Abstract
Association rules are used to investigate large databases. The analyst is usually confronted with large lists of such rules and has to find the most relevant ones for his purpose. Based on results about knowledge representation within the theoretical framework of Formal Concept Analysis, we present relatively small bases for association rules from which all rules can be deduced. We also provide algorithms for their calculation.1
This paper is a revised and extended version of a presentation given at the workshop “Bases de Données Avancées”, Bordeaux, France, 1999 [29], and of the technical report [37].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Reference
R. Agrawal, T. Imielinski, A. Swami. Mining association rules between sets of items in large databases. Proc. SIGMOD Conf., 1993, 207–216
R. Agrawal and R. Srikant. Fast algorithms for mining association rules. Proc. VLDB Conf., 1994, 478–499 (Expanded version in IBM Report RJ9839)
F. Baader, R. Molitor: Building and structuring Description Logic knowledge bases using least common subsumers and Concept Analysis. In: B. Ganter, G. W. Mineau (eds.): Conceptual Structures: Logical, Linguistic, and Computational Issues. Proc. ICCS 2000. LNAI 1867, Springer, Heidelberg 2000, 292–305
E. Baralis and G. Psaila. Designing templates for mining association rules. Journal of Intelligent Information Systems 9(1), 1997, 7–32
Y. Bastide, N. Pasquier, R. Taouil, G. Stumme, L. Lakhal: Mining minimal nonredundant association rules using frequent closed itemsets. In: J. Lloyd, V. Dahl, U. Furbach, M. Kerber, K.-K. Lau, C. Palamidessi, L. M. Pereira, Y. Sagiv, P. J. Stuckey (Eds.): Computational Logic-CL 2000. Proc. 1st Intl. Conf. on CL (6th Intl. Conf. on Database Systems). LNAI 1861, Springer, Heidelberg 2000, 972–986
Y. Bastide, R. Taouil, N. Pasquier, G. Stumme, L. Lakhal: Mining Frequent Patterns with Counting Inference. SIGKDD Explorations 2(2), Special Issue on Scalable Algorithms, 2000, 66–75
R. J. Bayardo. Efficiently mining long patterns from databases. Proc. SIGMOD Conf., 1998, 85–93
R. J. Bayardo, R. Agrawal, D. Gunopulos. Constraint-based rule mining in large, dense databases. Proc. ICDE Conf., 1999, 188–197
K. Becker, G. Stumme, R. Wille, U. Wille, M. Zickwolff: Conceptual Information Systems discussed through an IT-security tool. In: R. Dieng, O. Corby (Eds.): Knowledge Engineering and Knowledge Management. Methods, Models, and Tools. Proc. EKAW’ 00. LNAI 1937, Springer, Heidelberg 2000, 352–365
S. Brin, R. Motwani, C. Silverstein: Beyond market baskets: Generalizing association rules to correlation. Proc. SIGMOD Conf., 1997, 265–276
S. Brin, R. Motwani, J. D. Ullman, S. Tsur: Dynamic itemset counting and implication rules for market basket data. Proc. SIGMOD Conf., 1997, 255–264
V. Duquenne, J.-L. Guigues: Famille minimale d’implication informatives résultant d’un tableau de données binaires. Mathématiques et Sciences Humaines 24(95), 1986, 5–18
U. M. Fayyad, G. Piatetsky-Shapiro, P. Smyth, R. Uthurusamy (eds.): Advances in knowledge discovery and data mining. AAAI Press, Cambridge 1996
B. Ganter, K. Reuter: Finding all closed sets: A general approach. Order. Kluwer Academic Publishers, 1991, 283–290
B. Ganter, R. Wille: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg 1999
A. Grosskopf and G. Harras: Eine TOSCANA-Anwendung für Sprechaktverben des Deutschen. In: G. Stumme and R. Wille (eds.), Begriffliche Wissensverarbeitung: Methoden und Anwendungen. Springer, Berlin-Heidelberg-New York 2000.
J. Han, Y. Fu: Discovery of multiple-level association rules from large databases. Proc. VLDB Conf., 1995, 420–431 1995.
J. Hereth, G. Stumme, U. Wille, R. Wille: Conceptual Knowledge Discovery and Data Analysis. In: B. Ganter, G. W. Mineau (eds.): Conceptual Structures: Logical, Linguistic, and Computational Issues. Proc. ICCS 2000. LNAI 1867, Springer, Heidelberg 2000, 421–437
J. Hipp, A. Myka, R. Wirth, U. Güntzer: A new algorithm for faster mining of generalized association rules. LNAI 1510, Springer, Heidelberg 1998
U. Kaufmann: Begriffliche Analyse über Flugereignisse-Implementierung eines Erkundungs-und Analysesystems mit TOSCANA. Diplomarbeit, FB4, TU Darmstadt 1996.
