Multidimensional Data Visualization Based on the Minimum Distance Between Convex Hulls of Classes

Abstract

The problem of data visualization in the analysis of two classes in a multidimensional feature space is considered. The two orthogonal axes by which the classes are maximally separated from each other are found in the mapping of classes as a result of linear transformation of coordinates. The proximity of the classes is estimated based on the minimum-distance criterion between their convex hulls. This criterion makes it possible to show cases of full class separability and random outliers. A support vector machine is used to obtain orthogonal vectors of the reduced space. This method ensures the obtaining of the weight vector that determines the minimum distance between the convex hulls of classes for linearly separable classes. Algorithms with reduction, contraction, and offset of convex hulls are used for intersecting classes. Experimental studies are devoted to the application of the considered visualization methods to biomedical data analysis.