Complexity of learning in concept lattices from positive and negative examples

Discrete Applied Mathematics

Volumn 142, Issue 1-3 SPEC. ISS., 2004, Pages 111-125

  Kuznetsov, Sergei O ^a,b  

^a All Russian Institute for Scientific and Technical Information   (Russian Federation)

^b DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Algorithmic complexity; Concept lattices; Learning

Indexed keywords

ALGORITHMS; GRAPH THEORY; LEARNING SYSTEMS; POLYNOMIALS; PROBLEM SOLVING; SET THEORY;

ALGORITHMIC COMPLEXITY; CONCEPT LATTICES; GALOIS CONNECTIONS;

COMPUTATIONAL COMPLEXITY;

EID: 3142645428     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2003.11.002     Document Type: Article

References (26)

1. Birkhoff G.D. Lattice Theory. 1979;American Mathematical Society, Providence, RI.
2. Blinova V.G., Dobrynin D.A., Finn V.K., Kuznetsov S.O., Pankratova E.S. Toxicology analysis by means of the JSM-method. Bioinformatics. 19:2003;1201-1207.
3. Bordat J.P. Calcul pratique du treillis de Galois d'une correspondence. Math. Sci. Hum. 96:1986;31-47.
4. Finn V.K. On machine-oriented formalization of plausible reasoning in the style of F. Backon-J.S. Mill. Semiotika Inform. 20:1983;35-101. (in Russian).
5. Finn V.K. Plausible reasoning in systems of JSM-type. Itogi Nauki Tekh., Inform. 15:1991;54-101. (in Russian).
6. B. Ganter, Two basic algorithms in concept analysis, preprint 831, Technische Hochshule, Darmstadt, 1984.
7. Ganter B., Wille R. Formal Concept Analysis: Mathematical Foundations. 1999;Springer, Berlin.
8. Ganter B., Kuznetsov S.O. Formalizing Hypotheses with Concepts. Mineau G., Ganter B. Proceedings of the Eigth International Conference on Conceptual Structures, ICCS'2000. Lecture Notes in Artificial Intelligence. Vol. 1867:2000;342-356 Springer, Berlin.
9. Garey M., Johnson D. Computers and Intractability: a Guide to the Theory of NP-Completeness. 1979;Freeman, San Francisco.
10. Guigues J.-L., Duquenne V. Familles minimales d'implications informatives résultant d'un tableau de données binaires. Math. Sci. Hum. 24(95):1986;5-18.
11. Johnson D.S., Yannakakis M., Papadimitriou C.H. On generating all maximal independent sets. Inform. Process. Lett. 27:1988;119-123.
12. Karp R., Hopcroft G.A. 2.5-algorithm for maximum matching in bipartite graphs. SIAM J. Comput. 2(2):1973;225-231.
13. A.V. Karzanov, Private communication, Moscow, 1991.
14. Kuznetsov S.O. Learning of simple conceptual graphs from positive and negative examples. Zytkow J., Rauch J. Proceedings Third European Conference on Principles of Data Mining and Knowledge Discovery, PKDD'99. Lecture Notes in Artificial Intelligence. Vol. 1704:1999;384-392 Springer, Berlin.
15. Kuznetsov S.O. On computing the size of a lattice and related decision problems. Order. 18(4):2001;313-321.
16. Kuznetsov S.O., Obiedkov S.A. Comparing performance of algorithms for generating concept lattices. J. Exp. Theoret. Artificial Intelligence. 14(2-3):2002;189-216.
17. S.O. Kuznetsov, Machine learning and formal concept analysis, in: P. Eklund (Ed.), Proceedings Second International Conference on Formal Concept Analysis, Lecture Notes in Artificial Intelligence, 2961 (2004) 287-312.
18. Mitchell T. Machine Learning. 1997;McGraw-Hill, New York.
19. Norris E.M. An algorithm for computing the maximal rectangles in a binary relation. Rev. Roumaine Math. Pures Appl. 23(2):1978;243-250.
20. Nourine L., Raynaud O. A fast algorithm for building lattices. Inform Process. Lett. 71:1999;199-204.
21. Prisner E. Bicliques in graphs I. bounds on their number Combinatorica. 20(1):2000;109-117.
22. Schütt D. Abschätzungen für die Anzahl der Begriffe von Kontexten. 1988;Diplomarbeit, TH Darmstadt, Darmstadt.
23. Valiant L.G. The complexity of enumeration and reliability problems. SIAM J. Comput. 8(3):1979;410-421.
24. West D.B. Introduction to Graph Theory. 1996;Prentice-Hall, Upper Saddle River.
25. Wille R. Restructuring lattice theory: an approach based on hierarchies of concepts. Rival I. Ordered Sets. 1982;445-470 Reidel, Dordrecht, Boston.
26. Yannakakis M. Node-deletion problems of bipartite graphs. SIAM J. Comput. 10(2):1981;310-327.