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.
Type de document :
Communication dans un congrès
Actes de la conférence d'apprentissage CAp, 2012, France. pp.223-237, 2012
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https://hal.archives-ouvertes.fr/hal-00952837
Contributeur : Maria-Irina Nicolae <>
Soumis le : jeudi 27 février 2014 - 15:56:00
Dernière modification le : jeudi 11 octobre 2018 - 08:48:04

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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, 2012. 〈hal-00952837〉

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