Graph Kernels

We present a unified framework to study graph kernels, special cases of which include the random walk graph kernel , marginalized graph kernel , and geometric kernel on graphs . Through extensions of linear algebra to Reproducing Kernel Hilbert Spaces (RKHS) and reduction to a Sylvester equation, we construct an algorithm that improves the time complexity of kernel computation from O(n^6) to O(n^3). When the graphs are sparse, conjugate gradient solvers or fixed-point iterations bring our algorithm into the sub-cubic domain. Experiments on graphs from bioinformatics and other application domains show that it is often more than a thousand times faster than previous approaches. We then explore connections between diffusion kernels , regularization on graphs , and graph kernels, and use these connections to propose new graph kernels. Finally, we show that rational kernels when specialized to graphs reduce to the random walk graph kernel.