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Distributed Algorithm for Computing Formal Concepts Using Map-Reduce Framework

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Advances in Intelligent Data Analysis VIII (IDA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 5772))

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Abstract

Searching for interesting patterns in binary matrices plays an important role in data mining and, in particular, in formal concept analysis and related disciplines. Several algorithms for computing particular patterns represented by maximal rectangles in binary matrices were proposed but their major drawback is their computational complexity limiting their application on relatively small datasets. In this paper we introduce a scalable distributed algorithm for computing maximal rectangles that uses the map-reduce approach to data processing.

Supported by institutional support, research plan MSM 6198959214.

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References

  1. Belohlavek, R., Vychodil, V.: Discovery of optimal factors in binary data via a novel method of matrix decomposition. Journal of Computer and System Sciences (to appear)

    Google Scholar 

  2. Berry, A., Bordat, J.-P., Sigayret, A.: A local approach to concept generation. Annals of Mathematics and Artificial Intelligence 49, 117–136 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Carpineto, C., Romano, G.: Concept data analysis. Theory and applications. J. Wiley, Chichester (2004)

    Book  MATH  Google Scholar 

  4. Dean, J., Ghemawat, S.: MapReduce: simplified data processing on large clusters. Commun. ACM 51(1), 107–113 (2008)

    Article  Google Scholar 

  5. Fu, H., Nguifo, E.M.: A parallel algorithm to generate formal concepts for large data. In: Eklund, P. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, pp. 394–401. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  6. Ganter, B.: Two basic algorithms in concept analysis (Technical Report FB4-Preprint No. 831). TH Darmstadt (1984)

    Google Scholar 

  7. Ganter, B., Wille, R.: Formal concept analysis. Mathematical foundations. Springer, Berlin (1999)

    Book  MATH  Google Scholar 

  8. Hadoop Core Framework, http://hadoop.apache.org/

  9. Hettich, S., Bay, S.D.: The UCI KDD Archive University of California, Irvine, School of Information and Computer Sciences (1999)

    Google Scholar 

  10. Kengue, J.F.D., Valtchev, P., Djamegni, C.T.: A parallel algorithm for lattice construction. In: Ganter, B., Godin, R. (eds.) ICFCA 2005. LNCS (LNAI), vol. 3403, pp. 249–264. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. Miettinen, P., Mielikäinen, T., Gionis, A., Das, G., Mannila, H.: The discrete basis problem. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) PKDD 2006. LNCS (LNAI), vol. 4213, pp. 335–346. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Krajca, P., Outrata, J., Vychodil, V.: Parallel Recursive Algorithm for FCA. In: Belohlavek, R., Kuznetsov, S.O. (eds.) Proc. CLA 2008, vol. 433, pp. 71–82. CEUR WS (2008) ISBN 978–80–244–2111–7

    Google Scholar 

  13. Krajca, P., Outrata, J., Vychodil, V.: Parallel Algorithm for Computing Fixpoints of Galois Connections. Annals of Mathematics and Artificial Intelligence (submitted)

    Google Scholar 

  14. Kuznetsov, S.: Interpretation on graphs and complexity characteristics of a search for specific patterns. Automatic Documentation and Mathematical Linguistics 24(1), 37–45 (1989)

    MATH  Google Scholar 

  15. Kuznetsov, S.: A fast algorithm for computing all intersections of objects in a finite semi-lattice Бьıстрый аЛгоритм построения всех пересечений оδЪектов изконечной полурешетки in Russian. Automatic Documentation and Mathematical Linguistics 27(5), 11–21 (1993)

    Google Scholar 

  16. 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)

    Chapter  Google Scholar 

  17. Kuznetsov, S., Obiedkov, S.: Comparing performance of algorithms for generating concept lattices. J. Exp. Theor. Artif. Int. 14, 189–216 (2002)

    Article  MATH  Google Scholar 

  18. Lindig, C.: Fast concept analysis. In: Working with Conceptual Structures -— Contributions to ICCS 2000, pp. 152–161. Shaker Verlag, Aachen (2000)

    Google Scholar 

  19. Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Ordered Sets, Dordrecht, Boston, pp. 445–470 (1982)

    Google Scholar 

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Author information

Authors and Affiliations

  1. T. J. Watson School, State University of New York at Binghamton, USA

    Petr Krajca & Vilem Vychodil

  2. Dept. Computer Science, Palacky University, Olomouc

    Petr Krajca & Vilem Vychodil

Authors
  1. Petr Krajca
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  2. Vilem Vychodil
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2PG, London, United Kingdom

    Niall M. Adams

  2. INSA Lyon, LIRIS CNRS UMR 5205, Bâtiment Blaise Pascal, University of Lyon, F-69621, Villeurbanne, France

    Céline Robardet

  3. Department of Information and Computer Science, Universiteit Utrecht, Utrecht, The Netherlands

    Arno Siebes

  4. INSA-Lyon, LIRIS CNRS UMR5205, University of Lyon, F-69621, Villeurbanne, France

    Jean-François Boulicaut

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© 2009 Springer-Verlag Berlin Heidelberg

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Krajca, P., Vychodil, V. (2009). Distributed Algorithm for Computing Formal Concepts Using Map-Reduce Framework. In: Adams, N.M., Robardet, C., Siebes, A., Boulicaut, JF. (eds) Advances in Intelligent Data Analysis VIII. IDA 2009. Lecture Notes in Computer Science, vol 5772. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03915-7_29

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  • DOI: https://doi.org/10.1007/978-3-642-03915-7_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03914-0

  • Online ISBN: 978-3-642-03915-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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