Graph Similarity, I-Divergences and Entropic Manifold Alignment
published: Sept. 13, 2010, recorded: August 2010, views: 3172
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In this paper we cast the problem of graph matching as one of non-rigid manifold alignment. The low dimensional manifolds are from the commute time embedding and are matched though coherent point drift. Although there have been a number of attempts to realise graph matching in this way, in this paper we propose a novel information-theoretic measure of alignment, the so-called symmetrized normalized-entropy-square variation. We succesfully test this dissimilarity measure between manifolds on a a challenging database. The measure is estimated by means of the bypass Leonenko entropy functional. In addition we prove that the proposed measure induces a positive definite kernel between the probability density functions associated with the manifolds and hence between graphs after deformation.
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