A local approach to concept generation

Annals of Mathematics and Artificial Intelligence

Volumn 49, Issue 1-4, 2007, Pages 117-136

  Berry, Anne ^a   Bordat, Jean Paul ^b   Sigayret, Alain ^a  

^a UNIVERSITÉ BLAISE PASCAL   (France)

^b LIRMM   (France)

Author keywords

Concept generation; Concept lattice; Galois lattice; Maximal rectangles

Indexed keywords

EID: 34547697700     PISSN: 10122443     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10472-007-9063-4     Document Type: Article

References (31)

1. Barbut, M., Monjardet, B.: Ordre et classification. In: Classiques Hachette (1970)
2. Berry, A., Bordat, J-P., Cogis, O.: Generating all the minimal separators of a graph. Int. J. Found. Comput. Sci. 11, 397-404 (2000)
3. Berry, A., Sigayret, A.: Representing a concept lattice by a graph. In: Proceedings of DM&DM'02 (Discrete Maths and Data Mining Workshop), 2nd SIAM Conference on Data Mining (Arlington, VA, April 2002). Discrete Applied Mathematics, special issue on Discrete Maths and Data Mining 144(1-2), 27-42 (2004)
4. Berry, A., Sigayret, A.: Maintaining class membership information. In: Workshop MASPEGHI (MAnaging of SPEcialization/Generalization HIerarchies), LNCS proceedings of OOIS'02 (Object-Oriented Information Systems) Montpellier, France (2002)
5. Birkhoff, G.: Lattice Theory (3rd edn.). American Mathematical Society, Providence, RI (1967)
6. Bordat, J.-P.: Calcul pratique du treillis de Galois d'une correspondance. Math. Inform. Sci. Hum. 96, 31-47 (1986)
7. Chein, M.: Algorithme de recherche de sous-matrices premières d'une matrice. Bull. Math. Soc. Sci. Répub. Social. Roum. 13 (1969)
8. Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. J. Symb. Comput. 9(3), 251-280 (1990)
9. Fu, H., N. Mephu, N.E.: Partitioning large data to scale-up lattice-based algorithm. In: Proceedings of ICTAI'03 (15th IEEE International Conference on Tools with Artificial Intelligence), Sacramento, CA, pp. 537-541. IEEE Press, Los Alamitos, CA (2003)
10. Fu, H., N. Mephu, N.E.: How well go lattice algorithms on currently used machine learning testbeds. In: Proc. Conference EGC'04, Clermont-Ferrand, France, pp. 373-384 (2004)
11. Ganter, B.: Two basic algorithms in concept analysis. In: Technische Hochschule Darmstadt, vol. 831 (1984)
12. Ganter, B., Wille, R.: Formal Concept Analysis. Springer, Berlin Heidelberg New York (1999)
13. Guénoche, A.: Construction du treillis de Galois d'une relation binaire. Math. Inform. Sci. Hum. 121, 23-34 (1993)
14. Hsu, W-L., Ma, T-H.: Substitution decomposition on chordal graphs and its applications. SIAM J. Comput. 28, 1004-1020 (1999)
15. Huchard, M., Dicky, H., Leblanc, H.: Galois lattice as a framework to specify building class hierarchies algorithms. Inform. Theor. Appl. 34, 521-548 (2000)
16. Huchard, M., Roume, C., Valtchev, P.: When concepts point at other concepts: the case of UML diagram reconstruction. In: Proceedings of FCAKDD'02 (Formal Concept Analysis for Knowledge Discovery in Databases), Int. Conf. ECAI'02, (Lyon, Fr, Juillet 2002) 32-43
17. Kloks, T., Kratsch, D.: Listing all minimal separators of a graph. SIAM J. Comput. 27, 605-613 (1998)
18. Kuznetsov, S.O., Obiedkov, S.A.: Comparing performance of algorithms for generating concept lattices. J. Exp. Theor. Artif. Intell. (JETAI) 14(2-3), 189-216 (2002)
19. Kuznetsov, S.O.: Algorithm for the construction of the set of all concepts and their line diagram. In: MATH-AI-05, TU-Dresden (2000)
20. Liquière, M., Sallantin, J.: Structural machine learning with Galois lattices and Graphs. In: Kaufmann, M. (ed.) Proceedings of ICML'98 (International Conference on Machine Learning), pp. 305-313 (1998)
21. Malgrange, Y.: Recherche des sous-matrices premières d'une matrice à coefficients binaires. In: 2nd congrès de l'AFCALTI, Gauthier-Villars (Oct. 1961)
22. Mephu, N.E., Njiwoua, P.: Using lattice-based framework as a tool for feature extraction. In: ECML, pp. 304-309 (1998)
23. Norris, E.M.: An algorithm for computing the maximal rectangles of a binary relation. Rev. Roumaine Math. Pures Appl. 23(2), 243-250 (1978)
24. Nourine, L., Raynaud, O.: A Fast Algorithm for building Lattices. Inf. Process. Lett. 71, 199-204 (1999)
25. Bastide, Y., Lakhal, L., Pasquier, N., Taouil, R.: Efficient mining of association rules using closed itemset lattices. J. Inf. Syst. 24(1), 25-46 (1999)
26. Rose, D., Tarjan, R.E., Lueker, G.: Algorithmic aspects of vertex elimination on graphs. SIAM J. Comput. 5, 146-160 (1976)
27. th Asian Computer Science Conference), (Phuket, Thailand, December 1999). LNCS, vol. 1742, pp. 347-358 (1999)
28. Sheng, H., Liang, W.: Efficient enumeration of all minimal separators in a graph. Theor. Comp. Sci. 180, 169-180 (1997)
29. Sigayret, A.: Data mining: une approche par les graphes. Ph.D. thesis, Université Blaise Pascal (Clermont-Ferrand, Fr), DU 1405 ∈-∈ EDSPIC 269 (2002)
30. Valtchef, P., Missaoui, R., Godin, R.: A Framework for Incremental Generation of Frequent Closed Item Sets. In: Proceedings of DM&DM'02 (Discrete Maths and Data Mining Workshop), 2nd SIAM Conference on Data Mining (SDM'02), Arlington, VA (2002)
31. Valtchev, P., Missaoui, R., Lebrun, P.: A partition-based approach towards building Galois (concept) lattices. Discrete Math. 256(3), 801-825 (2002)