Optimal Transport vs Many-to-many assignment for Graph Matching

Graph matching for shape comparison or network analysis is a challenging issue in machine learning and computer vision. Gener-ally, this problem is formulated as an assignment task, where we seek the optimal matching between the vertices that minimizes the differencebetween the graphs. We compare a standard approach to perform graph matching, to a slightly-adapted version of regularized optimal transport,initially conceived to obtain the Gromov-Wassersein distance between structured objects (e.g. graphs) with probability masses associated to thenodes. We adapt the latter formulation to undirected and unlabeled graphs of different dimensions, by adding dummy vertices to cast the probleminto an assignment framework. The experiments are performed on randomly generated graphs onto which different spatial transformations areapplied. The results are compared with respect to the matching cost and execution time, showcasing the different limitations and/or advantagesof using these techniques for the comparison of graph networks.