Incremental Maintenance of Association Rule Bases

Association rule mining from transaction databases (TDB) is a classical data mining task, whereby the most computationally intensive step is the detection of frequently occurring patterns, called frequent itemsets (FIs), from which the rules are further extracted. The number of FIs may be potentially large, leading to an even greater number of rules. Approaches based on closure operators, Galois conections and Galois (concept) lattices have been proposed in an attempt to reduce the size of the resulting rule set. Thus, the search for frequent patterns has been limited to closed itemsets, while looking for a representative and reduced set of association rules, called a basis, which nevertheless conveys all the relevant information. In thess approaches, the minimal generators of a closed itemset play a key role for the itemset/rule construction. In our paper, we present a straightforward method for the maintenance of an association rule basis when a new transaction is added to the TDB. To that end, we utilize results on the incremental update of lattices and extend them with new properties to form a complete framework for association rule base maintenance. In particular, we define a simple and efficient method for on-line computation of the generators for closed itemsets and show how its output is used in the update of the rule basis.