Granular association rules on two universes with four measures

Relational association rules reveal patterns hide in multiple tables. Existing rules are usually evaluated through two measures, namely support and confidence. However, these two measures may not be enough to describe the strength of a rule. In this paper, we introduce granular association rules with four measures to reveal connections between granules in two universes, and propose three algorithms for rule mining. An example of such a rule might be "40% men like at least 30% kinds of alcohol; 45% customers are men and 6% products are alcohol." Here 45%, 6%, 40%, and 30% are the source coverage, the target coverage, the source confidence, and the target confidence, respectively. With these measures, our rules are semantically richer than existing ones. Three subtypes of rules are obtained through considering special requirements on the source/target confidence. Then we define a rule mining problem, and design a sandwich algorithm with different rule checking approaches for different subtypes. Experiments on a real world dataset show that the approaches dedicated to three subtypes are 2-3 orders of magnitudes faster than the one for the general case. A forward algorithm and a backward algorithm for one particular subtype can speed up the mining process further. This work opens a new research trend concerning relational association rule mining, granular computing and rough sets.