  In this paper we consider the numerical solution to the soft-margin support
vector machine optimization problem. This problem is typically solved using the
SMO algorithm, given the high computational complexity of traditional
optimization algorithms when dealing with large-scale kernel matrices. In this
work, we propose employing an NFFT-accelerated matrix-vector product using an
ANOVA decomposition for the feature space that is used within an interior point
method for the overall optimization problem. As this method requires the
solution of a linear system of saddle point form we suggest a preconditioning
approach that is based on low-rank approximations of the kernel matrix together
with a Krylov subspace solver. We compare the accuracy of the ANOVA-based
kernel with the default LIBSVM implementation. We investigate the performance
of the different preconditioners as well as the accuracy of the ANOVA kernel on
several large-scale datasets.
