Knowledge Discovery in Databases: The Search for Frequent Patterns

Definition 1.1.2 Let R be a set and r a 0/1 relation over R, and let X ⊆ R be a set of items. The item set X matches a transaction t ∈ r, if X ⊆ t, we also say that t supports X. The (multi) set of transactions in r matched by X is the support ofX, denoted by suppr(X), i.e., suppr(X) = {t ∈ r X ⊆ t}. The frequency of X in r, denoted by fr(X, r), is |suppr(X)| |r| . We write simply supp(X) and fr(X) if the database is unambiguous in the context. Given a frequency threshold min_fr ∈ [0, 1], the set X is frequent1 if fr(X, r) ≥ min_fr.