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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
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)
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)
Wu, X., Zhang, C., Zhang, S.: Mining both positive and negative rules. ACM J. Information Systems 22, 381–405 (2004)
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)
Birkhoff, G.: Lattice theory. 3rd edn., Coll. Publ., XXV. American Mathematical Society, Providence, RI (1967)
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)
Luxemburger, M.: Implications partielles dans un contexte. Math. Inf. Sci. hum. 113, 35–55 (1991)
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)
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)
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)
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)
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)
Barbut, M., Monjardet, B.: Ordre et classification. In: Hachette, Paris (1970)
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)
Armstrong, W.W.: Dependency structures of data base relationships. Information Processing 74, 580–583 (1974)
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)
Day, A.: The lattice theory of functional dependencies and normal decompositions. Internat. J. Algebra Comput. 2, 409–431 (1992)
Caspard, N.: A characterization theorem for the canonical basis of a closure operator. Order 16, 227–230 (1999)
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)
Domenach, F., Leclerc, B.: Closure systems, implicational systems, overhanging relations and the case of hierarchical classification. Mathematical Social Sciences 47, 349–366 (2004)
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)
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)
Mannila, H., Toivonen, H.: Levelwise search and borders of theories in knowledge discovery. Data Mining Knowledge Discovery 1, 241–258 (1997)
Pasquier, N., Bastide, Y., Taouil, R., Lakhal, L.: Efficient mining of association rules using closed itemset lattices. Information Systems 24, 25–46 (1999)
Plott, C.R.: Path independence, rationality and social choice. Econometrica 41, 1075–1091 (1973)
Author information
Authors and Affiliations
Editor information
Rights 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)