mlsanityData to 7 Oct 2026

Unbalanced CO-Optimal Transport

arXiv 2205.14923 ↗First posted 30 May 2022stat.ML cs.LGcited by 6

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Abstract (arXiv)

Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples. CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well. While this approach leads to better alignments and generalizes both OT and Gromov-Wasserstein distances, we provide a theoretical result showing that it is sensitive to outliers that are omnipresent in real-world data. This prompts us to propose unbalanced COOT for which we provably show its robustness to noise in the compared datasets. To the best of our knowledge, this is the first such result for OT methods in incomparable spaces. With this result in hand, we provide empirical evidence of this robustness for the challenging tasks of heterogeneous domain adaptation with and without varying proportions of classes and simultaneous alignment of samples and features across single-cell measurements.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 27 of its 73 references that are in the map. First posted on arXiv 30 May 2022.

Builds on

27 of 73 references.

References · 27

  1. 2014Going Deeper with Convolutionscited by 4,231
  2. 2015Optimal Transport for Domain Adaptationcited by 457
  3. 2014Caffe: Convolutional Architecture for Fast Feature Embeddingcited by 287
  4. 2015Learning with a Wasserstein Losscited by 194
  5. 2018Optimal Transport for structured data with application on graphscited by 170
  6. 2015Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measurescited by 138
  7. 2019Gromov-Wasserstein Learning for Graph Matching and Node Embeddingcited by 125
  8. 2021Unbalanced minibatch Optimal Transport; applications to Domain Adaptationcited by 123
  9. 2018Gromov-Wasserstein Alignment of Word Embedding Spacescited by 119
  10. 2019Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matchingcited by 102
  11. 2020Robust Optimal Transport with Applications in Generative Modeling and Domain Adaptationcited by 86
  12. 2016Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problemscited by 69
15 more
  1. 2018Optimal Transport for Multi-source Domain Adaptation under Target Shiftcited by 67
  2. 2021Low-Rank Sinkhorn Factorizationcited by 66
  3. 2020On Unbalanced Optimal Transport: An Analysis of Sinkhorn Algorithmcited by 61
  4. 2020The Unbalanced Gromov Wasserstein Distance: Conic Formulation and Relaxationcited by 55
  5. 2013Regularized Discrete Optimal Transportcited by 54
  6. 2020Outlier-Robust Optimal Transportcited by 45
  7. 2020CO-Optimal Transportcited by 42
  8. 2018Scalable Unbalanced Optimal Transport using Generative Adversarial Networkscited by 41
  9. 2019Multi-marginal Wasserstein GANcited by 32
  10. 2021Unbalanced Optimal Transport through Non-negative Penalized Linear Regressioncited by 31
  11. 2021Hypergraph Co-Optimal Transport: Metric and Categorical Propertiescited by 10
  12. 2019Parallel Unbalanced Optimal Transport Regularization for Large Scale Imaging Problemscited by 8
  13. 2021Cycle Consistent Probability Divergences Across Different Spacescited by 5
  14. 2019Group level MEG/EEG source imaging via optimal transport: minimum Wasserstein estimatescited by 2
  15. 2020Entropy-Transport distances between unbalanced metric measure spacescited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 1; 2025: 1; 2026: 1.

6 papers.

  1. 2023Outlier-Robust Gromov-Wasserstein for Graph Datacited by 6
  2. 2024Quantum Theory and Application of Contextual Optimal Transportcited by 3
  3. 2023OT-Net: A Reusable Neural Optimal Transport Solvercited by 2
  4. 2025Conic Formulations of Transport Metrics for Unbalanced Measure Networks and Hypernetworkscited by 2
  5. 2023Computing the Distance between unbalanced Distributions -- The flat Metriccited by 1
  6. 2026MS-COOT: Comparing Morse-Smale Complexes with Co-Optimal Transportcited by 0