Construction of a new spherical kernel function

A new spherical kernel function was proposed for spherically separable data base. Unlike previous kernels constructed with an implicit feature mapping, this kernel was constructed explicitly with inner products of spherical feature mappings, which fully utilized the prior knowledge and avoided dimensionality curse by embedding the input space into a same-dimensional feature space. First, the symmetric and Cauchy-Schwarz unequal properties were investigated. Then the necessary and sufficient condition for verifying a valid kernel function was given. By examining with this condition, the spherical kernel function was proven to be well defined. Further, comparative experiments with Gaussian kernel were conducted. Both the theoretical proofs and the experimental results show that the new spherical kernel is valid and feasible. © 2008 Binary Information Press.