Using Pairs of Data-Points to Define Splits for Decision Trees

CART either split the data using axis-aligned hyperplanes or they perform a computationally expensive search in the continuous space of hyperplanes with unrestricted orientations. We show that the limitations of the former can be overcome without resorting to the latter. For every pair of training data-points, there is one hyperplane that is orthogonal to the line joining the data-points and bisects this line. Such hyperplanes are plausible candidates for splits. In a comparison on a suite of 12 datasets we found that this method of generating candidate splits outperformed the standard methods, particularly when the training sets were small. 1 Introduction Binary decision trees come in many flavours, but they all rely on splitting the set of k-dimensional data-points at each internal node into two disjoint sets.