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Border Algorithms for Computing Hasse Diagrams of Arbitrary Lattices

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Formal Concept Analysis (ICFCA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6628))

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Abstract

The Border algorithm and the iPred algorithm find the Hasse diagrams of FCA lattices. We show that they can be generalized to arbitrary lattices. In the case of iPred, this requires the identification of a join-semilattice homomorphism into a distributive lattice.

This work has been partially supported by project FORMALISM (TIN2007-66523) of Programa Nacional de Investigación, Ministerio de Ciencia e Innovación (MICINN), Spain, by the Juan de la Cierva contract JCI-2009-04626 of the same ministry, and by the Pascal-2 Network of the European Union.

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References

  1. Aggarwal, C.C., Yu, P.S.: A new approach to online generation of association rules. IEEE Transactions on Knowledge and Data Engineering 13(4), 527–540 (2001)

    Article  Google Scholar 

  2. Baixeries, J.: Lattice Characterization of Armstrong and Symmetric Dependencies. Ph.D. thesis, Universitat Politècnica de Catalunya (2007)

    Google Scholar 

  3. Baixeries, J.: A formal context for symmetric dependencies. In: Medina and Obiedkov [15], pp. 90–105

    Google Scholar 

  4. Baixeries, J., Balcázar, J.L.: Unified characterization of symmetric dependencies with lattices. In: Ganter, B., Kwuida, L. (eds.) Contributions to the 4th International Conference on Formal Concept Analysis (ICFCA). Verlag Allgemeine Wissensch (2006)

    Google Scholar 

  5. Baixeries, J., Szathmary, L., Valtchev, P., Godin, R.: Yet a faster algorithm for building the Hasse diagram of a concept lattice. In: Ferré, S., Rudolph, S. (eds.) ICFCA 2009. LNCS, vol. 5548, pp. 162–177. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  6. Balcázar, J.L.: Redundancy, deduction schemes, and minimum-size bases for association rules. Logical Methods in Computer Science 6(2:3), 1–33 (2010)

    MathSciNet  MATH  Google Scholar 

  7. Davey, B., Priestley, H.: Introduction to Lattices and Orders, 2nd edn. Cambridge University Press, Cambridge (1991)

    MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  9. Godin, R., Missaoui, R., Alaoui, H.: Incremental concept formation algorithms based on Galois (concept) lattices. Computational Intelligence 11, 246–267 (1995)

    Article  Google Scholar 

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

    Google Scholar 

  11. Kryszkiewicz, M.: Representative association rules. In: Wu, X., Ramamohanarao, K., Korb, K.B. (eds.) PAKDD 1998. LNCS (LNAI), vol. 1394, pp. 198–209. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  12. Kuznetsov, S.O., Obiedkov, S.A.: Algorithms for the construction of concept lattices and their diagram graphs. In: Raedt, L.D., Siebes, A. (eds.) PKDD 2001. LNCS (LNAI), vol. 2168, pp. 289–300. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  13. Luxenburger, M.: Implications partielles dans un contexte. Mathématiques et Sciences Humaines 29, 35–55 (1991)

    MathSciNet  MATH  Google Scholar 

  14. Martin, B., Eklund, P.W.: From concepts to concept lattice: A border algorithm for making covers explicit. In: Medina and Obiedkov [15], pp. 78–89

    Google Scholar 

  15. Medina, R., Obiedkov, S. (eds.): ICFCA 2008. LNCS (LNAI), vol. 4933. Springer, Heidelberg (2008)

    Google Scholar 

  16. Nourine, L., Raynaud, O.: A fast algorithm for building lattices. Information Processing Letters 71(5-6), 199–204 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  17. Sagiv, Y., Delobel, C., Parker Jr., D.S., Fagin, R.: An equivalence between relational database dependencies and a fragment of propositional logic. Journal of the ACM 28(3), 435–453 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  18. Sagiv, Y., Delobel, C., Parker Jr., D.S., Fagin, R.: Correction to “An equivalence between relational database dependencies and a fragment of propositional logic”. Journal of the ACM 34(4), 1016–1018 (1987)

    Article  MATH  Google Scholar 

  19. Savnik, I., Flach, P.A.: Discovery of multivalued dependencies from relations. Intelligent Data Analysis 4(3-4), 195–211 (2000)

    MATH  Google Scholar 

  20. Valtchev, P., Missaoui, R., Lebrun, P.: A fast algorithm for building the Hasse diagram of a Galois lattice. In: Leroux, P. (ed.) Publications du LaCIM, pp. 293–306 (2000)

    Google Scholar 

  21. Zaki, M.J., Hsiao, C.J.: Efficient algorithms for mining closed itemsets and their lattice structure. IEEE Transactions on Knowledge and Data Engineering 17(4), 462–478 (2005)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Santander, Spain

    José L. Balcázar & Cristina Tîrnăucă

Authors
  1. José L. Balcázar
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  2. Cristina Tîrnăucă
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Editor information

Editors and Affiliations

  1. Département d’Informatique, Université du Québec à Montréal, Succ. Centre-Ville, Montréal, C.P.8888, H3C 3P8, Québec, Canada

    Petko Valtchev

  2. Universität Kassel, Fachgebiet Wissensverarbeitung, Wilhelmshöher Allee 73, 34121, Kassel, Germany

    Robert Jäschke

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Balcázar, J.L., Tîrnăucă, C. (2011). Border Algorithms for Computing Hasse Diagrams of Arbitrary Lattices. In: Valtchev, P., Jäschke, R. (eds) Formal Concept Analysis. ICFCA 2011. Lecture Notes in Computer Science(), vol 6628. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20514-9_6

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  • DOI: https://doi.org/10.1007/978-3-642-20514-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20513-2

  • Online ISBN: 978-3-642-20514-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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