Learning Combinatorial Solver for Graph Matching

Learning-based approaches to graph matching have been developed and explored for more than a decade, have grown rapidly in scope and popularity in recent years. However, previous learning-based algorithms, with or without deep learning strategy, mainly focus on the learning of node and/or edge affinities generation, and pay less attention on the learning of the combinatorial solver. In this paper we propose a fully trainable framework for graph matching, in which learning of affinities and solving for combinatorial optimization are not explicitly separated as in many previous arts. We firstly convert the problem of building node correspondences between two input graphs to the problem of selecting reliable nodes from a constructed assignment graph. Subsequently, the graph network block module is adopted to perform computation on the graph to form structured representations for each node. It finally predicts a label for each node that is used for node classification, and the training is performed under the supervision of both permutation differences and the one-to-one matching constraints. The proposed method is evaluated on four public benchmarks in comparison with several state-of-the-art algorithms, and the experimental results illustrate its excellent performance.