A novel algorithm to optimize classification trees

Breiman et al. (1984) expounded a method called Classification and Regression Trees, or CART, which is of use for nonparametric discrimination and regression. In this paper we present an algorithm which is able to increase the quality of classification trees beyond the quality of trees, which are based on direct evaluation of a splitting criterion. The novel algorithm calculates a large number of possible segments of trees instead of a single tree, and recursively selects the best of these parts to form an optimal tree. The presented method makes use of a (and works for an arbitrary) splitting criterion. But the criterion is only used to speed up the algorithm, not to determine directly the resulting tree. It includes the evaluation of trees resulting from direct splitting as a special case. Examples are given.