ICFCA 2015: Formal Concept Analysis pp 287-302 | Cite as
Simple Undirected Graphs as Formal Contexts
Conference paper
First Online:
Abstract
The adjacency matrix of a graph is interpreted as a formal context. Then, the counterpart of Formal Concept Analysis (FCA) tools are introduced in graph theory. Moreover, a formal context is seen as a Boolean information table, the structure at the basis of Rough Set Theory (RST). Hence, we also apply RST tools to graphs. The peculiarity of the graph case, put in evidence and studied in the paper, is that both FCA and RST are based on a (different) binary relation between objects.
References
- 1.Alexe, G., Alexe, S., Crama, Y., Foldes, S., Hammer, P.L., Simeone, B.: Consensus algorithms for the generation of all maximal bicliques. Discrete Appl. Math. 145, 11–21 (2004)CrossRefMATHMathSciNetGoogle Scholar
- 2.Ciucci, D., Dubois, D., Prade, H.: The structure of oppositions in rough set theory and formal concept analysis - toward a new bridge between the two settings. In: Beierle, C., Meghini, C. (eds.) FoIKS 2014. LNCS, vol. 8367, pp. 154–173. Springer, Heidelberg (2014) CrossRefGoogle Scholar
- 3.Dawande, M., Keskinocak, P., Swaminathan, J.M., Tayur, S.: On bipartite and multipartite clique problems. J. Algorithms 41, 388–403 (2001)CrossRefMATHMathSciNetGoogle Scholar
- 4.Dubois, D., Dupin de Saint Cyr, F., Prade, H.: A possibility-theoretic view of formal concept analysis. Fundamenta Informaticae 75, 195–213 (2007)MATHMathSciNetGoogle Scholar
- 5.Dubois, D., Prade, H.: From Blanché’s hexagonal organization of concepts to formal concept analysis and possibility theory. Log. Univers. 6, 149–169 (2012)CrossRefMATHMathSciNetGoogle Scholar
- 6.Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999) CrossRefMATHGoogle Scholar
- 7.Gaume, B., Navarro, E., Prade, H.: A parallel between extended formal concept analysis and bipartite graphs analysis. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS, vol. 6178, pp. 270–280. Springer, Heidelberg (2010) CrossRefGoogle Scholar
- 8.Kuznetsov, S.O., Obiedkov, S.A.: Comparing performance of algorithms for generating concept lattices. J. Exp. Theor. Artif. Intell. 14, 189–216 (2002)CrossRefMATHGoogle Scholar
- 9.Li, J., Liu, G., Li, H., Wong, L.: Maximal biclique subgraphs and closed pattern pairs of the adjacency matrix: a one-to-one correspondence and mining algorithms. IEEE Trans. Knowl. Data Eng. 19, 1625–1637 (2007)CrossRefGoogle Scholar
- 10.Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Publisher, The Netherlands (1991) CrossRefMATHGoogle Scholar
Copyright information
© Springer International Publishing Switzerland 2015