Universal Kernels on Non-Standard Input Spaces

During the last years support vector machines (SVMs) have been successfully applied even in situations where the input space X is not necessarily a subset of R d . Examples include SVMs using probability measures to analyse e.g. Moreover, SVMs are known to be consistent to the Bayes risk, if either the input space is a complete separable metric space and the reproducing kernel Hilbert space (RKHS) H\subset L_p(P_X) is dense, or if the SVM is based on a universal kernel k . So far, however, there are no RKHSs of practical interest known that satisfy these assumptions on \cH or k if X ot\subset R d . We close this gap by providing a general technique based on Taylor-type kernels to explicitly construct universal kernels on compact metric spaces which are not subset of R d .