Optimal Partitioning for Classification Trees

This paper introduces a unified method of choosing the most explanatory and significant multiway partitions for classification tree design and analysis. The method is derived based on the proportional-reduction-in-impurity(PRI) measure of association, which is proposed to extend the proportional-reduction-in-error(PRE) measure in the decision-theory context. For the method derivation, the PRI measure is analyzed to characterize its statistical distribution and association properties which are used to consistently handle the subjects of feature formation, feature selection, and feature deletion required in the associated classification tree construction. The PRI criterion is applied to a numerical problem for illustration.