Data Discrimination via Nonlinear Generalized Support Vector Machines

The main purpose of this paper is to show that new formulations of support vector machines can generate nonlinear separating surfaces which can discriminate between elements of a given set better than a linear surface. The principal approach used is that of generalized support vector machines (GSVMs) which employ possibly indeenite kernels 17]. The GSVM training procedure is carried out by either the simple successive overrelaxation (SOR) 18] iterative method or by linear programming. This novel combination of powerful support vector machines 24, 5] with the highly eeective SOR computational algorithm 15, 16, 14] or with linear programming allows us to use a nonlinear surface to discriminate between elements of a dataset that belong to one of two categories. Numerical results on a number of datasets show improved testing set correctness, by as much as a factor of two, when comparing the nonlinear GSVM surface to a linear separating surface.