mlsanityData to 7 Oct 2026

A Framework for Wasserstein-1-Type Metrics

arXiv 1701.01945 ↗First posted 8 Jan 2017math.OC cs.CV cs.NAcited by 8

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Abstract (arXiv)

We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy measure between nonnegative measures of different mass. This generalization inherits the convexity and computational efficiency from the Wasserstein-1 metric, and it includes several previous approaches from the literature as special cases. For various specific instances of the generalized Wasserstein-1 metric we furthermore demonstrate their usefulness in applications by numerical experiments.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Jan 2017.

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Citing papers per year: 2021: 2; 2022: 3; 2023: 1; 2024: 2.

8 papers.

  1. 2021Unbalanced minibatch Optimal Transport; applications to Domain Adaptationcited by 123
  2. 2022Unbalanced Optimal Transport, from Theory to Numericscited by 45
  3. 2021Outlier-Robust Optimal Transport: Duality, Structure, and Statistical Analysiscited by 27
  4. 2022Faster Unbalanced Optimal Transport: Translation invariant Sinkhorn and 1-D Frank-Wolfecited by 22
  5. 2023Robust Estimation under the Wasserstein Distancecited by 8
  6. 2022Partial Wasserstein Adversarial Network for Non-rigid Point Set Registrationcited by 5
  7. 2024Robust Distribution Learning with Local and Global Adversarial Corruptionscited by 5
  8. 2024Partial Distribution Matching via Partial Wasserstein Adversarial Networkscited by 1