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Graph Kernels

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Encyclopedia of Machine Learning and Data Mining

Definition

The term graph kernel is used in two related but distinct contexts: On the one hand, graph kernels can be defined between graphs, that is, as a kernel function\(k : \mathcal{G}\times \mathcal{G}\rightarrow \mathbb{R}\) where \(\mathcal{G}\) denotes the set of all graphs un-der consideration. In the most common setting \(\mathcal{G}\) is the set of all labeled undirected graphs. On the other hand, graph kernels can be defined between the vertices of a single graph, that is, as a kernel function k : \(V \times V \rightarrow \mathbb{R}\) where V is the vertex set of the graph G under consideration. In the most common setting G is an undirected graph.

Motivation and Background

Kernel methodsare a class of machine learning algorithms that can be applied to any data set on which a valid, that is, positive definite, kernel function has been defined. Many kernel methods are theoretically well founded in statistical learning theory and have shown good predictive performance on many...

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Author information

Authors and Affiliations

  1. Fraunhofer IAIS, Schloss Birlinghoven, University of Bonn, Sankt Augustin, Germany

    Thomas Gärtner, Tamás Horváth & Stefan Wrobel

Authors
  1. Thomas Gärtner
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  2. Tamás Horváth
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  3. Stefan Wrobel
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Editor information

Editors and Affiliations

  1. The University of New South Wales, Sydney, NSW, Australia

    Claude Sammut

  2. Faculty of Information Technology, Monash University, Melbourne, VIC, Australia

    Geoffrey I. Webb

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Gärtner, T., Horváth, T., Wrobel, S. (2017). Graph Kernels. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning and Data Mining. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7687-1_349

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