  Recently, graph convolutional networks (GCNs) have shown great potential for
the task of graph matching. It can integrate graph node feature embedding,
node-wise affinity learning and matching optimization together in a unified
end-to-end model. One important aspect of graph matching is the construction of
two matching graphs. However, the matching graphs we feed to existing graph
convolutional matching networks are generally fixed and independent of graph
matching, which thus are not guaranteed to be optimal for the graph matching
task. Also, existing GCN matching method employs several general
smoothing-based graph convolutional layers 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 learn a pair of optimal graphs that best serve
graph matching task. (2) It further employs a Laplacian sharpening
convolutional module 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 on two benchmarks demonstrate the effectiveness of
GLMNet and advantages of its main modules.
