Recently, graph convolutional networks (GCNs) have been employed for graph matching problem. It can integrate graph node feature embedding, node-wise affinity learning and matching optimization together in a unified end-to-end model. However, first, the matching graphs feeding to existing graph matching networks are generally fixed and independent of graph matching task, which thus are not guaranteed to be optimal for the graph matching task. Second, existing methods generally employ smoothing-based graph convolution to generate graph node embeddings, in which extensive smoothing convolution operation may dilute the desired discriminatory information of graph nodes. To overcome these issues, we propose a novel Graph Learning-Matching Network (GLMNet) for graph matching problem. GLMNet has three main aspects. (1) It integrates graph learning into graph matching which thus adaptively learns a pair of optimal graphs for graph matching task. (2) It further employs a Laplacian sharpening graph convolution to generate more discriminative node embeddings for graph matching. (3) A new constraint regularized loss is designed for GLMNet training which can encode the desired one-to-one matching constraints in matching optimization. Experiments demonstrate the effectiveness of GLMNet.

最近，图卷积网络（GCN）已被用于解决图匹配问题。它可以将图节点特征嵌入、节点亲和学习和匹配优化集成到一个统一的端到端模型中。然而，首先，馈送到现有图匹配网络的匹配图通常是固定的并且独立于图匹配任务，因此不能保证对于图匹配任务是最佳的。其次，现有方法通常采用基于平滑的图卷积来生成图节点嵌入，其中广泛的平滑卷积操作可能会稀释图节点所需的判别信息。为了克服这些问题，我们为图匹配问题提出了一种新颖的图学习匹配网络（GLMNet）。GLMNet 具有三个主要方面。(1) 它将图学习集成到图匹配中，从而自适应地学习一对最佳图用于图匹配任务。(2) 进一步采用拉普拉斯锐化图卷积来生成更具判别性的节点嵌入用于图匹配。(3) 为 GLMNet 训练设计了一种新的约束正则化损失，可以在匹配优化中编码所需的一对一匹配约束。实验证明了 GLMNet 的有效性。