Quadratic Assignment Contrastive Loss and Application on Graph Matching

The Quadratic assignment problem (QAP), referring to finding an optimal assignment between two sets of interrelated objects, is a fundamental problem in combinatorial optimization. It is widely applied in computer science fields such as the traveling salesman problem, the maximum clique problem, graph matching, etc. In recent works, the alignment problem has been integrated with contrastive learning, providing a set-based contrastive loss with respect to quadratic assignment. In this paper, we extended a theorem related to the upper and lower bound of quadratic item of QAP by relaxing the condition. Our generalized theorem can be directly employed in the set-based quadratic assignment contrastive loss, thereby broadening its range of applications. We then introduce the graph matching problem, which is suitable for contrastive learning to examine the effectiveness of our method. Experimental results on representative datasets demonstrate that our method out-performs most of the previous works. The code is available at: https://github.com/xsshi/qagm.