Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Closed Itemset Mining and Nonredundant Association Rule Mining

  • Mohammed J. ZakiEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_66


Frequent concepts; Rule bases


Let I be a set of binary-valued attributes, called items. A set XI 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 AB, where A and B are itemsets, and AB =∅. The support of the rule is the joint probability of a transaction containing both A and B, given as sup(AB) = P(AB) = sup(AB). 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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Rensselaer Polytechnic InstituteTroyUSA

Section editors and affiliations

  • Jian Pei
    • 1
  1. 1.School of Computing ScienceSimon Fraser Univ.BurnabyCanada