Regularization networks with indefinite kernels

Learning with indefinite kernels attracted considerable attention in recent years due to their success in various learning scenarios. In this paper we study the asymptotic properties of the regularization kernel networks where the kernels are assumed to be indefinite, without the usual restrictions of symmetry and positive semi-definiteness as in the traditional study of kernel methods. The kernels are characterized in terms of the singular value decomposition of the corresponding kernel integrals. Two reproducing kernel Hilbert spaces are induced to characterize the approximation ability. Capacity independent error bounds are proved. Fast convergence rates are obtained both in reproducing kernel Hilbert spaces and in L2L2 sense.