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On a linear Gromov-Wasserstein distance

arXiv 2112.11964 ↗First posted 22 Dec 2021math.NA cs.NA math.OCcited by 17

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Abstract (arXiv)

Gromov-Wasserstein distances are generalization of Wasserstein distances, which are invariant under distance preserving transformations. Although a simplified version of optimal transport in Wasserstein spaces, called linear optimal transport (LOT), was successfully used in practice, there does not exist a notion of linear Gromov-Wasserstein distances so far. In this paper, we propose a definition of linear Gromov-Wasserstein distances. We motivate our approach by a generalized LOT model, which is based on barycentric projection maps of transport plans. Numerical examples illustrate that the linear Gromov-Wasserstein distances, similarly as LOT, can replace the expensive computation of pairwise Gromov-Wasserstein distances in applications like shape classification.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Dec 2021.

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Citing papers per year: 2022: 2; 2023: 3; 2024: 1; 2025: 5; 2026: 6.

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  1. 2022On a linear fused Gromov-Wasserstein distance for graph structured datacited by 9
  2. 2025A Novel Sliced Fused Gromov-Wasserstein Distancecited by 9
  3. 2023Globally solving the Gromov-Wasserstein problem for point clouds in low dimensional Euclidean spacescited by 7
  4. 2023Uncovering Challenges of Solving the Continuous Gromov-Wasserstein Problemcited by 6
  5. 2025Slicing Wasserstein Over Wasserstein Via Functional Optimal Transportcited by 5
  6. 2025Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classificationcited by 3
  7. 2024Linear Partial Gromov-Wasserstein Embeddingcited by 1
  8. 2026Generalized Wasserstein Flow Matching: Transport Plans, Everywhere, All at Oncecited by 1
  9. 2022Approximative Algorithms for Multi-Marginal Optimal Transport and Free-Support Wasserstein Barycenterscited by 0
  10. 2023Structure-Sensitive Graph Dictionary Embedding for Graph Classificationcited by 0
  11. 2025Gromov-Wasserstein and optimal transport: from assignment problems to probabilistic numericcited by 0
  12. 2025Generalizations of the Normalized Radon Cumulative Distribution Transform for Limited Data Recognitioncited by 0
5 more
  1. 2026Well-Posed KL-Regularized Control via Wasserstein and Kalman-Wasserstein KL Divergencescited by 0
  2. 2026Beyond Rigid Alignment: Graph Federated Learning via Dual Manifold Calibrationcited by 0
  3. 2026k-Nearest Neighbors in Gromov--Wasserstein Spacecited by 0
  4. 2026Gromov-Wasserstein Quantization and Clustering: Structure, Rates, and Algorithmscited by 0
  5. 2026Gromov-Monge Flow Matching for Equivariant Graph Generationcited by 0