51(8), 9:1–9:11 (2016). https://doi.org/10.1145/3016078.2851152

    Article  Google Scholar 

  8. Krajca, P., Outrata, J., Vychodil, V.: Advances in algorithms based on CbO. In: Kryszkiewicz, M., Obiedkov, S.A. (eds.) Proceedings of the 7th International Conference on Concept Lattices and Their Applications, Sevilla, Spain, 19–21 October 2010. CEUR Workshop Proceedings, vol. 672, pp. 325–337. CEUR-WS.org (2010)

    Google Scholar 

  9. 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). https://doi.org/10.1007/978-3-540-48247-5_47

    Chapter  Google Scholar 

  10. Lucchese, C., Orlando, S., Perego, R.: A unifying framework for mining approximate top-k binary patterns. IEEE Trans. Knowl. Data Eng. 26(12), 2900–2913 (2014). https://doi.org/10.1109/TKDE.2013.181

    Article  Google Scholar 

  11. Miettinen, P., Mielikäinen, T., Gionis, A., Das, G., Mannila, H.: The discrete basis problem. IEEE Trans. Knowl. Data Eng. 20(10), 1348–1362 (2008). https://doi.org/10.1109/TKDE.2008.53

    Article  Google Scholar 

  12. Outrata, J., Trnecka, M.: Parallel exploration of partial solutions in Boolean matrix factorization. J. Parallel Distrib. Comput. 123, 180–191 (2019). https://doi.org/10.1016/j.jpdc.2018.09.014

    Article  Google Scholar 

  13. Stockmeyer, L.J.: The Set Basis Problem is NP-complete. Research reports, IBM Thomas J. Watson Research Division (1975)

    Google Scholar 

  14. Tatti, N., Mielikäinen, T., Gionis, A., Mannila, H.: What is the dimension of your binary data? In: Proceedings of the 6th IEEE International Conference on Data Mining (ICDM 2006), Hong Kong, China, 18–22 December 2006, pp. 603–612. IEEE Computer Society (2006). https://doi.org/10.1109/ICDM.2006.167

  15. Xiang, Y., Jin, R., Fuhry, D., Dragan, F.F.: Summarizing transactional databases with overlapped hyperrectangles. Data Min. Knowl. Discov. 23(2), 215–251 (2011). https://doi.org/10.1007/s10618-010-0203-9

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Palacký University Olomouc, 17. listopadu 12, 77146, Olomouc, Czech Republic

    Petr Krajča & Martin Trnecka

Authors
  1. Petr Krajča
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martin Trnecka
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Petr Krajča .

Editor information

Editors and Affiliations

  1. Babeș-Bolyai University, Cluj-Napoca, Romania

    Diana Cristea

  2. University of Strasbourg, ENGEES, Strasbourg, France

    Florence Le Ber

  3. Frankfurt University of Applied Sciences, Frankfurt, Germany

    Baris Sertkaya

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Krajča, P., Trnecka, M. (2019). Parallelization of the GreConD Algorithm for Boolean Matrix Factorization. In: Cristea, D., Le Ber, F., Sertkaya, B. (eds) Formal Concept Analysis. ICFCA 2019. Lecture Notes in Computer Science(), vol 11511. Springer, Cham. https://doi.org/10.1007/978-3-030-21462-3_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-21462-3_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-21461-6

  • Online ISBN: 978-3-030-21462-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation