Global graph matching using diffusion maps

We present a new algorithm, global positioning graph matching (GPGM), to perform global network alignments between pairs of undirected graphs by minimizing a dissimilarity score over matched vertices. We define structural dissimilarities based on a random walk over each graph to provide a robust measure of the global graph topology using a nonlinear manifold learning algorithm known as diffusion maps. Measures of vertex-vertex dissimilarity are straightforwardly incorporated in a convex combination. We have tested our approach in pairwise alignments of protein-protein interaction networks of Xenopus laevis (frog), Rattus norvegicus (rat), Caenorhabditis elegans (worm), Mus musculus (mouse), and Drosophila melanogaster (fly). When vertex-vertex dissimilarities are incorporated using homology scores between protein sequences, the performance of GPGM is comparable to that of the IsoRank algorithm (Singh et al. Proc. Natl. Acad. Sci. USA 105 35 12763 (2008)). When homology information is not included, GPGM discovers superior alignments, making it well suited to graph matching applications where vertex labels are unknown or undefined.