  We propose a method for support vector machine classification using
indefinite kernels. Instead of directly minimizing or stabilizing a nonconvex
loss function, our algorithm simultaneously computes support vectors and a
proxy kernel matrix used in forming the loss. This can be interpreted as a
penalized kernel learning problem where indefinite kernel matrices are treated
as a noisy observations of a true Mercer kernel. Our formulation keeps the
problem convex and relatively large problems can be solved efficiently using
the projected gradient or analytic center cutting plane methods. We compare the
performance of our technique with other methods on several classic data sets.
