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arXiv · 0807.0093

Graph Kernels

S. V. N. Vishwanathan·Karsten M. Borgwardt·Imre Risi Kondor·Nicol N. Schraudolph
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Abstract

We present a unified framework to study graph kernels, special cases of which include the random walk graph kernel \citep{GaeFlaWro03,BorOngSchVisetal05}, marginalized graph kernel \citep{KasTsuIno03,KasTsuIno04,MahUedAkuPeretal04}, and geometric kernel on graphs \citep{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 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 \citep{KonLaf02}, regularization on graphs \citep{SmoKon03}, and graph kernels, and use these connections to propose new graph kernels. Finally, we show that rational kernels \citep{CorHafMoh02,CorHafMoh03,CorHafMoh04} when specialized to graphs reduce to the random walk graph kernel.

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BibTeXRIS

S. V. N. Vishwanathan, Karsten M. Borgwardt, Imre Risi Kondor, Nicol N. Schraudolph. 2008-07-01. Graph Kernels. https://arxiv.org/abs/0807.0093

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