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 $R d$. We apply this technique for the following special cases: universal kernels on the set of probability measures, universal kernels based on Fourier transforms, and universal kernels for signal processing.