Classification trees with bivariate splits

摘要

We extend the recursive partitioning approach to classifier learning to use more complex types of split at each decision node. The new split types we permit are bivariate and can thus be interpreted visually in plots and tables. In order to find optimal splits of these new types, a new split criterion is introduced that allows the development of divide-and-conquer type algorithms. Two experiments are presented in which the bivariate trees—both with the Gini split criterion and with the new split criterion—are compared to a traditional tree-growing procedure. With the Gini criterion, the bivariate trees show a slight improvement in predictive accuracy and a considerable improvement in tree size over univariate trees. Under the new split criterion, accuracy is also improved, but there is no consistent improvement in tree size.