Analysis of monotonicity properties of some rule interestingness measures

One of the crucial problems in the field of knowledge discovery is development of good interestingness measures for evaluation of the discovered patterns. In this paper, we consider quantitative, objective interestingness measures for "if..., then..." association rules. We focus on three popular interestingness measures, namely rule interest function of Piatetsky-Shapiro, gain measure of Fukuda et al., and dependency factor used by Pawlak. We verify whether they satisfy the valuable property M of monotonic dependency on the number of objects satisfying or not the premise or the conclusion of a rule, and property of hypothesis symmetry (HS). Moreover, analytically and through experiments we show an interesting relationship between those measures and two other commonly used measures of rule support and anti-support.