Diffusion Kernels on Graphs and Other Discrete Input Spaces

The application of kernel-based learning algorithms has, so far, largely been confined to realvalued data and a few special data types, such as strings. In this paper we propose a general method of constructing natural families of kernels over discrete structures, based on the matrix exponentiation idea. In particular, we focus on generating kernels on graphs, for which we propose a special class of exponential kernels called diffusion kernels, which are based on the heat equation and can be regarded as the discretization of the familiar Gaussian kernel of Euclidean space.