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{{About|machine learning|the graph-theoretical notion|Glossary of graph theory}}
In [[structure mining
Graph kernels can be intuitively understood as functions measuring the similarity of pairs of graphs. They allow [[Kernel trick|kernelized]] learning algorithms such as [[support vector machine]]s to work directly on graphs, without having to do [[feature extraction]] to transform them to fixed-length, real-valued [[feature vector]]s. They find applications in [[bioinformatics]], in [[chemoinformatics]] (as a type of [[molecule kernel]]s<ref name="Ralaivola2005">{{cite journal |author1=L. Ralaivola |author2=S. J. Swamidass |author3=H. Saigo |author4=P. Baldi |title=Graph kernels for chemical informatics |journal=Neural Networks |year=2005 |volume=18 |issue=8 |pages=1093–1110 |doi=10.1016/j.neunet.2005.07.009|pmid=16157471 }}</ref>), and in [[social network analysis]].<ref name="Vishwanathan"/>
Concepts of graph kernels have been around since the 1999, when D. Haussler<ref>{{Cite book|title=Convolution Kernels on Discrete Structures|last=Haussler|first=David|date=1999|citeseerx = 10.1.1.110.638}}</ref> introduced convolutional kernels on discrete structures. The term graph kernels was more officially coined in 2002 by R. I. Kondor and [[John D. Lafferty|J. Lafferty]]<ref>{{cite conference
|title=Diffusion Kernels on Graphs and Other Discrete Input Spaces
|author1=Risi Imre Kondor
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|url=http://people.cs.uchicago.edu/~risi/papers/diffusion-kernels.pdf
}}</ref>
as kernels ''on'' graphs, i.e. similarity functions between the nodes of a single graph, with the [[World Wide Web]] [[hyperlink]] graph as a suggested application. In 2003,
|title=On graph kernels: Hardness results and efficient alternatives
|author1=Thomas
|author2=Peter A. Flach
|author3=Stefan Wrobel
|conference=Proc. the 16th Annual Conference on Computational Learning Theory (COLT) and the 7th Kernel Workshop
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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-Leman 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-Leman 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.
Note that the Weisfeiler-Leman kernel in theory has an infinite dimension as the number of possible colors assigned by the Weisfeiler-Leman algorithm is infinite. By restricting to the colors that occur in both graphs, the computation is still feasible.
==See also==▼
* [[Tree kernel]], as special case of non-cyclic graphs▼
==References==
{{reflist}}
▲==See also==
[[Category:Kernel methods for machine learning]]
▲* [[Tree kernel]], as special case of non-cyclic graphs
▲*[[Category:Graph algorithms]]
▲[[Category:Kernel methods for machine learning]] [[Molecule mining]], as special case of small multi-label graphs
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