Synonyms
Frequent concepts; Rule bases
Definition
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...
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Bastide Y, Pasquier N, Taouil R, Stumme G, Lakhal L. Mining minimal non-redundant association rules using frequent closed itemsets. In: Proceedings of the 1st International Conference on Computational Logic; 2000. p. 972–86.
Calders T, Rigotti C, Boulicaut J-F. A survey on condensed representation for frequent sets. In: Boulicaut J-F, De Raedt L, Mannila H, editors. Constraint-based mining and inductive databases, LNCS, vol. 3848. Berlin: Springer; 2005. p. 64–80.
Ganter B, Wille R. Formal concept analysis: mathematical foundations. Berlin/Heidelberg/New York: Springer; 1999.
Goethals B, Zaki MJ. Advances in frequent itemset mining implementations: report on FIMI’03. SIGKDD Explor. 2003;6(1):109–17.
Guigues JL, Duquenne V. Familles minimales d'implications informatives resultant d'un tableau de donnees binaires. Math Sci Hum. 1986;24(95):5–18.
Luxenburger M. Implications partielles dans un contexte. Math Inf Sci Hum. 1991;29(113):35–55.
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.
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.
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.
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.
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.
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Zaki, M.J. (2018). Closed Itemset Mining and Nonredundant Association Rule Mining. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_66
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DOI: https://doi.org/10.1007/978-1-4614-8265-9_66
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