Mathematical analysis of classifying convex clusters based on support functionals

Abstract

Classification is one of the core topics in data mining technologies. This paper studies the geometry of classifying convex clusters based on support functionals in the dual spaces. For the convex clusters that are to be classified, a combination of linear discriminant functions could solve the problem. The geometrical depiction of linear discriminant functions and supporting hyperplanes for the convex clusters help to characterize the relations of the convex clusters, and the distances to the convex clusters and complement of convex clusters calibrate the measures between the support functionals and convex clusters. Examples are given. © Springer-Verlag Berlin Heidelberg 2005.