Generalizing Association Rules to Ordinal Rules

The development of good measures of interestingness of the discovered rules is one of the important problems in data mining. Such measures of interestingness are divided into objective measures : – those that depend only on the structure of a rule and the underlying data used in the discovery process, and the subjective measures – those that depend on the class of users who examine the rule. However, most objective measures are suitable for binary attributes and require an appropriate transformation of the initial set of attributes into binary attributes for all unsupervised usual algorithms for the discovery of association rules. As a result, the complexity of these algorithms increases exponentially with the number of attributes, and this transformation can lead us, on the one hand to a combinatorial explosion, and on the other hand to a prohibitive number of weakly significant rules with many redundancies. Moreover, the few measures suitable for numeric attributes, like for example correlation coefficient, are not selective. In this paper, we propose a new objective measure, called ordinal intensity of implication, which generalizes intensity of implication suitable for binary attributes and which evaluates whether the number of transactions not clearly verifying rule X→Y (i.e., the number of transactions containing a high value for attribute X and a low value for attribute Y) is significantly small as compared to a random draw. We finish the study with an evaluation on banking data and show some discovered ordinal rules, and connection between data / information and quality.