Regularization with Dot-Product Kernels

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.

Authors

• Alex Smola
• Zoltán Óvári
• Robert Williamson

Keywords

No keywords are indexed for this paper.