An algebraic semigroup method for discovering maximal frequent itemsets

Abstract Discovering maximal frequent itemsets is an important issue and key technique in many data mining problems such as association rule mining. In the literature, generating proves either to be NP-hard or have O ( l 3 4 m + n ) O\left({l}^{3}{4}^{l}\left(m+n)) complexity worst case from perspective of complete bipartite graphs a graph, where m , n are item number transaction number, respectively, l denotes maximum ∣ C Ψ / − 1 | C| \Psi \left(C)| \hspace{0.1em}\text{/}\hspace{0.1em}\left(| +| -1) with taken over all C . this article, we put forward method for discovering itemsets, whose 2 β O\left(3mn{2}^{\beta }+{4}^{\beta }n) lower than known both case, semigroup algebra, \beta items support more minimum threshold. Experiments also show that algorithm based on algebraic performs better other three well-known algorithms. Meanwhile, explore some properties respect transactions, prove exactly simplified generators give necessary sufficient condition i i+1 -frequent itemset being subset closed i itemset, provide recurrence formula itemsets.