Skip to main content

Distributed and Parallel Computation of the Canonical Direct Basis

  • Conference paper
  • First Online:
Formal Concept Analysis (ICFCA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10308))

Included in the following conference series:

  • 529 Accesses

Abstract

Mining association rules, including implications, is an important topic in Knowledge Discovery research area and in Formal Concept Analysis (FCA). In this paper, we present a novel algorithm that computes in a parallel way the canonical direct unit basis of a formal context in FCA. To that end, the algorithm first performs a horizontal split of the initial context into subcontexts and then exploits the notion of minimal dual transversal to merge the canonical direct unit bases generated from subcontexts.

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

Access this chapter

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

References

  1. Adaricheva, K., et al.: Measuring the implications of the D-basis in analysis of data in biomedical studies. In: Baixeries, J., Sacarea, C., Ojeda-Aciego, M. (eds.) ICFCA 2015. LNCS, vol. 9113, pp. 39–57. Springer, Cham (2015). doi:10.1007/978-3-319-19545-2_3

    Chapter  Google Scholar 

  2. Adaricheva, K.V., Nation, J.B., Rand, R.: Ordered direct implicational basis of a finite closure system. In: ISAIM (2012)

    Google Scholar 

  3. Armstrong, W.W., Deobel, C.: Decompositions and functional dependencies in relations. ACM Trans. Datab. Syst. (TODS) 5(4), 404–430 (1980)

    Article  MATH  Google Scholar 

  4. Bertet, K., Monjardet, B.: The multiple facets of the canonical direct unit implicational basis. Theoret. Comput. Sci. 411(22–24), 2155–2166 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bertet, K., Demko, C., Viaud, J.F., Guérin, C.: Lattices, closures systems and implication bases: a survey of structural aspects and algorithms. Theoret. Comput. Sci. (2016)

    Google Scholar 

  6. Cordero, P., Enciso, M., Mora, A.: Automated reasoning to infer all minimal keys. In: Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence, IJCAI 2013, pp. 817–823. AAAI Press (2013)

    Google Scholar 

  7. Cordero, P., Enciso, M., Mora, A., Ojeda-Aciego, M.N.: Computing minimal generators from implications: a logic-guided approach. In: Szathmary, L., Priss, U. (eds.) CLA. CEUR Workshop Proceedings, vol. 972, pp. 187–198. CEUR-WS.org (2012)

    Google Scholar 

  8. Cordero, P., Enciso, M., Mora, A., Ojeda-Aciego, M.N.: Computing left-minimal direct basis of implications. In: CLA, pp. 293–298 (2013)

    Google Scholar 

  9. Fu, H., Nguifo, E.: Partitioning large data to scale up lattice-based algorithm. In: Proceedings of 15th IEEE International Conference on Tools with Artificial Intelligence, pp. 537–541, November 2003

    Google Scholar 

  10. Ganter, B., Wille, R.: Formal Concept Analysis - Mathematical Foundations. Springer, Heidelberg (1999)

    Book  MATH  Google Scholar 

  11. Guigues, J.L., Duquenne, V.: Familles minimales d’implications informatives résultant d’un tableau de données binaires. Mathématiques et Sciences Humaines 95, 5–18 (1986)

    Google Scholar 

  12. Krajca, P., Outrata, J., Vychodil, V.: Parallel algorithm for computing fixpoints of Galois connections. Ann. Math. Artif. Intell. 59(2), 257–272 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Krajca, P., Vychodil, V.: Distributed algorithm for computing formal concepts using map-reduce framework. In: Adams, N., Robardet, C., Siebes, A., Boulicaut, J.F. (eds.) Advances in Intelligent Data Analysis VIII. LNCS, vol. 5772, pp. 333–344. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  14. Kriegel, F., Borchmann, D.: Nextclosures: parallel computation of the canonical base. In: Proceedings of the Twelfth International Conference on Concept Lattices and Their Applications, Clermont-Ferrand, France, 13–16 October 2015, pp. 181–192 (2015). http://ceur-ws.org/Vol-1466/paper15.pdf

  15. Kryszkiewicz, M.: Concise representations of association rules. In: Proceedings of Pattern Detection and Discovery, ESF Exploratory Workshop, London, UK, 16–19 September 2002, pp. 92–109 (2002)