M. Klemettinen, H. Mannila, P. Ronkainen, H. Toivonen, A. I. Verkamo: Finding interesting rules from large sets of discovered association rules. Proc. CIKM Conf., 1994, 401–407
M. Luxenburger: Implications partielles dans un contexte. Mathématiques, Informatique et Sciences Humaines, 29(113), 1991, 35–55
M. Luxenburger: Partial implications. Part I of Implikationen, Abhängigkeiten und Galois Abbildungen. PhD thesis, TU Darmstadt. Shaker, Aachen 1993
H. Mannila, H. Toivonen: Multiple uses of frequent sets and condensed representations (Extended abstract). Proc. KDD 1996, 189–194
R. Meo, G. Psaila, S. Ceri: A new SQL-like operator for mining association rules. Proc. VLDB Conf., 1996, 122–133
R. T. Ng, V. S. Lakshmanan, J. Han, A. Pang: Exploratory mining and pruning optimizations of constrained association rules. Proc. SIGMOD Conf., 1998, 13–24
N. Pasquier: Data Mining: algorithmes d’extraction et de réduction des régles d’association dans les bases de données. PhD thesis. Université Blaise Pascal, Clermont-Ferrand II, 2000
N. Pasquier, Y. Bastide, R. Taouil, L. Lakhal: Pruning closed itemset lattices for association rules. Proc. 14iémes Journées Bases de Données Avancées (BDA’98), Hammamet, Tunisie, 177–196
N. Pasquier, Y. Bastide, R. Taouil, L. Lakhal: Closed set based discovery of small covers for association rules. Proc. 15émes Journées Bases de Données Avancées, Bordeaux, France, 25-27 October 1999, 361–381
N. Pasquier, Y. Bastide, R. Taouil, L. Lakhal: Discovering frequent closed itemsets for association rules. Proc. ICDT Conf., 1999, 398–416
N. Pasquier, Y. Bastide, R. Taouil, L. Lakhal: Efficient mining of association rules using closed itemset lattices. Journal of Information Systems, 24(1), 1999, 25–46
J. Pei, J. Han, R. Mao:CLOSET: An efficient algorithm for mining frequent closed itemsets. Proc. ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery2000, 21–30
M. Roth-Hintz, M. Mieth, T. Wetter, S. Strahringer, B. Groh, R. Wille: Investgating SNOMED by Formal Concept Analysis. Preprint, FB4, TU Darmstadt 1997.
R. Srikant, R. Agrawal: Mining generalized association rules. Proc. VLDB Conf., 1995, 407–419
R. Srikant, Q. Vu, R. Agrawal: Mining association rules with item constraints. Proc. KDD Conf., 1997, 67–73
G. Stumme, R. Wille, U. Wille: Conceptual Knowledge Discovery in Databases Using Formal Concept Analysis Methods. In: J. M. Żytkow, M. Quafofou (eds.): Principles of Data Mining and Knowledge Discovery. Proc. 2nd European Symposium on PKDD’98, LNAI 1510, Springer, Heidelberg 1998, 450–458
G. Stumme: Conceptual Knowledge Discoverywith Frequent Concept Lattices. FB4-Preprint 2043, TU Darmstadt 1999
G. Stumme, R. Taouil, Y. Bastide, N. Pasquier, L. Lakhal: Fast Computation of Concept Lattices Using Data Mining Techniques. Proc. 7th Intl. Workshop on Knowledge Representation Meets Databases, Berlin, 21 22. August 2000. CEUR-Workshop Proceeding. http://sunsite.informatik.rwthaachen. de/Publications/CEUR-WS/
G. Stumme, R. Taouil, Y. Bastide, N. Pasquier, L. Lakhal: Computing Iceberg Concept Lattices with Titanic. J. on Knowledge and Data Engineering. (submitted)
F. Vogt, R. Wille: TOSCANA-A graphical tool for analyzing and exploring data. LNCS 894, Springer, Heidelberg 1995, 226–233
R. Wille: Restructuring lattice theory: an approach based on hierarchies of concepts. In: I. Rival (ed.). Ordered sets. Reidel, Dordrecht-Boston 1982, 445–470
M. J. Zaki, M. Ogihara: Theoretical Foundations of Association Rules, 3rd SIGMOD’ 98 Workshop on Research Issues in Data Mining and Knowledge Discovery (DMKD), Seattle, WA, June 1998, 7:1–7:8
M. J. Zaki, C.-J. Hsiao: ChARM: An efficient algorithm for closed association rule mining. Technical Report 99-10, Computer Science Dept., Rensselaer Polytechnic Institute, October 1999
M. J. Zaki: Generating non-redundant association rules. Proc. KDD 2000. 34–43
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Stumme, G., Taouil, R., Bastide, Y., Pasquier, N., Lakhal, L. (2001). Intelligent Structuring and Reducing of Association Rules with Formal Concept Analysis. In: Baader, F., Brewka, G., Eiter, T. (eds) KI 2001: Advances in Artificial Intelligence. KI 2001. Lecture Notes in Computer Science(), vol 2174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45422-5_24
Download citation
DOI: https://doi.org/10.1007/3-540-45422-5_24
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42612-7
Online ISBN: 978-3-540-45422-9
eBook Packages: Springer Book Archive