mlsanityData to 7 Oct 2026

Linear Optimal Partial Transport Embedding

arXiv 2302.03232 ↗First posted 7 Feb 2023cs.LG math.OCcited by 8

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Abstract (arXiv)

Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To address these limitations, variants of the OT problem, including unbalanced OT, Optimal partial transport (OPT), and Hellinger Kantorovich (HK), have been proposed. In this paper, we propose the Linear optimal partial transport (LOPT) embedding, which extends the (local) linearization technique on OT and HK to the OPT problem. The proposed embedding allows for faster computation of OPT distance between pairs of positive measures. Besides our theoretical contributions, we demonstrate the LOPT embedding technique in point-cloud interpolation and PCA analysis.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 20 of its 46 references that are in the map. First posted on arXiv 7 Feb 2023.

Builds on

20 of 46 references.

References · 20

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  2. 2017Joint Distribution Optimal Transportation for Domain Adaptationcited by 280
  3. 2013Fast Computation of Wasserstein Barycenterscited by 216
  4. 2015Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measurescited by 138
  5. 2021Unbalanced minibatch Optimal Transport; applications to Domain Adaptationcited by 123
  6. 2020Faster Wasserstein Distance Estimation with the Sinkhorn Divergencecited by 73
  7. 2020Wasserstein Embedding for Graph Learningcited by 56
  8. 2021Improving Mini-batch Optimal Transport via Partial Transportationcited by 40
  9. 2020Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbationscited by 37
  10. 2015Fast Discrete Distribution Clustering Using Wasserstein Barycenter with Sparse Supportcited by 30
  11. 2022Low-rank Optimal Transport: Approximation, Statistics and Debiasingcited by 21
  12. 2017GAN and VAE from an Optimal Transport Point of Viewcited by 19
8 more
  1. 2022Sliced Optimal Partial Transportcited by 19
  2. 2018Wasserstein regularization for sparse multi-task regressioncited by 18
  3. 2020Linearized Optimal Transport for Collider Eventscited by 16
  4. 2020Partitioning signal classes using transport transforms for data analysis and machine learningcited by 15
  5. 2021The Linearized Hellinger--Kantorovich Distancecited by 11
  6. 2014Imaging with Kantorovich-Rubinstein discrepancycited by 10
  7. 2023Self-Attention Amortized Distributional Projection Optimization for Sliced Wasserstein Point-Cloud Reconstructioncited by 7
  8. 2017Discovery and visualization of structural biomarkers from MRI using transport-based morphometrycited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 4; 2025: 0; 2026: 1.

8 papers.

  1. 2024Expected Sliced Transport Planscited by 19
  2. 2023Manifold learning in Wasserstein spacecited by 6
  3. 2023PTLp: Partial Transport Lp Distancescited by 2
  4. 2023Partial Transport for Point-Cloud Registrationcited by 2
  5. 2024Resistance Distance and Linearized Optimal Transport on Graphscited by 1
  6. 2024Linear Partial Gromov-Wasserstein Embeddingcited by 1
  7. 2026Geometry-Aware Dataset Condensation for Diffusion Model Trainingcited by 1
  8. 2024Fused Gromov-Wasserstein Variance Decomposition with Linear Optimal Transportcited by 0