Linear Optimal Partial Transport Embedding

Yikun Bai, Ivan Medri, Rocio Diaz Martin, Rana Muhammad Shahroz Khan, Soheil Kolouri
2/12/2026

No official code found. Best implementation: yikun-baio/LinearOPT (2 stars, last commit 2024-05-23).

Abstract

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.

View on arXivView PDF

Code Implementations(1)

yikun-baio/LinearOPTCommunity100%
20Python, Jupyter NotebookDec 9, 20222 years ago

Similar Papers

Linear Partial Gromov-Wasserstein Embedding

90% match1 repo42026

Expected Sliced Transport Plans

83% match2026

PT$\mathrm{L}^{p}$: Partial Transport $\mathrm{L}^{p}$ Distances

82% match2023

Generalized Sobolev Transport for Probability Measures on a Graph

81% match2026

Bisimulation Metrics are Optimal Transport Distances, and Can be Computed Efficiently

81% match2026

Slicing Unbalanced Optimal Transport

80% match1 repo12023

Cite this paper

@article{bai2026linear,
  title  = {Linear Optimal Partial Transport Embedding},
  author = {Yikun Bai and Ivan Medri and Rocio Diaz Martin and Rana Muhammad Shahroz Khan and Soheil Kolouri},
  year   = {2026},
  eprint = {2302.03232},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/pdf/2302.03232},
  journal = {ICML 2023 2023}
}

Add a badge to your README

Shows whether official code is linked for this paper.

Code of Paper badge
[![Code of Paper](https://codeofpaper.com/badge/2302.03232.svg)](https://codeofpaper.com/paper/2302.03232)

Discussion