Some Spherical Separation Variants for Classification Problems

We face the problem of separating two sets of points by means of a sphere, focusing on the case where the center of the sphere is xed. Such approach reduces to the minimization of a convex and nonsmooth function of just one variable (the radius), revealing very eective in terms of computational time, as shown in [2]. In particular, we analyze the case where the center of the sphere is selected far from both the two sets, embedding the grossone idea [3] and obtaining a kind of linear separation. This approach is suitable for use in connection with kernel transformations and can be easily extended by introducing the margin concept [1] of the type adopted in the support vector machine (SVM) technique. Preliminary numerical results are presented on classical binary datasets drawn from the literature.