Machine Learning Methods Based on Convex Hulls Analysis in Medical Diagnostics Tasks

Abstract

The methods of machine learning using the apparatus of computational geometry are investigated. The use of convex hulls of sets in a multidimensional feature space allows implementing algorithms for visualization of class intersection area, reduction of feature space dimension and classification algorithms. A method of measurement of convex hull proximity to test point, if the test point is within the convex hull, is proposed. It is based on assessment of directional penetration depth of convex hull vertices projected onto the direction vector from this point to class centroid. Nearest convex hull algorithm, based on the proposed simplified method of assessment of proximity to convex hull, is described. Results of classification for breast cancer diagnosis task solution are presented. The results showed sufficient efficiency of the proposed methods..