Linear components of quadratic classifiers

Abstract

We obtain a decomposition of any quadratic classifier in terms of products of hyperplanes. These hyperplanes can be viewed as relevant linear components of the quadratic rule (with respect to the underlying classification problem). As an application, we introduce the associated multidirectional classifier; a piecewise linear classification rule induced by the approximating products. Such a classifier is useful to determine linear combinations of the predictor variables with ability to discriminate. We also show that this classifier can be used as a tool to reduce the dimension of the data and helps identify the most important variables to classify new elements. Finally, we illustrate with a real data set the use of these linear components to construct oblique classification trees.