Closed-set-based Discovery of Bases of Association Rules

TL;DR

This paper revisits an existing algorithm for mining representative association rules, identifies its incompleteness, and proposes alternative complete methods and an improved basis for more concise rule representation.

Contribution

It corrects and extends a previous algorithm for association rule basis discovery, ensuring completeness and efficiency in rule representation.

Findings

The original Kryszkiewicz algorithm can be incomplete.

Proposed alternative generators are complete for mining representative rules.

Extended approach yields a smaller, closure-aware basis B*.

Abstract

The output of an association rule miner is often huge in practice. This is why several concise lossless representations have been proposed, such as the "essential" or "representative" rules. We revisit the algorithm given by Kryszkiewicz (Int. Symp. Intelligent Data Analysis 2001, Springer-Verlag LNCS 2189, 350-359) for mining representative rules. We show that its output is sometimes incomplete, due to an oversight in its mathematical validation. We propose alternative complete generators and we extend the approach to an existing closure-aware basis similar to, and often smaller than, the representative rules, namely the basis B*.