On the mining of substitution rules for statistically dependent items

In this paper a new mining capability, called mining of substitution rules, is explored. A substitution refers to the choice made by a customer to replace the purchase of items with that of others. The process of mining substitution rules can be decomposed into two procedures. The first identifies concrete itemsets among a large number of frequent itemsets, where a concrete itemset is a frequent itemset whose items are statistically dependent. The second is substitution rule generation. Two concrete itemsets X and Y form a substitution rule, denoted by X ▵ Y to mean that X is a substitute for Y if and only if X and Y are negatively correlated and the negative association rule X → Y~ exists. We derive theoretical properties for the model of substitution rule mining. Then, in light of these properties, the SRM algorithm (substitution rule mining) is designed and implemented to discover substitution rules efficiently while attaining good statistical significance. Empirical studies are performed to evaluate the performance of the SRM algorithm. It is shown that SRM produces substitution rules of very high quality.