A CART extention using Quadratic Decision Borders

In this article we put forward an extention to the hierarchical CART classification method which uses quadratic decision borders. The original CART applies univariate splits on individual variables as well as splits on combinations of variables to recursively partition the feature-space into subsets which are successively more class-homogeneous.

Guided by the fact that class-distributions in feature-space are very often hyper-elliptical shaped, we give an extension to the original CART which also uses quadratic shaped decision borders which can be modelled by a mean-vector and a dispersion matrix. We propose a scheme for finding a good starting guess for a quadratic decision border, and a scheme for subsequently improving the guess, through adjustments of the size and shape of the decision border.