mlsanityData to 7 Oct 2026

Optimal Transport for structured data with application on graphs

arXiv 1805.09114 ↗First posted 23 May 2018stat.ML cs.LGcited by 170

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Abstract (arXiv)

This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a total cost of transporting probability masses) that unveils the geometric nature of the structured objects space. Unlike Wasserstein or Gromov-Wasserstein metrics that focus solely and respectively on features (by considering a metric in the feature space) or structure (by seeing structure as a metric space), our new distance exploits jointly both information, and is consequently called Fused Gromov-Wasserstein (FGW). After discussing its properties and computational aspects, we show results on a graph classification task, where our method outperforms both graph kernels and deep graph convolutional networks. Exploiting further on the metric properties of FGW, interesting geometric objects such as Fr'echet means or barycenters of graphs are illustrated and discussed in a clustering context.

Key facts. Cited by 170 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 May 2018.

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Citing papers per year: 2021: 14; 2022: 26; 2023: 31; 2024: 33; 2025: 28; 2026: 38.

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  1. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  2. 2022Tree Mover's Distance: Bridging Graph Metrics and Stability of Graph Neural Networkscited by 39
  3. 2021Online Graph Dictionary Learningcited by 37
  4. 2024Temporally Consistent Unbalanced Optimal Transport for Unsupervised Action Segmentationcited by 37
  5. 2021Unbalanced Optimal Transport through Non-negative Penalized Linear Regressioncited by 31
  6. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  7. 2023GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomicscited by 27
  8. 2023Hierarchical Multi-Marginal Optimal Transport for Network Alignmentcited by 24
  9. 2022Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenterscited by 22
  10. 2021Semi-relaxed Gromov-Wasserstein divergence with applications on graphscited by 21
  11. 2024Optimizing OOD Detection in Molecular Graphs: A Novel Approach with Diffusion Modelscited by 21
  12. 2022Partially Does It: Towards Scene-Level FG-SBIR with Partial Inputcited by 20
38 more
  1. 2022Template based Graph Neural Network with Optimal Transport Distancescited by 20
  2. 2021Using Optimal Transport as Alignment Objective for fine-tuning Multilingual Contextualized Embeddingscited by 19
  3. 2023On Structural Expressive Power of Graph Transformerscited by 19
  4. 2021Quantized Gromov-Wassersteincited by 18
  5. 2022Sobolev Transport: A Scalable Metric for Probability Measures with Graph Metricscited by 18
  6. 2022Implicit Graphon Neural Representationcited by 18
  7. 2025Pave Your Own Path: Graph Gradual Domain Adaptation on Fused Gromov-Wasserstein Geodesicscited by 17
  8. 2023A Fused Gromov-Wasserstein Framework for Unsupervised Knowledge Graph Entity Alignmentcited by 16
  9. 2021On Transportation of Mini-batches: A Hierarchical Approachcited by 15
  10. 2023Robust Attributed Graph Alignment via Joint Structure Learning and Optimal Transportcited by 15
  11. 2023A Gromov--Wasserstein Geometric View of Spectrum-Preserving Graph Coarseningcited by 15
  12. 2023Fused Gromov-Wasserstein Graph Mixup for Graph-level Classificationscited by 15
  13. 2023DELFlow: Dense Efficient Learning of Scene Flow for Large-Scale Point Cloudscited by 14
  14. 2022RMS-FlowNet: Efficient and Robust Multi-Scale Scene Flow Estimation for Large-Scale Point Cloudscited by 13
  15. 2024Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wassersteincited by 12
  16. 2024The Z-Gromov-Wasserstein Distancecited by 12
  17. 2022Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsificationcited by 11
  18. 2024Graph Classification via Reference Distribution Learning: Theory and Practicecited by 11
  19. 2025Joint Self-Supervised Video Alignment and Action Segmentationcited by 11
  20. 2021Scalable Optimal Transport in High Dimensions for Graph Distances, Embedding Alignment, and Morecited by 10
  21. 2023Scalable Unbalanced Sobolev Transport for Measures on a Graphcited by 10
  22. 2023A Convergent Single-Loop Algorithm for Relaxation of Gromov-Wasserstein in Graph Datacited by 10
  23. 2023Semidefinite Relaxations of the Gromov-Wasserstein Distancecited by 10
  24. 2025Joint Optimal Transport and Embedding for Network Alignmentcited by 10
  25. 2022On a linear fused Gromov-Wasserstein distance for graph structured datacited by 9
  26. 2022InfoOT: Information Maximizing Optimal Transportcited by 9
  27. 2023PEARL: Zero-shot Cross-task Preference Alignment and Robust Reward Learning for Robotic Manipulationcited by 9
  28. 2024Accelerating Sinkhorn Algorithm with Sparse Newton Iterationscited by 9
  29. 2024Generalized Sobolev Transport for Probability Measures on a Graphcited by 9
  30. 2024Improving the Expressiveness of K-hop Message-Passing GNNs by Injecting Contextualized Substructure Informationcited by 9
  31. 2024Can Modifying Data Address Graph Domain Adaptation?cited by 9
  32. 2025Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-seq Data Analysiscited by 9
  33. 2021FGOT: Graph Distances based on Filters and Optimal Transportcited by 7
  34. 2023Efficient Graph Field Integrators Meet Point Cloudscited by 7
  35. 2023Optimal Transport for Measures with Noisy Tree Metriccited by 7
  36. 2024Gaussian process regression with Sliced Wasserstein Weisfeiler-Lehman graph kernelscited by 7
  37. 2024Any2Graph: Deep End-To-End Supervised Graph Prediction With An Optimal Transport Losscited by 7
  38. 2025Modeling Microenvironment Trajectories on Spatial Transcriptomics with NicheFlowcited by 7

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