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Fast Computation of Graph Kernels

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons75313

Borgwardt,  KM
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Zitation

Vishwanathan, S., Borgwardt, K., & Schraudolph, N. (2007). Fast Computation of Graph Kernels. In Advances in Neural Information Processing Systems 19 (pp. 1449-1456). Cambridge, MA, USA: MIT Press.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0013-CBDF-8
Zusammenfassung
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 G¨artner 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.