Visualizing the behavior and some symmetry properties of Bayesian confirmation measures

Bayesian confirmation measures, a special class of interestingness measures, are functions usually adopted in ranking inductive rules generated by data mining methods such as association rule mining, decision trees, rough sets. Till now a plethora of measures have been defined in many different ways. Identifying and effectively distinguishing among them is a difficult task. In this paper we propose a unified visual approach aimed at comparing and classifying a large subset of Bayesian confirmation measures (those satisfying the initial and final probability dependence condition). We first reduce the set of variables in their analytical expression to only two, thus allowing to draw their contour lines on the plane. We observe that two dimensional contour lines plots represent a sort of fingerprints of the confirmation measures and, therefore, this geometric visualization can be used as an effective tool in order to investigate properties and behavior of the measures. We highlight the potential of this approach not only to study known measures but also in order to invent new measures satisfying given required characteristics. We finally define, following the geometry of the plots, a new set of symmetry properties of confirmation measures and describe geometrically four classical symmetries.