Graph Matching Using Manifold Embedding
This paper describes how graph-spectral methods can be used to transform the node correspondence problem into one of point-set alignment. We commence by using a heat kernel analysis to compute geodesic distances between nodes in the graphs. With geodesic distances to hand, we use the ISOMAP algorithm to embed the nodes of a graph in a low-dimensional Euclidean space. With the nodes in the graph transformed to points in a metric space, we can recast the problem of graph-matching into that of aligning the points. Here we use a variant of the Scott and Longuet-Higgins algorithm to find point correspondences. We experiment with the resulting algorithm on a number of real-world problems.
KeywordsHeat Kernel Geodesic Distance Graph Match Spectral Graph Theory Embed Point
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- 2.Chung, F.R.K.: Spectral graph theory. CBMS series 92 (1997)Google Scholar
- 4.Hjaltason, G.R., Samet, H.: Properties of embedding methods for similarity searching in metric spaces. PAMI 25, 530–549 (2003)Google Scholar
- 8.Luo, B., Hancock, E.R.: Structural graph matching using the em algorithm and singular value decomposition. IEEE PAMI 23, 1120–1136 (2001)Google Scholar
- 9.Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. IEEE PAMI 18 (1996)Google Scholar
- 13.Christmas, W., Kittler, J., Petrou, M.: Structural matching in computer vision using probabilistic relaxation. IEEE PAMI 17 (1995)Google Scholar