Mining Interesting Disjunctive Association Rules from Unfrequent Items

In most approaches to mining association rules, interestingness relies on frequent items, i.e., rules are built using items that frequently occur in the transactions. However, in many cases, data sets contain unfrequent items that can reveal useful knowledge that most standard algorithms fail to mine. For example, if items are products, it might be that each of the products \(p_1\) and \(p_2\) does not sell very well (i.e., none of them appears frequently in the transactions) but, that selling products \(p_1\) or \(p_2\) is frequent (i.e., transactions containing \(p_1\) or \(p_2\) are frequent). Then, assuming that \(p_1\) and \(p_2\) are similar enough with respect to a given similarity measure, the set \(\{p_1, p_2\}\) can be considered for mining relevant rules of the form \(\{p_1, p_2\} \rightarrow \{p_3, p_4\}\) (assuming that \(p_3\) and \(p_4\) are unfrequent similar products such that \(\{p_3,p_4\}\) is frequent), meaning that most of customers buying \(p_1\) or \(p_2\), also buy \(p_3\) or \(p_4\). The goal of our work is to mine association rules of the form \(D_1 \rightarrow D_2\) such that \((i)\) \(D_1\) and \(D_2\) are disjoint homogeneous frequent itemsets made up with unfrequent items, and \((ii)\) the support and the confidence of the rule are respectively greater than or equal to given thresholds. The main contributions of this paper towards this goal are to set the formal definitions, properties and algorithms for mining such rules.