Efficient Construction of Regression Trees with Range and Region Splitting

We propose a method for constructing regression trees with range and region splitting. We present an efficient algorithm for computing the optimal two-dimensional region that minimizes the mean squared error of an objective numeric attribute in a given database. As two-dimensional regions, we consider a class R of grid-regions, such as x-monotone, rectilinear-convex, and rectangular, in the plane associated with two numeric attributes. We compute the optimal region R. We propose to use a test that splits data into those that lie inside the region R and those that lie outside the region in the construction of regression trees. Experiments confirm that the use of region splitting gives compact and accurate regression trees in many domains.