Towards a unifying probabilistic implicative normalized quality measure for association rules

Abstract

We define the so-called normalized probabilistic quality measures (PQM) for association rules; that is, PQMs whose values lay between minus one and plus one, and which take into account reference situations such as incompatibility, repulsion, independence, attraction, and logical implication, between the antecedent and the consequent of association rules. Moreover, we characterize the PQMs that can be normalized and propose a way to normalize them. On the other hand, we consider a normalized and implicative PQM called MGK. It appears that MGK is the normalized PQM associated to most of the PQMs proposed in the literature. Furthermore, it satisfies additional properties, including Piatetsky-Shapiro's principles and Freitas's. © Springer-Verlag Berlin Heidelberg 2007.