Studying the Behavior of Generalized Entropy in Induction Trees Using a M-of-N Concept

This paper study splitting criterion in decision trees using three original points of view. First we propose a unified formalization for association measures based on entropy of type beta. This formalization includes popular measures such as Gini index or Shannon entropy. Second, we generate artificial data from M-of-N concepts whose complexity and class distribution are controlled. Third, our experiment allows us to study the behavior of measures on datasets of growing complexity. The results show that the differences of performances between measures, which are significant when there is no noise in the data, disappear when the level of noise increases.