Part of Advances in Neural Information Processing Systems 13 (NIPS 2000)
Alex Smola, Zoltán Óvári, Robert C. Williamson
In this paper we give necessary and sufficient conditions under which kernels of dot product type k(x, y) = k(x . y) satisfy Mer(cid:173) cer's condition and thus may be used in Support Vector Ma(cid:173) chines (SVM), Regularization Networks (RN) or Gaussian Pro(cid:173) cesses (GP). In particular, we show that if the kernel is analytic (i.e. can be expanded in a Taylor series), all expansion coefficients have to be nonnegative. We give an explicit functional form for the feature map by calculating its eigenfunctions and eigenvalues.