Abstract
The problem of the relevance and the usefulness of extracted association rules is of primary importance because, in the majority of cases, real-life databases lead to several thousands association rules with high confidence and among which are many redundancies. Using the closure of the Galois connection, we define two new bases for association rules which union is a generating set for all valid association rules with support and confidence. These bases are characterized using frequent closed itemsets and their generators; they consist of the non-redundant exact and approximate association rules having minimal antecedents and maximal consequents, i.e. the most relevant association rules. Algorithms for extracting these bases are presented and results of experiments carried out on real-life databases show that the proposed bases are useful, and that their generation is not time consuming.
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References
R. Agrawal, T. Imielinski, and A. Swami. Mining association rules between sets of items in large databases. Proc. SIGMOD conf., pp 207–216, May 1993.
R. Agrawal and R. Srikant. Fast algorithms for mining association rules in large databases. Proc. VLDB conf., pp 478–499, September 1994.
W. W. Armstrong. Dependency structures of data base relationships. Proc. IFIP congress, pp 580–583, August 1974.
R. J. Bayardo, R. Agrawal, and D. Gunopulos. Constraint-based rule mining in large, dense databases. Proc. ICDE conf., pp 188–197, March 1999.
R. J. Bayardo, and R. Agrawal. Mining the most interesting rules. Proc. KDD Conference, pp 145–154, August 1999.
C. Beeri, P. A. Bernstein. Computational problems related to the design of normal form relational schemas. Transactions on Database Systems, 4(1):30–59, 1979.
S. Brin, R. Motwani, and C. Silverstein. Beyond market baskets: Generalizing association rules to correlation. Proc. SIGMOD conf., pp 265–276, May 1997.
V. Duquenne and J.-L. Guigues. Famille minimale d’implications informatives résultant d’un tableau de données binaires. Mathématiques et Sciences Humaines, 24(95):5–18, 1986.
B. Ganter and R. Wille. Formal Concept Analysis: Mathematical foundations. Springer, 1999.
J. Han and Y. Fu. Discovery of multiple-level association rules from large databases. Proc. VLDB conf., pp 420–431, September 1995.
D. Heckerman. Bayesian networks for knowledge discovery. Advances in Knowledge Discovery and Data Mining, pp 273–305, 1996.
KMR+94._M. Klemettinen, H. Mannila, P. Ronkainen, H. Toivonen, and A. I. Verkamo. Finding interesting rules from large sets of discovered association rules. Proc. CIKM conf., pp 401–407, November 1994.
M. Luxenburger. Implications partielles dans un contexte. Mathématiques, Informatique et Sciences Humaines, 29(113):35–55, 1991.
D. Maier. Minimum covers in relational database model. Journal of the ACM, 27(4):664–674, 1980.
R. T. Ng, V. S. Lakshmanan, J. Han, and A. Pang. Exploratory mining and pruning optimizations of constrained association rules. Proc. SIGMOD conf., pp 13–24, June 1998.
N. Pasquier, Y. Bastide, R. Taouil, and L. Lakhal. Pruning closed itemset lattices for association rules. Proc. BDA conf., pp 177–196, Octobre 1998.
N. Pasquier, Y. Bastide, R. Taouil, and L. Lakhal. Efficient mining of association rules using closed itemset lattices. Information Systems, 24(1):25–46, 1999.
N. Pasquier, Y. Bastide, R. Taouil, and L. Lakhal. Discovering frequent closed itemsets for association rules. Proc. ICDT conf., LNCS 1540, pp 398–416, January 1999.
N. Pasquier, Y. Bastide, R. Taouil, and L. Lakhal. Closed set based discovery of small covers for association rules. Proc. BDA conf., pp 361–381, Octobre 1999.
G. Piatetsky-Shapiro and C. J. Matheus. The interestingness of deviations. AAAI KDD workshop, pp 25–36, July 1994.
A. Silberschatz and A. Tuzhilin. What makes patterns interesting in knowledge discovery systems. IEEE Transactions on Knowledge and Data Engineering, 8(6):970–974, December 1996.
C. Silverstein, S. Brin, and R. Motwani. Beyond market baskets: Generalizing association rules to dependence rules. Data Mining and Knowledge Discovery, 2(1):39–68, January 1998.
R. Srikant and R. Agrawal. Mining generalized association rules. Proc. VLDB conf., pp 407–419, September 1995.
R. Srikant, Q. Vu, and R. Agrawal. Mining association rules with item constraints. Proc. KDD conf., pp 67–73, August 1997.
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Bastide, Y., Pasquier, N., Taouil, R., Stumme, G., Lakhal, L. (2000). Mining Minimal Non-redundant Association Rules Using Frequent Closed Itemsets. In: Lloyd, J., et al. Computational Logic — CL 2000. CL 2000. Lecture Notes in Computer Science(), vol 1861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44957-4_65
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DOI: https://doi.org/10.1007/3-540-44957-4_65
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