A Generic Diffusion Kernel for Semi-supervised Learning

In this paper, we present a generic diffusion kernel for graph-based semi-supervised learning, whose kernel matrix is generated with a Taylor expansion on the generating function of diffusion similarity matrix. The generic diffusion kernel subsumes common known diffusion kernels, and provides a kernel framework for semi-supervised learning. Specifically, we first present the definition of diffusion similarity matrix, and lay the theoretical foundation for our approach. Then we derive the 2- and d-diffusion kernels, and naturally extend them to the generic diffusion kernel. Further we prove that small eigenvalues of the generic diffusion kernel correspond to smooth eigenvectors over the graph. This property is critical for the construction of generic diffusion kernels. Experiments on simulated and benchmark databases demonstrate that the generic diffusion kernel is sound and effective.