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A Riemannian Approach to Graph Embedding

Robles-Kelly, Antonio; Hancock, Edwin R

Description

In this paper, we make use of the relationship between the Laplace-Beltrami operator and the graph Laplacian, for the purposes of embedding a graph onto a Riemannian manifold. To embark on this study, we review some of the basics of Riemannian geometry and explain the relationship between the Laplace-Beltrami operator and the graph Laplacian. Using the properties of Jacobi fields, we show how to compute an edge-weight matrix in which the elements reflect the sectional curvatures associated with...[Show more]

CollectionsANU Research Publications
Date published: 2007
Type: Journal article
URI: http://hdl.handle.net/1885/29516
Source: Pattern Recognition
DOI: 10.1016/j.patcog.2006.05.031

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