Abstract
Minimal generators (mingens) of concept intents are valuable elements of the Formal Concept Analysis (FCA) landscape, which are widely used in the database field, for data mining but also for database design purposes. The volatility of many real-world datasets has motivated the study of the evolution in the concept set under various modifications of the initial context. We believe this should be extended to the evolution of mingens. In the present paper, we build up on previous work about the incremental maintenance of the mingen family of a context to investigate the case of lattice merge upon context subposition. We first recall the theory underlying the singleton increment and show how it generalizes to lattice merge. Then we present the design of an effective merge procedure for concepts and mingens together with some preliminary experimental results about its performance.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berge, C.: Hypergraphs: Combinatorics of Finite Sets. North Holland, Amsterdam (1989)
Le Floc’h, A., Fisette, C., Missaoui, R., Valtchev, P., Godin, R.: Jen: un algorithme efficace de construction de générateurs pour l’identification des règles d’association. Numéro spécial de la revue des Nouvelles Technologies de l’Information 1(1), 135–146 (2003)
Ganter, B.: Two basic algorithms in concept analysis, preprint 831, Technische Hochschule, Darmstadt (1984)
Ganter, B., Wille, R.: Formal Concept Analysis. Mathematical Foundations. Springer, Heidelberg (1999)
Godin, R., Missaoui, R., Alaoui, H.: Incremental Concept Formation Algorithms Based on Galois (Concept) Lattices. Computational Intelligence 11(2), 246–267 (1995)
Guigues, J.L., Duquenne, V.: Familles minimales d’implications informatives résultant d’un tableau de données binaires. Mathématiques et Sciences Humaines 95, 5–18 (1986)
Kengue, J.F.D., Valtchev, P., Djamegni, C.T.: A parallel algorithm for lattice construction. In: Ganter, B., Godin, R. (eds.) ICFCA 2005. LNCS (LNAI), vol. 3403, pp. 249–264. Springer, Heidelberg (2005)
Kryszkiewicz, M., Gajek, M.: Concise representation of frequent patterns based on generalized disjunction-free generators. In: Chen, M.-S., Yu, P.S., Liu, B. (eds.) PAKDD 2002. LNCS (LNAI), vol. 2336, pp. 159–171. Springer, Heidelberg (2002)
Maier, D.: The theory of Relational Databases. Computer Science Press (1983)
Mannila, H., Räihä, K.-J.: On the complexity of inferring functional dependencies. Discrete Applied Mathematics 40(2), 237–243 (1992)
Pasquier, N.: Data Mining: Algorithmes d’extraction et de réduction des règles d’association dans les bases de données. Ph. d. thesis, Université Blaise Pascal,Clermont- Ferrand II (2000)
Pfaltz, J., Taylor, C.: Scientific discovery through iterative transformations of concept lattices. In: Proceedings of the 1st International Workshop on Discrete Mathematics and Data Mining, Washington, DC, USA, April 2002, pp. 65–74 (2002)
Stumme, G., Taouil, R., Bastide, Y., Pasquier, N., Lakhal, L.: Computing Iceberg Concept Lattices with Titanic. Data and Knowledge Engineering 42(2), 189–222 (2002)
Valtchev, P., Duquenne, V.: Towards scalable divide-and-conquer methods for computing concepts and implications. In: SanJuan, E., Berry, A., Sigayret, A., Napoli, A. (eds.) Proceedings of the 4th Intl. Conference Journées de l’Informatique Messine (JIM 2003): Knowledge Discovery and Discrete Mathematics, Metz (FR), September 3-6, pp. 3–14. INRIA (2003)
Valtchev, P., Rouane Hacene, M., Missaoui, R.: A generic scheme for the design of efficient on-line algorithms for lattices. In: Ganter, B., de Moor, A., Lex, W. (eds.) ICCS 2003. LNCS, vol. 2746, pp. 282–295. Springer, Heidelberg (2003)
Valtchev, P., Missaoui, R.: Building concept (Galois) lattices from parts: generalizing the incremental methods. In: Delugach, H.S., Stumme, G. (eds.) ICCS 2001. LNCS (LNAI), vol. 2120, pp. 290–303. Springer, Heidelberg (2001)
Valtchev, P., Missaoui, R., Godin, R.: Formal Concept Analysis for Knowledge Discovery and Data Mining: The New Challenges. In: Eklund, P. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, pp. 352–371. Springer, Heidelberg (2004)
Valtchev, P., Missaoui, R., Lebrun, P.: A partition-based approach towards building Galois (concept) lattices. Discrete Mathematics 256(3), 801–829 (2002)
Valtchev, P., Missaoui, R., Rouane-Hacene, M., Godin, R.: Incremental maintenance of association rule bases. In: Proceedings of the 2nd Workshop on Discrete Mathematics and Data Mining, San Francisco (CA), USA (May 2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Frambourg, C., Valtchev, P., Godin, R. (2005). Merge-Based Computation of Minimal Generators. In: Dau, F., Mugnier, ML., Stumme, G. (eds) Conceptual Structures: Common Semantics for Sharing Knowledge. ICCS 2005. Lecture Notes in Computer Science(), vol 3596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11524564_12
Download citation
DOI: https://doi.org/10.1007/11524564_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27783-5
Online ISBN: 978-3-540-31885-9
eBook Packages: Computer ScienceComputer Science (R0)