Pattern mining is a fundamental problem in data mining. The problem is to find all the patterns appearing in the given database frequently. For a set E D f1; : : : ; ng of items, an itemset (also called a pattern) is a subset of E. Let D be a given database composed of transactions R1; : : : ; Rm, Ri E. For an itemset P , an occurrence of P is a transaction of D such that P R, and the occurrence set Occ.P / is the set of occurrences of P . The frequency of P , also called support, is jOcc.P /j and denoted by frq.P /. For a given constant called minimum support, an itemset P is frequent if frq.P / . For given a database and a minimum support, frequent itemset mining is the problem of enumerating all frequent itemsets in D.
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