%A O. L. mangasarian and David R. Musicant
%T Data Discrimination via Nonlinear Generalized Support Vector Machines
%D March 1999
%R 99-03
%I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN
%C MADISON, WI
%X
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
indefinite kernels \cite{olm:98}. The GSVM training procedure is carried out
by either the simple successive overrelaxation (SOR) \cite{mm:98} iterative
method or by linear programming.
This novel combination of powerful support vector machines
\cite{vap:95,cm:98} with the highly effective
SOR computational algorithm \cite{man:77,man:91,lt:93c}
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.