OTGM: Graph Matching with Noisy Correspondence via Optimal Transports

ICLR 2025 Conference Submission1323 Authors

Keywords: Optimal Transport

Abstract: Graph matching is a significant task for handling the matching problem of finding correspondences between keypoints in different graphs. Prior research primarily concentrates on performing one-to-one matching in topologic perspective for keypoints across various graphs, assuming that the paired keypoints are accurately linked. However, these approaches have two limitations: (1) because of different observation perspectives, some keypoints in the reference figure may become occluded or transformed, leading to situations where keypoint matches are a mess in topologic; (2) in practice, the manual annotation process is susceptible to poor recognizability and viewpoint differences between images, which probably results in offset and even erroneous keypoint annotations. To address these limitations, we revisit the graph matching problem from the distributional alignment perspective and propose an \textbf{O}ptimal \textbf{T}ransport \textbf{G}raph \textbf{M}atching model (\textbf{OTGM}). Specifically, (1) to effectively model the real-world keypoint matching scenarios, we have redefined the graph matching process as a transportation plan, which involves transferring node or edge sets from one distribution to another while minimizing the Wasserstein distance between these distributions. (2) To achieve robust matching, we introduce a well-designed graph denoising module to eliminate noisy edges in the input graph with the assistance of self-supervised learning. On top of this, we theoretically provide assurances regarding the generalization ability of OTGM. Furthermore, comprehensive experiments on three real-world datasets demonstrate that our model exhibits strong robustness and achieves state-of-the-art performance compared to competitive baselines.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 1323