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Graph Kernels ― a Synthesis Note on Positive Definiteness

Abstract : We review the problem of extending the applicability of support vector machines (SVM) to graph data. Many similarity measures, generally called kernels, on graph data have been proposed in the last decade. Yet some of them, like the optimum assignment kernel (15), are not positive semidefinite, which limits their application in SVM. In this paper we recall the necessary conditions for using SVM. While the Mercer theorem gives necessary and sufficient conditions for vectorial data, we show that for graph data an embedding in a Hilbert space has to be defined explicitly, and that weaker conditions do not suffice. For several kernels proposed in the literature we demonstrate that an underlying Hilbert space does exist by specifying the corresponding basis.Our findings are illustrated with small examples from the graph kernel literature.
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https://hal.archives-ouvertes.fr/hal-00952837
Contributor : Maria-Irina Nicolae <>
Submitted on : Thursday, February 27, 2014 - 3:56:00 PM
Last modification on : Monday, April 20, 2020 - 11:24:01 AM

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  • HAL Id : hal-00952837, version 1

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Cornelia Metzig, Gilles Bisson, Cécile Amblard, Mirta B. Gordon. Graph Kernels ― a Synthesis Note on Positive Definiteness. Actes de la conférence d'apprentissage CAp, 2012, France. pp.223-237. ⟨hal-00952837⟩

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