Abstract
Frequent closures (FCIs) and generators (FGs) as well as the precedence relation on FCIs are key components in the definition of a variety of association rule bases. Although their joint computation has been studied in concept analysis, no scalable algorithm exists for the task at present. We propose here to reverse a method from the latter field using a fundamental property of hypergraph theory. The goal is to extract the precedence relation from a more common mining output, i.e. closures and generators. The resulting order computation algorithm proves to be highly efficient, benefiting from peculiarities of generator families in typical mining datasets. Due to its genericity, the new algorithm fits an arbitrary FCI/FG-miner.
This is a preview of subscription content, log in via an institution to check access.
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
Agrawal, R., Srikant, R.: Fast Algorithms for Mining Association Rules in Large Databases. In: Proc. of the 20th Intl. Conf. on Very Large Data Bases (VLDB 1994), pp. 487–499. Morgan Kaufmann Publishers Inc., San Francisco (1994)
Kryszkiewicz, M.: Concise Representations of Association Rules. In: Proc. of the ESF Exploratory Workshop on Pattern Detection and Discovery, pp. 92–109 (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)
Pasquier, N., Bastide, Y., Taouil, R., Lakhal, L.: Discovering Frequent Closed Itemsets for Association Rules. In: Beeri, C., Bruneman, P. (eds.) ICDT 1999. LNCS, vol. 1540, pp. 398–416. Springer, Heidelberg (1998)
Zaki, M.J., Hsiao, C.J.: Efficient Algorithms for Mining Closed Itemsets and Their Lattice Structure. IEEE Transactions on Knowledge and Data Engineering 17(4), 462–478 (2005)
Carpineto, C., Romano, G.: Concept Data Analysis: Theory and Applications. John Wiley & Sons, Ltd., Chichester (2004)
Pfaltz, J.L.: Incremental Transformation of Lattices: A Key to Effective Knowledge Discovery. In: Corradini, A., Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2002. LNCS, vol. 2505, pp. 351–362. Springer, Heidelberg (2002)
Nehme, K., Valtchev, P., Rouane, M.H., Godin, R.: On Computing the Minimal Generator Family for Concept Lattices and Icebergs. In: Ganter, B., Godin, R. (eds.) ICFCA 2005. LNCS (LNAI), vol. 3403, pp. 192–207. Springer, Heidelberg (2005)
Nourine, L., Raynaud, O.: A fast algorithm for building lattices. Inf. Process. Lett. 71(5–6), 199–204 (1999)
Eiter, T., Gottlob, G.: Identifying the Minimal Transversals of a Hypergraph and Related Problems. SIAM Journal on Computing 24(6), 1278–1304 (1995)
Bastide, Y., Taouil, R., Pasquier, N., Stumme, G., Lakhal, L.: Mining frequent patterns with counting inference. SIGKDD Explor. Newsl. 2(2), 66–75 (2000)
Ganter, B., Wille, R.: Formal concept analysis: mathematical foundations, p. 284. Springer, Heidelberg (1999)
Calders, T., Rigotti, C., Boulicaut, J.F.: A Survey on Condensed Representations for Frequent Sets. In: Boulicaut, J.-F., De Raedt, L., Mannila, H. (eds.) Constraint-Based Mining and Inductive Databases. LNCS (LNAI), vol. 3848, pp. 64–80. Springer, Heidelberg (2006)
Pasquier, N.: Mining association rules using formal concept analysis. In: Proc. of the 8th Intl. Conf. on Conceptual Structures (ICCS 2000), August 2000, pp. 259–264. Shaker-Verlag (2000)
Pfaltz, J.L., Taylor, C.M.: Scientific Knowledge Discovery through Iterative Transformation of Concept Lattices. In: Proc. of the Workshop on Discrete Applied Mathematics in conjunction with the 2nd SIAM Intl. Conf. on Data Mining, Arlington, VA, USA, pp. 65–74 (2002)
Berge, C.: Hypergraphs: Combinatorics of Finite Sets. North Holland, Amsterdam (1989)
Szathmary, L., Napoli, A., Kuznetsov, S.O.: ZART: A Multifunctional Itemset Mining Algorithm. In: Proc. of the 5th Intl. Conf. on Concept Lattices and Their Applications (CLA 2007), Montpellier, France, October 2007, pp. 26–37 (2007)
Szathmary, L., Valtchev, P., Napoli, A., Godin, R.: An Efficient Hybrid Algorithm for Mining Frequent Closures and Generators. In: Proc. of the 6th Intl. Conf. on Concept Lattices and Their Applications (CLA 2008), Olomouc, Czech Republic (accepted, 2008)
Szathmary, L.: Symbolic Data Mining Methods with the Coron Platform. PhD Thesis in Computer Science, Univ. Henri Poincaré – Nancy 1, France (November 2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer Berlin Heidelberg
About this paper
Cite this paper
Szathmary, L., Valtchev, P., Napoli, A., Godin, R. (2008). Constructing Iceberg Lattices from Frequent Closures Using Generators. In: Jean-Fran, JF., Berthold, M.R., Horváth, T. (eds) Discovery Science. DS 2008. Lecture Notes in Computer Science(), vol 5255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88411-8_15
Download citation
DOI: https://doi.org/10.1007/978-3-540-88411-8_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88410-1
Online ISBN: 978-3-540-88411-8
eBook Packages: Computer ScienceComputer Science (R0)