Factorized Embedding Graph Matching Network For Learning Lawler’s Quadratic Assignment Problem

Graph matching refers to establishing correspondence between two sets of point while keeping consistency between their edge sets. Recent works in learning-based graph matching have attempted to solve the problem either by linear assignment, which transfers local structure information into node embedding at individual graphs, or by quadratic assignment through vertex classification over their association graph. However, the former embedding-based pipeline methods often neglect second-order edge similarity, leading to decreased accuracy; while the latter quadratic assignment solvers consume significant memory due to huge computation on the association graph. To addressthese issues, our key idea is to integrate a factorized embedding module to efficiently propogate information over the association graph. To this end, we propose a novel factorized embedding-based network, namely FEGM, which takes into account the secondorder edge similarity, as well as a factorization model of GCN network, so that we extend the embedding-based pipeline for learning the Lawler’s QAP while reducing memory consumption. Experimental results show that FEGM achieves a competitive matching accuracy while being superior in time and space efficiency.