Computer geometry algorithms in feature space dimension reduction problems

Abstract

One of the goals of multidimensional feature space dimension reduction is to visualize the arrangement of classes on a plane. The quality of such a representation depends on the dimension-reduction method and the used measure of the closeness of classes. In this paper, we propose a technology of dimension reduction to two dimensions based on the calculation of convex hulls of classes and determination of their intersection degree. Experiments carried out in the MATLAB system show that this technology on the training sample makes it possible to identify the minimum potentially achievable intersection degree of classes intersecting in a multidimensional space and to obtain a mutual mapping of classes on the plane corresponding to the minimum degree of their intersection.