TY - GEN

T1 - Fast computation of graph kernels

AU - Vishwanathan, S. V.N.

AU - Borgwardt, Karsten M.

AU - Schraudolph, Nicol N.

PY - 2007

Y1 - 2007

N2 - Using extensions of linear algebra concepts to Reproducing Kernel Hilbert Spaces (RKHS), we define a unifying framework for random walk kernels on graphs. Reduction to a Sylvester equation allows us to compute many of these kernels in O(n3) worst-case time. This includes kernels whose previous worst-case time complexity was O(n6), such as the geometric kernels of Gärtner et al. [1] and the marginal graph kernels of Kashima et al. [2]. Our algebra in RKHS allow us to exploit sparsity in directed and undirected graphs more effectively than previous methods, yielding sub-cubic computational complexity when combined with conjugate gradient solvers or fixed-point iterations. Experiments on graphs from bioinformatics and other application domains show that our algorithms are often more than 1000 times faster than existing approaches.

AB - Using extensions of linear algebra concepts to Reproducing Kernel Hilbert Spaces (RKHS), we define a unifying framework for random walk kernels on graphs. Reduction to a Sylvester equation allows us to compute many of these kernels in O(n3) worst-case time. This includes kernels whose previous worst-case time complexity was O(n6), such as the geometric kernels of Gärtner et al. [1] and the marginal graph kernels of Kashima et al. [2]. Our algebra in RKHS allow us to exploit sparsity in directed and undirected graphs more effectively than previous methods, yielding sub-cubic computational complexity when combined with conjugate gradient solvers or fixed-point iterations. Experiments on graphs from bioinformatics and other application domains show that our algorithms are often more than 1000 times faster than existing approaches.

UR - http://www.scopus.com/inward/record.url?scp=84864066856&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9780262195683

T3 - Advances in Neural Information Processing Systems

SP - 1449

EP - 1456

BT - Advances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference

T2 - 20th Annual Conference on Neural Information Processing Systems, NIPS 2006

Y2 - 4 December 2006 through 7 December 2006

ER -