Skip to main content

Galois Lattices and Bases for MGK-Valid Association Rules

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4923))

Abstract

We review the main properties of the quality measure MGK, which has been shown to be the normalized quality measure associated to most of the quality measures used in the data mining literature, and which enables to handle negative association rules. On the other hand, we characterize bases for MGK-valid association rules in terms of a closure operator induced by a Galois connection. Thus, these bases can be derived from a Galois lattice, as do well known bases for Confidence-valid association rules.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Hilderman, R.J., Hamilton, H.J.: Knowledge discovery and interestingness measures: A survey. Technical Report CS 99-04, Department of Computer Science, University of Regina (1999)

    Google Scholar 

  2. Agrawal, R., Imielinski, T., Swami, A.: Mining association rules between sets of items in large databases. In: Buneman, P., Jajodia, S. (eds.) Proc. of the ACM SIGMOD International Conference on Management of Data, Washington, vol. 22, pp. 207–216. ACM Press, New York (1993)

    Google Scholar 

  3. Guillaume, S.: Traitement des données volumineuses. Mesures et algorithmes d’extraction des règles d’association et règles ordinales. PhD thesis, Université de Nantes, France (2000)

    Google Scholar 

  4. Wu, X., Zhang, C., Zhang, S.: Mining both positive and negative rules. ACM J. Information Systems 22, 381–405 (2004)

    Article  Google Scholar 

  5. Feno, D., Diatta, J., Totohasina, A.: Normalisée d’une mesure probabiliste de qualité des règles d’association: étude de cas. In: Actes du 2nd Atelier Qualité des Données et des Connaissances, Lille, France, pp. 25–30 (2006)

    Google Scholar 

  6. Birkhoff, G.: Lattice theory. 3rd edn., Coll. Publ., XXV. American Mathematical Society, Providence, RI (1967)

    Google Scholar 

  7. Guigues, J.L., Duquenne, V.: Famille non redondante d’implications informatives résultant d’un tableau de données binaires. Mathématiques et Sciences humaines 95, 5–18 (1986)

    MathSciNet  Google Scholar 

  8. Luxemburger, M.: Implications partielles dans un contexte. Math. Inf. Sci. hum. 113, 35–55 (1991)

    Google Scholar 

  9. Brin, S., Motwani, R., Ullman, J.D., Tsur, S.: Dynamic itemset counting and implication rules for market basket data. In: Proc. of the ACM SIGMOD Conference, pp. 255–264 (1997)

    Google Scholar 

  10. Lerman, I., Gras, R., Rostam, H.: Elaboration et évaluation d’un indice d’implication pour des données binaires. Math Sc. Hum. 74, 5–35 (1981)

    MATH  Google Scholar 

  11. Huynh, X., Guillet, F., Briand, H.: Une plateforme exploratoire pour la qualité des règles d’association: Apport pour l’analyse implicative. In: Troisièmes Rencontres Internationales A.S.I., pp. 339–349 (2005)

    Google Scholar 

  12. Brin, S., Motwani, R., Silverstein, C.: Beyond market baskets: Generalizing association rules to correlation. In: Proc. of the ACM SIGMOD Conference, pp. 265–276 (1997)

    Google Scholar 

  13. Totohasina, A., Ralambondrainy, H.: Lon: A pertinent new measure for mining information from many types of data. In: IEEE SITIS 2005, pp. 202–207 (2005)

    Google Scholar 

  14. Barbut, M., Monjardet, B.: Ordre et classification. In: Hachette, Paris (1970)

    Google Scholar 

  15. Wille, R.: Restructuring lattice theory: An approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered sets, pp. 445–470. Ridel, Dordrecht-Boston (1982)

    Google Scholar 

  16. Armstrong, W.W.: Dependency structures of data base relationships. Information Processing 74, 580–583 (1974)

    MathSciNet  Google Scholar 

  17. Diatta, J.: Charactérisation des ensembles critiques d’une famille de Moore finie. In: Rencontres de la Société Francophone de Classification, Montréal, Canada, pp. 126–129 (2005)

    Google Scholar 

  18. Day, A.: The lattice theory of functional dependencies and normal decompositions. Internat. J. Algebra Comput. 2, 409–431 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  19. Caspard, N.: A characterization theorem for the canonical basis of a closure operator. Order 16, 227–230 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  20. Caspard, N., Monjardet, B.: The lattices of closure systems, closure operators, and implicational systems on a finite set: a survey. Discrete Applied Mathematics 127, 241–269 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  21. Domenach, F., Leclerc, B.: Closure systems, implicational systems, overhanging relations and the case of hierarchical classification. Mathematical Social Sciences 47, 349–366 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  22. Zaki, M.J., Ogihara, M.: Theoretical Foundations of Association Rules. In: 3rd SIGMOD 1998 Workshop on Research Issues in Data Mining and Knowledge Discovery (DMKD), pp. 1–8 (1998)

    Google Scholar 

  23. Pasquier, N., Bastide, Y., Taouil, R., Lakhal, L.: Closed set based discovery of small covers for association rules. In: Proc. 15emes Journees Bases de Donnees Avancees, BDA, pp. 361–381 (1999)

    Google Scholar 

  24. Mannila, H., Toivonen, H.: Levelwise search and borders of theories in knowledge discovery. Data Mining Knowledge Discovery 1, 241–258 (1997)

    Article  Google Scholar 

  25. Pasquier, N., Bastide, Y., Taouil, R., Lakhal, L.: Efficient mining of association rules using closed itemset lattices. Information Systems 24, 25–46 (1999)

    Article  Google Scholar 

  26. Plott, C.R.: Path independence, rationality and social choice. Econometrica 41, 1075–1091 (1973)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Sadok Ben Yahia Engelbert Mephu Nguifo Radim Belohlavek

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Diatta, J., Feno, D.R., Totohasina, A. (2008). Galois Lattices and Bases for MGK-Valid Association Rules. In: Yahia, S.B., Nguifo, E.M., Belohlavek, R. (eds) Concept Lattices and Their Applications. CLA 2006. Lecture Notes in Computer Science(), vol 4923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78921-5_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-78921-5_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78920-8

  • Online ISBN: 978-3-540-78921-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics