Representative Association Rules and Minimum Condition Maximum Consequence Association Rules

Discovering association rules (AR) among items in a large database is an important database mining problem. The number of association rules may be large. To alleviate this problem, we introduced in [1] a notion of representative association rules (RR). RR is a least set of rules that covers all association rules. The association rules, which are not representative ones, may be generated by means of a cover operator without accessing a database. On the other hand, a subset of association rules that allows to predict as much as possible from minimum facts is ~ l y of interest to analysts, This kind of rules we will call minimum condition maximum consequence rules (M~R). In this paper, we investigate the relationship between RR andM3AR. We prove that MMR is a subset of RR and it may be extracted from RR. I I n t r o d u c t i o n Discovering association rules (AR) among items in large databases is recognized as an important database mining problem. The problem was introduced in [2] for sales transaction database. The association rules identify sets of items that are purchased together with other sets of items. For example, an association rule may state that 90% of customers who buy butter and bread buy also milk. Several extensions of the notion of an association rule were offered in the literaatre (see e.g. [3-4]). One of such extensions is a generalized rule that can be discovered from a taxonomic database [3]. Applications for association rules range from decision support to telecommunications alarm diagnosis and prediction [5-6]. The number of association roles is usually large. A user should not be presented with all of them, but rather with these which are original, novel, interesting. There were proposed several definitions of what is an interesting association rule (see e.g. [3,7]). In particular, pruning out uninteresting rules which exploits the information in taxonomies seems to be quite useful (resulting in the rule number reduction amounting to 60% [31). The interestingness of a ride is usually expressed by some quantitative measure.