Graph Matching using Spectral Embedding and Semidefinite Programming

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 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 semidefinite programming to develop 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.