A Maximal Margin Hypersphere SVM

In this work we propose a generalization of the Support Vector Machine (SVM) method in which the separator is a curve, but the concept of margin and maximization of the margin is still present. The idea of using different functions for the separation has been explored in particular in the scope of hyperspheres. However, most of these proposals use two spheres, using concepts different from maximal margin or one sphere but with a poor performance when data from the classes have a linear shape. In this paper we present a formulation of the linear SVM that generalizes it to a spherical separation shape, but still maximizing the margin. A linear relaxation of this quadratic formulation is also presented. The performance of these two formulations for classification purpose is tested and the results are encouraging.