Graph matching is one of the most significant graph analytic tasks, which
aims to find the node correspondence across different graphs. Most existing
graph matching approaches mainly rely on topological information, whose
performances are often sub-optimal and sensitive to data noise because of not
fully leveraging the multi-modal information hidden in graphs, such as node
attributes, subgraph structures, etc. In this study, we propose a novel and
robust graph matching method based on an unbalanced hierarchical optimal
transport (UHOT) framework, which, to our knowledge, makes the first attempt to
exploit cross-modal alignment in graph matching. In principle, applying
multi-layer message passing, we represent each graph as layer-wise node
embeddings corresponding to different modalities. Given two graphs, we align
their node embeddings within the same modality and across different modalities,
respectively. Then, we infer the node correspondence by the weighted average of
all the alignment results. This method is implemented as computing the UHOT
distance between the two graphs -- each alignment is achieved by a node-level
optimal transport plan between two sets of node embeddings, and the weights of
all alignment results correspond to an unbalanced modality-level optimal
transport plan. Experiments on various graph matching tasks demonstrate the
superiority and robustness of our method compared to state-of-the-art
approaches. Our implementation is available at
this https URL