Finding all closed frequent itemsets is a key step of association rule mining since the non-redundant association rule can be inferred from all the closed frequent itemsets. In this paper we present a new method for finding closed frequent itemsets based on attribute value lattice. In the new method, we argue that vertical data representation and attribute value lattice can find all closed frequent itemsets efficiently, thus greatly improve the efficiency of association rule mining algorithm. We discuss how these techniques and methods are applied to find closed frequent itemsets. In our method, the data are represented vertically; each frequent attribute value is associated with its granule, which is represented as a hybrid bitmap. Based on the partial order defined between the attribute values among the databases, an attribute value lattice is constructed, which is much smaller compared with the original databases. Instead of searching all the items in the databases, which is adopted by almost all the association rule algorithms to find frequent itemsets, our method only searches the attribute-value lattice. A bottom-up breadth-first approach is employed to search the attribute value lattice to find the closed frequent itemsets.
An attribute value, in a relational model, is a meaningful label of a collection of objects; the collection is referred to as a granule of the universe of discourse. The granule itself can be regarded a label of the collection (granule); it will be referred to as the canonical name of the granule. A relational model using these canonical names themselves as attribute values (their bit patterns or lists of members) is called a machine oriented data model. For moderate size databases, finding association rules, decision rules, and etc., are reduced to easy computation of set theoretical operations of these collections. In this paper, a very fast computing algorithm is presented.