Attribute-incremental construction of the canonical implication basis

Annals of Mathematics and Artificial Intelligence

Volumn 49, Issue 1-4, 2007, Pages 77-99

  Obiedkov, S ^a   Duquenne, V ^b  

^a NATIONAL RESEARCH UNIVERSITY HIGHER SCHOOL OF ECONOMICS   (Russian Federation)

^b CNRS   (France)

Author keywords

Duquenne Guigues basis; Formal concept analysis; Galois lattice; Implication; Incremental algorithm

Indexed keywords

EID: 34547657950     PISSN: 10122443     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10472-007-9057-2     Document Type: Article

References (24)

1. Armstrong, W.W.: Dependency structure of data base relationships. In: Proc. IFIP Congress. Geneva, Switzerland, pp. 580-583 (1974)
2. Ausiello, G., D'Atri, A., Saccà, D.: Minimal representation of directed hypergraphs. SIAM J. Comput. 15(2), 418-431 (1986)
3. Birkhoff, G.: Lattice Theory. Amer. Math. Soc. Coll. Publ., Providence, R.I. (1973)
4. Blake, C.L., Merz, C.J.: UCI Repository of machine learning databases, Irvine, CA, University of California, Department of Information and Computer Science, Web Page http://www.ics.uci.edu/ mlearn/MLRepository.html (1998)
5. Carpineto, C., Romano, G.: A lattice conceptual clustering system and its application to browsing retrieval. Mach. Learn. 24(2), 95-122 (1996)
6. Day, A.: The lattice theory of functional dependencies and normal decompositions. Int. J. Algebra Comput. 2(4), 409-431 (1992)
7. Dowling, C.E.: On the irredundant generation of knowledge spaces. J. Math. Psychol. 37(1), 49-62 (1993)
8. Ferré, S.: Incremental concept formation made more efficient by the use of associative concepts, INRIA Research Report no. 4569 (2002)
9. Ganter, B.: Two Basic Algorithms in Concept Analysis, FB4-Preprint No. 831, TH Darmstadt (1984)
10. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Berlin (1999)
11. Godin, R., Missaoui, R., Alaoui, H.: Incremental concept formation algorithms based on Galois lattices. Comput. Intell. 11(2), 246-267 (1995)
12. Guigues, J.-L., Duquenne, V.: Familles minimales d'implications informatives resultant d'un tableau de données binaires. Math. Sci. Hum. 95, 5-18 (1986)
13. Liquière, M., Ganter, B., Duquenne, V., Mephu Nguifo, E., Stumme, G.: ECAI 2002 International Workshop on Advances in Formal Concept Analysis for Knowledge Discovery in Databases. Lyon, France (2002)
14. Kuznetsov, S.: On the intractability of computing the Duquenne-Guigues base. J. Univers. Comput. Sci. 10(8), 927-933 (2004)
15. Kuznetsov, S., Obiedkov, S.: Comparing performance of algorithms for generating concept lattices. J. Exp. Theor. Artif. Intell. 14(2-3), 189-216 (2002)
16. Maier, D.: The Theory of Relational Databases. Computer Science, Rockville, MD (1983)
17. Mannila, H., Räihä, K.J.: The Design of Relational Databases. Addison Wesley, Boston, MA (1992)
18. Mephu Nguifo, E., Duquenne, V., Liquière, M.: ICCS-2001 International Workshop on Concept Lattices-Based Theory, Methods and Tools for Knowledge Discovery in Databases. Stanford CA, USA (2001)
19. Norris, E.M.: An algorithm for computing the maximal rectangles in a binary relation. Rev. Roum. Math. Pures. Appl. 23(2), 243-250 (1978)
20. Taouil, R., Bastide, Y.: Computing proper implications. In: Proc. ICCS-2001 International Workshop on Concept Lattices-Based Theory, Methods and Tools for Knowledge Discovery in Databases, pp. 49-61. Stanford CA, USA (2001)
21. Valtchev, P., Missaoui, R.: Building concept (Galois) lattices from parts: Generalizing the incremental methods. In: Proc. ICCS 2001, Lecture Notes in Artificial Intelligence, vol. 2120, pp. 290-303. Springer, Berlin (2001)
22. Van Der Merwe, F.J., Obiedkov, S., Kourie, D.G.: AddIntent: A new incremental lattice construction algorithm. Concept Lattices: Proc. of the 2nd Int. Conf. on Formal Concept Analysis, Lecture Notes in Artificial Intelligence, vol. 2961, pp. 372-385. Springer, Berlin (2004)
23. Wild, M.: Implicational bases for finite closure systems. In: Lex, W. (ed.) Arbeitstagung, Begriffsanalyse und Künstliche Intelligenz, pp. 147-169 Informatik-Bericht 89/3, TU Clausthal (1991)
24. Wild, M.: Computations with finite closure systems and implications, Preprint-Nr: 1708, TH Darmstadt (1994)