Graph Kernels [article]

S.V.N. Vishwanathan, Karsten M. Borgwardt, Imre Risi Kondor, Nicol N. Schraudolph
2008 arXiv   pre-print
We present a unified framework to study graph kernels, special cases of which include the random walk graph kernel GaeFlaWro03,BorOngSchVisetal05, marginalized graph kernel KasTsuIno03,KasTsuIno04,MahUedAkuPeretal04, and geometric kernel on graphs Gaertner02. 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
more » ... 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 KonLaf02, regularization on graphs SmoKon03, and graph kernels, and use these connections to propose new graph kernels. Finally, we show that rational kernels CorHafMoh02,CorHafMoh03,CorHafMoh04 when specialized to graphs reduce to the random walk graph kernel.
arXiv:0807.0093v1 fatcat:s4zdxsd32fd4xmloezwbja6324