Concise Representations of Association Rules

Abstract

Strong association rules are one of basic types of knowledge. The number of rules is often huge, which limits their usefulness. Applying concise rule representations with appropriate inference mechanisms can lessen the problem. Ideally, a rule representation should be lossless (should enable derivation of all strong rules), sound (should forbid derivation of rules that are not strong) and informative (should allow determination of rules’ support and confidence). In the paper, we overview the following lossless representations: representative rules, Duquenne- Guigues basis, proper basis, Luxenburger basis, structural basis, minimal non-redundant rules, generic basis, informative basis and its transitive reduction. For each representation, we examine whether it is sound and informative. For the representations that are not sound, we discuss ways of turning them into sound ones. Some important theoretical results related to the relationships among the representations are offered as well.