Size of random Galois lattices and number of closed frequent itemsets

Discrete Applied Mathematics

Volumn 157, Issue 13, 2009, Pages 2945-2957

  Emilion, Richard ^a   Lévy, Gérard ^b  

^a UNIVERSITÉ D'ORLÉANS   (France)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

Association rule; Bernoulli distribution; Classification; Complexity; Data mining; Frequent itemset; Galois lattice; Winning coalition

Indexed keywords

BERNOULLI DISTRIBUTION; CLASSIFICATION; COMPLEXITY; FREQUENT ITEMSET; GALOIS LATTICE; WINNING COALITION;

ASSOCIATION RULES; ASSOCIATIVE PROCESSING; DATA MINING; INFORMATION MANAGEMENT; MINING;

CLASSIFICATION (OF INFORMATION);

EID: 67349211761     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2009.02.025     Document Type: Article

References (22)

1. R. Agrawal, T. Imielinski, A. Swamy, Mining association rules between sets of items in large databases, in: Proceed. ACM SIGMOD, Int'l Conf. on Management of Data, 1993, pp. 207-216
2. R. Agrawal, R. Srikant, Fast algorithm for mining association, in: Proceed. 20th. Int'l conf. VLDB, 1994, pp. 478-499
3. Baklouti F., Lévy G., and Emilion R. A fast algorithm for Galois lattice building. Electron J. Symb. Data Anal. 3 (2005) 19-31
4. M. Barbut, B. Monjardet, Ordre et classification, Hachette, Paris, 1970
5. G. Birkhoff, Lattice Theory, AMS Colloq. Public. Vol. XXV, 1967
6. Caspard N., and Montjardet B. The lattice of closure systems. Discrete Appl. Math. 127 (2003) 241-269
7. M. Courtine, I. Bournaud, Building a pruned inheritance lattice structure for relational description, Workshop on Concept Lattice-based, IICS, 2001
8. Diday E., and Emilion R. Maximal and stochastic Galois lattices. C. R. Acad. Sci. Paris 325 I (1997) 261-266
9. Diday E., and Emilion R. Maximal and stochastic Galois lattices. Discrete Appl. Math. 27 2 (2003) 271-284
10. V. Duquenne, Contextual Implications, Rapport CAMS, Paris, 1986
11. R. Emilion, G. Lambert, G. Lévy, Algorithms for Galois lattices, Indo-French Worksh., Univ. Paris IX-Dauphine, lise-ceremade, 1997
12. Ferré S., and King R.D. BLID: An application of logical information systems to bioinformatics. In: Eklund P. (Ed). Int. Conf. Formal Concept Analysis. LNCS vol. 2961 (2004), Springer 47-54
13. B. Ganter, Two basic algorithms in Concept analysis, 831, Technische Hoschscschule Darmstad, 1984
14. R. Godin, H. Mili, Building and maintaining analysis-level class hierarchies using Galois Lattices, in: Proceed. Eighth Conf. on Object-oriented Programming Systems, Languages, and Applications, 1993, pp. 394-410
15. R. Godin, R. Missaoui, H. Aloui, Learning algorithms using Galois lattice structure, in: Proc. of the IEEE Int. Conf. on Tools for AI, San Jose, CA, 1991, pp. 22-29
16. Kuznetsov S., and Ob'edkov S. Comparing the performance of algorithms for generating concept lattices. J. Exp. Theor. Artif. Intell. 14 (2002) 189-216
17. L. Lhote, F. Rioult, A. Soulet, Average of frequent and closed patterns in Random Databases, CAP, 2005, pp. 345-360 http://www-sop.inria.fr/acacia/afia2005/actes/ActesCAp2005.pdf
18. Matsui T., and Matsui Y. A survey of algorithms for calculating power indices of weighted majority games. J. Oper. Res. Soc. Japan 43 (2000)
19. Ore O. Galois connections. Trans. Amer. Math. Soc. 55 (1944) 494-513
20. Stewart J. Galois Theory (1975), Chapman Hall, New York
21. Wille R. Restructuring lattice theory, Ordered sets I. Rival ed. (1980), Reider
22. Zenou E., and Samuelides M. Galois lattice theory for probabilistic visual landmarks. J. Univ. Comp. Sci. 10 8 (2004) 1014