    Google Scholar 

  16. Mora, A., Cordero, P., Enciso, M., Fortes, I., Aguilera, G.: Closure via functional dependence simplification. Int. J. Comput. Math. 89(4), 510–526 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Mora, A., de Guzmán, I.P., Enciso, M., Cordero, P.: Ideal non-deterministic operators as a formal framework to reduce the key finding problem. Int. J. Comput. Math. 88, 1860–1868 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Obiedkov, S., Duquenne, V.: Attribute-incremental construction of the canonical implication basis. Ann. Math. Artif. Intell. 49(1–4), 77–99 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  19. Renaud, Y.: Join on closure systems using direct implicational basis representation. In: Le Thi, H.A., Bouvry, P., Pham Dinh, T. (eds.) MCO 2008. CCIS, vol. 14, pp. 450–457. Springer, Heidelberg (2008). doi:10.1007/978-3-540-87477-5_48

    Chapter  Google Scholar 

  20. Rodríguez-Lorenzo, E., Bertet, K.: From implicational systems to direct-optimal bases: a logic-based approach. Appl. Math. Inf. Sci. 9(305), 305–317 (2015)

    MathSciNet  Google Scholar 

  21. Rodríguez-Lorenzo, E., Bertet, K., Cordero, P., Enciso, M., Mora, A.: The direct-optimal basis via reductions. In: Proceedings of the Eleventh International Conference on Concept Lattices and Their Applications, Košice, Slovakia, 7–10 October 2014, pp. 145–156 (2014)

    Google Scholar 

  22. Ryssel, U., Distel, F., Borchmann, D.: Fast algorithms for implication bases and attribute exploration using proper premises. Ann. Math. Artif. Intell. 70(1–2), 25–53 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  23. Tsiporkova, E., Boeva, V., Kostadinova, E.: MapReduce and FCA approach for clustering of multiple-experiment data compendium. In: Causmaecker, P.D., Maervoet, J., Messelis, T., Verbeeck, K., Vermeulen, T. (eds.) Proceedings of the 23rd Benelux Conference on Artificial Intelligence (2011)

    Google Scholar 

  24. Valtchev, P., Duquenne, V.: Towards scalable divide-and-conquer methods for computing concepts and implications. In: Proceedings of the 4th International Conference Journées de l’Informatique Messine (JIM 2003): Knowledge Discovery and Discrete Mathematics, Metz (FR), pp. 3–6 (2003)

    Google Scholar 

  25. Valtchev, P., Duquenne, V.: On the merge of factor canonical bases. In: Medina, R., Obiedkov, S. (eds.) ICFCA 2008. LNCS (LNAI), vol. 4933, pp. 182–198. Springer, Heidelberg (2008). doi:10.1007/978-3-540-78137-0_14

    Chapter  Google Scholar 

  26. Vu, L., Alaghband, G.: Novel parallel method for association rule mining on multi-core shared memory systems. Parallel Comput. 40(10), 768–785 (2014)

    Article  Google Scholar 

  27. Xu, B., Fréin, R., Robson, E., Ó Foghlú, M.: Distributed formal concept analysis algorithms based on an iterative MapReduce framework. In: Domenach, F., Ignatov, D.I., Poelmans, J. (eds.) ICFCA 2012. LNCS (LNAI), vol. 7278, pp. 292–308. Springer, Heidelberg (2012). doi:10.1007/978-3-642-29892-9_26

    Chapter  Google Scholar 

  28. Zaki, M.J., Pan, Y.: Introduction: recent developments in parallel and distributed data mining. Distrib. Parallel Datab. 11(2), 123–127 (2002)

    Google Scholar 

Download references

Acknowledgment

One of the authors acknowledges the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) and all the authors would like to warmly thank referees for their comments and suggestions that helped improve the quality of this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jean-François Viaud .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Viaud, JF., Bertet, K., Missaoui, R., Demko, C. (2017). Distributed and Parallel Computation of the Canonical Direct Basis. In: Bertet, K., Borchmann, D., Cellier, P., Ferré, S. (eds) Formal Concept Analysis. ICFCA 2017. Lecture Notes in Computer Science(), vol 10308. Springer, Cham. https://doi.org/10.1007/978-3-319-59271-8_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-59271-8_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59270-1

  • Online ISBN: 978-3-319-59271-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics