Skip to main content

Pruning Techniques in LinCbO for Computation of the Duquenne-Guigues Basis

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12733))

Abstract

We equip our algorithm LinCbO with a pruning technique similar to that of LCM. Our experimental evaluation shows that it significantly improves the performance of the algorithm.

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   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

Learn about institutional subscriptions

Notes

  1. 1.

    The pruning is utilized in the implementation LCM2 (available at http://research.nii.ac.jp/~uno/codes.htm). However it is not described in the related paper. An interested reader can find the description of the LCM’s pruning in [9].

  2. 2.

    For now, ignore the argument y and line 16 as it will be explained later.

  3. 3.

    Available at https://github.com/yazevnul/fcai.

References

  1. Andrews, S.: In-Close, a fast algorithm for computing formal concepts. In: International Conference on Conceptual Structures (ICCS), Moscow (2009)

    Google Scholar 

  2. 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 

  3. Andrews, S.: A new method for inheriting canonicity test failures in close-by-one type algorithms (2018)

    Google Scholar 

  4. Bazhanov, K., Obiedkov, S.A.: Optimizations in computing the Duquenne-Guigues basis of implications. Ann. Math. Artif. Intell. 70(1–2), 5–24 (2014)

    Article  MathSciNet  Google Scholar 

  5. Beeri, C., Bernstein, P.A.: Computational problems related to the design of normal form relational schemas. ACM Trans. Database Syst. (TODS) 4(1), 30–59 (1979)

    Article  Google Scholar 

  6. Dua, D., Graff, C.: UCI machine learning repository (2017)

    Google Scholar 

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

    Book  Google Scholar 

  8. Guigues, J.-L., Duquenne, V.: Familles minimales d’implications informatives resultant d’un tableau de données binaires. Math. Sci. Humaines 95, 5–18 (1986)

    Google Scholar 

  9. Janostik, R., Konecny, J., Krajča, P.: LCM is well implemented CbO: study of LCM from FCA point of view. CoRR, abs/2010.06980 (2020)

    Google Scholar 

  10. Janostik, R., Konecny, J., Krajča, P.: LinCbO: fast algorithm for computation of the Duquenne-Guigues basis. CoRR, abs/2011.04928 (2020)

    Google Scholar 

  11. Konecny, J., Krajča, P.: Pruning in map-reduce style CbO algorithms. In: Alam, M., Braun, T., Yun, B. (eds.) ICCS 2020. LNCS (LNAI), vol. 12277, pp. 103–116. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-57855-8_8

    Chapter  Google Scholar 

  12. Krajča, P., Outrata, J., Vychodil, V.: Advances in algorithms based on CbO. CLA 672, 325–337 (2010)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  14. Krajca, P., Vychodil, V.: Distributed algorithm for computing formal concepts using map-reduce framework. In: Adams, N.M., Robardet, C., Siebes, A., Boulicaut, J.-F. (eds.) IDA 2009. LNCS, vol. 5772, pp. 333–344. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03915-7_29

    Chapter  MATH  Google Scholar 

  15. Kuznetsov, S.O.: A fast algorithm for computing all intersections of objects from an arbitrary semilattice. Nauchno-Tekhnicheskaya Informatsiya Seriya 2-Informatsionnye Protsessy i Sistemy, (1), 17–20 (1993)

    Google Scholar 

  16. Kuznetsov, S.O.: On the intractability of computing the Duquenne-Guigues base. J. Univ. Comput. Sci. 10(8), 927–933 (2004)

    MathSciNet  MATH  Google Scholar 

  17. Maier, D.: The Theory of Relational Databases, vol. 11. Computer Science Press, Rockville (1983)

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  19. 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 

  20. Uno, T., Asai, T., Uchida, Y., Hiroki A.: LCM: an efficient algorithm for enumerating frequent closed item sets. In: FIMI, vol. 90. Citeseer (2003)

    Google Scholar 

  21. Uno, T., Asai, T., Uchida, Y., Arimura, H.: An efficient algorithm for enumerating closed patterns in transaction databases. In: Suzuki, E., Arikawa, S. (eds.) DS 2004. LNCS (LNAI), vol. 3245, pp. 16–31. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30214-8_2

    Chapter  Google Scholar 

  22. Uno, T., Kiyomi, M., Arimura, H.: LCM ver. 2: efficient mining algorithms for frequent/closed/maximal itemsets. In: FIMI, vol. 126 (2004)

    Google Scholar 

  23. Uno, T., Kiyomi, M., Arimura, H.: LCM ver. 3: collaboration of array, bitmap and prefix tree for frequent itemset mining. In: Proceedings of the 1st International Workshop on Open Source Data Mining: Frequent Pattern Mining Implementations, pp. 77–86. ACM (2005)

    Google Scholar 

  24. Wild, M.: Computations with finite closure systems and implications. In: Du, D.-Z., Li, M. (eds.) COCOON 1995. LNCS, vol. 959, pp. 111–120. Springer, Heidelberg (1995). https://doi.org/10.1007/BFb0030825

    Chapter  Google Scholar 

Download references

Acknowledgment

The authors acknowledge support by the grants

– IGA UP 2020 of Palacký University Olomouc, No. IGA_PrF_2020_019,

– JG 2019 of Palacký University Olomouc, No. JG_2019_008.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jan Konecny .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Janostik, R., Konecny, J., Krajča, P. (2021). Pruning Techniques in LinCbO for Computation of the Duquenne-Guigues Basis. In: Braud, A., Buzmakov, A., Hanika, T., Le Ber, F. (eds) Formal Concept Analysis. ICFCA 2021. Lecture Notes in Computer Science(), vol 12733. Springer, Cham. https://doi.org/10.1007/978-3-030-77867-5_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-77867-5_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-77866-8

  • Online ISBN: 978-3-030-77867-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics