Rank discrimination measures for enforcing monotonicity in decision tree induction

Monotone classification is a relatively recent topic in machine learning in which the classification function to learn is asked to guarantee a sort of monotonicity of the class with respect to attribute values. Nevertheless, real datasets are quite far from being monotone and this can sharply limit the performance of purely monotone classifiers while standard classifiers are simply insensitive to monotonicity. Here we focus on rank discrimination measures to be used in decision tree induction, i.e., functions able to measure the discrimination power of an attribute with respect to the class taking into account the monotonicity of the class with respect to the attribute. Three new measures are studied in detail and a hierarchical construction model is derived allowing the formal definition of a general rank discrimination measure. Our measures have been compared with other well-known proposals, quantifying both the accuracy and the monotonicity of the resulting binary decision tree classifiers.