A Theoretical Framework for Association Mining based on the Boolean Retrieval Model

Data mining has been defined as the non- trivial extraction of implicit, previously unknown and potentially useful information from data. Association mining is one of the important sub-fields in data mining, where rules that imply certain association relationships among a set of items in a transaction database are discovered. The efforts of most researchers focus on discovering rules in the form of implications between itemsets, which are subsets of items that have adequate supports. Having itemsets as both antecedent and precedent parts was motivated by the original application pertaining to market baskets and they represent only the simplest form of predicates. This simplicity is also due in part to the lack of a theoretical framework that includes more expressive predicates. The framework we develop derives from the observation that information retrieval and association mining are two complementary processes on the same data records or transactions. In information retrieval, given a query, we need to find the subset of records that matches the query. In contrast, in data mining, we need to find the queries (rules) having adequate number of records that support them. In this paper we introduce the theory of association mining that is based on a model of retrieval known as the Boolean Retrieval Model. The potential implications of the proposed theory are presented.