Achieving Structurally Robust Gromov Wasserstein Distance via Adaptive Dual-Mask

The Gromov-Wasserstein (GW) distance enables comparison across different spaces but remains fragile to structural noise due to its global quadratic coupling. Existing robust extensions primarily rely on node-centric mass relaxation. However, we argue that this strategy is far from sufficient: it only addresses node-induced structural noise (outliers) while neglecting edge-induced distortions where spurious connections exist between valid nodes. To overcome this limitation, we propose the Structurally Robust Gromov-Wasserstein (SRGW) distance, a novel formulation that adaptively filters geometric distortions during optimization. By introducing a structure-aware dual-mask mechanism, our method effectively isolates these stubborn structural outliers while preserving strict marginal constraints for balanced transport. We solve this objective using a Mask-Guided GW Algorithm, which jointly optimizes the transport plan and the structural noise filters. We provide a rigorous theoretical analysis proving that our algorithm converges to a critical point under the Kurdyka-Łojasiewicz framework. Extensive experiments on synthetic geometric matching and real-world subgraph alignment benchmarks demonstrate that Mask-Guided GW achieves superior alignment quality, particularly under severe structural noise.

Many real-world data objects are best understood by their relationships: for example, atoms in a molecule, points in an image, or connections in a network. A common goal is to match two such objects even when they have different sizes, positions, or layouts. Existing methods can do this well when the data is clean, but they often break down when the structure contains noise, such as extra points or misleading connections. This paper introduces a new method, Mask-Guided GW, for making these matches more reliable. Instead of simply ignoring suspicious data points, the method looks for unreliable relationships between points and reduces their influence during matching. This allows it to preserve the overall structure while avoiding being misled by noisy or false connections. Experiments on synthetic shapes and real-world graph matching tasks show that the proposed method finds more accurate matches than existing approaches, especially when the data contains strong structural noise. The results suggest that relationship-level noise filtering can make structure matching more dependable in practical applications.