An information-theoretic approach to quantitative association rule mining

Quantitative association rule (QAR) mining has been recognized an influential research problem over the last decade due to the popularity of quantitative databases and the usefulness of association rules in real life. Unlike boolean association rules (BARs), which only consider boolean attributes, QARs consist of quantitative attributes which contain much richer information than the boolean attributes. However, the combination of these quantitative attributes and their value intervals always gives rise to the generation of an explosively large number of itemsets, thereby severely degrading the mining efficiency. In this paper, we propose an information-theoretic approach to avoid unrewarding combinations of both the attributes and their value intervals being generated in the mining process. We study the mutual information between the attributes in a quantitative database and devise a normalization on the mutual information to make it applicable in the context of QAR mining. To indicate the strong informative relationships among the attributes, we construct a mutual information graph (MI graph), whose edges are attribute pairs that have normalized mutual information no less than a predefined information threshold. We find that the cliques in the MI graph represent a majority of the frequent itemsets. We also show that frequent itemsets that do not form a clique in the MI graph are those whose attributes are not informatively correlated to each other. By utilizing the cliques in the MI graph, we devise an efficient algorithm that significantly reduces the number of value intervals of the attribute sets to be joined during the mining process. Extensive experiments show that our algorithm speeds up the mining process by up to two orders of magnitude. Most importantly, we are able to obtain most of the high-confidence QARs, whereas the QARs that are not returned by MIC are shown to be less interesting.