mlsanityData to 7 Oct 2026

Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties

arXiv 1811.02834 ↗First posted 7 Nov 2018stat.ML cs.LGcited by 93

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Abstract (arXiv)

Optimal transport theory has recently found many applications in machine learning thanks to its capacity for comparing various machine learning objects considered as distributions. The Kantorovitch formulation, leading to the Wasserstein distance, focuses on the features of the elements of the objects but treat them independently, whereas the Gromov-Wasserstein distance focuses only on the relations between the elements, depicting the structure of the object, yet discarding its features. In this paper we propose to extend these distances in order to encode simultaneously both the feature and structure informations, resulting in the Fused Gromov-Wasserstein distance. We develop the mathematical framework for this novel distance, prove its metric and interpolation properties and provide a concentration result for the convergence of finite samples. We also illustrate and interpret its use in various contexts where structured objects are involved.

Key facts. Cited by 93 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Nov 2018.

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Citing papers per year: 2021: 7; 2022: 15; 2023: 10; 2024: 15; 2025: 22; 2026: 24.

93 papers.

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  1. 2021Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and Costscited by 61
  2. 2022Unbalanced Optimal Transport, from Theory to Numericscited by 45
  3. 2021Online Graph Dictionary Learningcited by 37
  4. 2024Temporally Consistent Unbalanced Optimal Transport for Unsupervised Action Segmentationcited by 37
  5. 2022Aligning individual brains with Fused Unbalanced Gromov-Wassersteincited by 23
  6. 2022Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenterscited by 22
  7. 2021Semi-relaxed Gromov-Wasserstein divergence with applications on graphscited by 21
  8. 2022Template based Graph Neural Network with Optimal Transport Distancescited by 20
  9. 2023CSOT: Curriculum and Structure-Aware Optimal Transport for Learning with Noisy Labelscited by 17
  10. 2025Pave Your Own Path: Graph Gradual Domain Adaptation on Fused Gromov-Wasserstein Geodesicscited by 17
  11. 2023Robust Attributed Graph Alignment via Joint Structure Learning and Optimal Transportcited by 15
  12. 2022Weisfeiler-Lehman meets Gromov-Wassersteincited by 14
38 more
  1. 2024The Z-Gromov-Wasserstein Distancecited by 12
  2. 2022Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsificationcited by 11
  3. 2024Graph Classification via Reference Distribution Learning: Theory and Practicecited by 11
  4. 2025Joint Self-Supervised Video Alignment and Action Segmentationcited by 11
  5. 2025InfiGFusion: Graph-on-Logits Distillation via Efficient Gromov-Wasserstein for Model Fusioncited by 11
  6. 2023A Convergent Single-Loop Algorithm for Relaxation of Gromov-Wasserstein in Graph Datacited by 10
  7. 2022InfoOT: Information Maximizing Optimal Transportcited by 9
  8. 2025A Novel Sliced Fused Gromov-Wasserstein Distancecited by 9
  9. 2023Structured Transforms Across Spaces with Cost-Regularized Optimal Transportcited by 8
  10. 2023Efficient Graph Field Integrators Meet Point Cloudscited by 7
  11. 2023Unbalanced Low-rank Optimal Transport Solverscited by 7
  12. 2024Any2Graph: Deep End-To-End Supervised Graph Prediction With An Optimal Transport Losscited by 7
  13. 2024Proximity Matters: Local Proximity Enhanced Balancing for Treatment Effect Estimationcited by 7
  14. 2025Graph Data Selection for Domain Adaptation: A Model-Free Approachcited by 7
  15. 2025Modeling Microenvironment Trajectories on Spatial Transcriptomics with NicheFlowcited by 7
  16. 2024Computing Approximate Graph Edit Distance via Optimal Transportcited by 5
  17. 2021Learning Graphon Autoencoders for Generative Graph Modelingcited by 4
  18. 2022Wasserstein Graph Distance Based on L1-Approximated Tree Edit Distance between Weisfeiler-Lehman Subtreescited by 4
  19. 2024Structure-Aware E(3)-Invariant Molecular Conformer Aggregation Networkscited by 4
  20. 2022MoReL: Multi-omics Relational Learningcited by 3
  21. 2022Improving word mover's distance by leveraging self-attention matrixcited by 3
  22. 2024Fast Tree-Field Integrators: From Low Displacement Rank to Topological Transformerscited by 3
  23. 2025Persistent Homology-induced Graph Ensembles for Time Series Regressionscited by 3
  24. 2025Unsupervised Learning for Optimal Transport plan prediction between unbalanced graphscited by 3
  25. 2026Expectations vs. Realities: The Cost of MSE-Optimal Forecasting Under Conditional Uncertaintycited by 3
  26. 2021Alignment and Comparison of Directed Networks via Transition Couplings of Random Walkscited by 2
  27. 2022Regularized Optimal Transport Layers for Generalized Global Pooling Operationscited by 2
  28. 2023Graph Matching Optimization Network for Point Cloud Registrationcited by 2
  29. 2023Enigma: Application-Layer Privacy for Quantum Optimization on Untrusted Computerscited by 2
  30. 2024SP2OT: Semantic-Regularized Progressive Partial Optimal Transport for Imbalanced Clusteringcited by 2
  31. 2024Fast Gradient Computation for Gromov-Wasserstein Distancecited by 2
  32. 2024Scalable unsupervised alignment of general metric and non-metric structurescited by 2
  33. 2024Metric properties of partial and robust Gromov-Wasserstein distancescited by 2
  34. 2025Gradual Domain Adaptation for Graph Learningcited by 2
  35. 2025Joint Metric Space Embedding by Unbalanced OT with Gromov-Wasserstein Marginal Penalizationcited by 2
  36. 2025Neural Estimation for Scaling Entropic Multimarginal Optimal Transportcited by 2
  37. 2026Conformal Graph Prediction with Z-Gromov-Wasserstein Distancescited by 2
  38. 2021Heterogeneous Wasserstein Discrepancy for Incomparable Distributionscited by 1

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