Graph kernel: Difference between revisions

Revision as of 14:04, 11 May 2021

Revision as of 18:24, 8 June 2022

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An example of a kernel between graphs is the '''random walk kernel''',<ref name="Gaertner"/><ref name="Kashima"/> which conceptually performs [[random walk]]s on two graphs simultaneously, then counts the number of [[Path (graph theory)|path]]s that were produced by ''both'' walks. This is equivalent to doing random walks on the [[Tensor product of graphs|direct product]] of the pair of graphs, and from this, a kernel can be derived that can be efficiently computed.<ref name="Vishwanathan"/>

Another examples is the '''Weisfeiler-Lehman graph kernel'''<ref>Shervashidze, Nino, et al. "Weisfeiler-lehman graph kernels." Journal of Machine Learning Research 12.9 (2011).</ref> which computes multiple rounds of the Weisfeiler-Lehman algorithm and then computes the similarity of two graphs as the inner product of the histogram vectors of both graphs. In those histogram vectors the kernel collects the number of times a color occurs in the graph in every iteration. For two isomorphic graphs, the kernel returns a maximal similarity since the two feature vectors are identical.

Note that the Weisfeiler-Lehman kernel in theory has an infinite dimension as the number of possible colors assigned by the Weisfeiler-Lehman algorithm is infinite. By restricting to the colors that occur in both graphs, the computation is still feasible.