Decision Trees Using the Minimum Entropy-of-Error Principle

Abstract

Binary decision trees based on univariate splits have traditionally employed so-called impurity functions as a means of searching for the best node splits. Such functions use estimates of the class distributions. In the present paper we introduce a new concept to binary tree design: instead of working with the class distributions of the data we work directly with the distribution of the errors originated by the node splits. Concretely, we search for the best splits using a minimum entropy-of-error (MEE) strategy. This strategy has recently been applied in other areas (e.g. regression, clustering, blind source separation, neural network training) with success. We show that MEE trees are capable of producing good results with often simpler trees, have interesting generalization properties and in the many experiments we have performed they could be used without pruning.