Two-stage Constructing Hyper-plane for Each Test Node of Decision Tree

How to construct the "appropriate" split hyper-plane in test nodes is the key of building decision trees. Unlike a univariate decision tree, a multivariate (oblique) decision tree could find the hyper-plane that is not orthogonal to the features' axes. In this paper, we re-explain the process of building test nodes in terms of geometry. Based on this, we propose a method of learning the hyper-plane with two stages. The tree (TSDT) induced in this way keeps the interpretability of univariate decision trees and the trait of multivariate decision trees which could find oblique hyper-plane. The tests of the impact of Combination methods tell us that TSDT based combination algorithm is much better than other tree based combination methods in accuracy.