Graph matching using manifold embedding

Abstract

This paper describes how graph-spectral methods can be used to transform the node correspondence problem into one of pointset 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 graphmatching 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. © Springer-Verlag 2004.