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 ×V → 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 real–world learning...
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Gärtner, T., Horváth, T., Wrobel, S. (2011). Graph Kernels. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30164-8_349
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DOI: https://doi.org/10.1007/978-0-387-30164-8_349
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