Closed Itemset Mining and Nonredundant Association Rule Mining
Frequent concepts; Rule bases
Let I be a set of binary-valued attributes, called items. A set X ⊆ I is called an itemset. A transaction database D is a multiset of itemsets, where each itemset, called a transaction, has a unique identifier, called a tid. The support of an itemset X in a dataset D, denoted sup(X), is the fraction of transactions in D where X appears as a subset. X is said to be a frequent itemset in D if sup(X) ≥ minsup, where minsup is a user defined minimum support threshold. An (frequent) itemset is called closed if it has no (frequent) superset having the same support.
An association rule is an expression A ⇒ B, where A and B are itemsets, and A ∩ B =∅. The support of the rule is the joint probability of a transaction containing both A and B, given as sup(A ⇒ B) = P(A ∧ B) = sup(A ∪ B). The confidence of a rule is the conditional probability that a transaction contains B, given that it contains A, given as: \( conf\left(A\Rightarrow...
- 5.Guigues JL, Duquenne V. Familles minimales d'implications informatives resultant d'un tableau de donnees binaires. Math Sci Hum. 1986;24(95):5–18.Google Scholar
- 7.Pasquier N, Bastide Y, Taouil R, Lakhal L. Discovering frequent closed itemsets for association rules. In: Proceedings of the 7th International Conference on Database Theory; 1999. p. 398–416.Google Scholar
- 8.Pei J, Han J, Mao R. Closet: an efficient algorithm for mining frequent closed itemsets. In: Proceedings of the ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery; 2000. p.~21–30.Google Scholar
- 9.Zaki MJ. Generating non-redundant association rules. In: Proceedings of the 6th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining; 2000. p. 34–43.Google Scholar
- 10.Zaki MJ, Hsiao CJ. CHARM: an efficient algorithm for closed itemset mining. In: Proceedings of the SIAM International Conference on Data Mining; 2002. p. 457–73.Google Scholar
- 11.Zaki MJ, Ogihara M. Theoretical foundations of association rules. In: Proceedings of the ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery; 1998.Google Scholar