# Sliced Optimal Partial Transport

arXiv: https://arxiv.org/abs/2212.08049 · HTML: https://mlsanity.com/paper/2212.08049/

## Key facts

- Cited by 19 papers in the map (data through 7 Oct 2026).
- Builds on 23 of its 72 references that are in the map.
- First posted on arXiv 15 Dec 2022.

## Builds on (most cited first, 23 of 23)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures](https://mlsanity.com/paper/1508.07941/) (2015)
- [Unbalanced minibatch Optimal Transport; applications to Domain Adaptation](https://mlsanity.com/paper/2103.03606/) (2021)
- [Max-Sliced Wasserstein Distance and its use for GANs](https://mlsanity.com/paper/1904.05877/) (2019)
- [A comprehensive survey on point cloud registration](https://mlsanity.com/paper/2103.02690/) (2021)
- [Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions](https://mlsanity.com/paper/1806.08141/) (2018)
- [Sliced Wasserstein Kernels for Probability Distributions](https://mlsanity.com/paper/1511.03198/) (2015)
- [Regularized Discrete Optimal Transport](https://mlsanity.com/paper/1307.5551/) (2013)
- [Tree-Sliced Variants of Wasserstein Distances](https://mlsanity.com/paper/1902.00342/) (2019)
- [The Radon cumulative distribution transform and its application to image classification](https://mlsanity.com/paper/1511.03206/) (2015)
- [GAN and VAE from an Optimal Transport Point of View](https://mlsanity.com/paper/1706.01807/) (2017)
- [Fast and Robust Comparison of Probability Measures in Heterogeneous Spaces](https://mlsanity.com/paper/2002.01615/) (2020)
- [Unnormalized Optimal Transport](https://mlsanity.com/paper/1902.03367/) (2019)
- [On properties of the Generalized Wasserstein distance](https://mlsanity.com/paper/1304.7014/) (2013)
- [Imaging with Kantorovich-Rubinstein discrepancy](https://mlsanity.com/paper/1407.0221/) (2014)
- [Generalized Unnormalized Optimal Transport and its fast algorithms](https://mlsanity.com/paper/2001.11530/) (2020)
- [Kantorovich-Rubinstein distance and barycenter for finitely supported measures: Foundations and Algorithms](https://mlsanity.com/paper/2112.03581/) (2021)

## Built on by (most cited first, 19 of 19)

- [Sliced Wasserstein with Random-Path Projecting Directions](https://mlsanity.com/paper/2401.15889/) (2024)
- [Markovian Sliced Wasserstein Distances: Beyond Independent Projections](https://mlsanity.com/paper/2301.03749/) (2023)
- [Linear Optimal Partial Transport Embedding](https://mlsanity.com/paper/2302.03232/) (2023)
- [Rethinking Optimal Transport in Offline Reinforcement Learning](https://mlsanity.com/paper/2410.14069/) (2024)
- [Tree-Sliced Wasserstein Distance: A Geometric Perspective](https://mlsanity.com/paper/2406.13725/) (2024)
- [Measure transfer via stochastic slicing and matching](https://mlsanity.com/paper/2307.05705/) (2023)
- [LCOT: Linear circular optimal transport](https://mlsanity.com/paper/2310.06002/) (2023)
- [Efficient Transferable Optimal Transport via Min-Sliced Transport Plans](https://mlsanity.com/paper/2511.19741/) (2025)
- [PTLp: Partial Transport Lp Distances](https://mlsanity.com/paper/2307.13571/) (2023)
- [Partial Transport for Point-Cloud Registration](https://mlsanity.com/paper/2309.15787/) (2023)
- [Learning Partial Graph Matching via Optimal Partial Transport](https://mlsanity.com/paper/2410.16718/) (2024)
- [Laplace Learning in Wasserstein Space](https://mlsanity.com/paper/2511.13229/) (2025)
- [Partial Distribution Matching via Partial Wasserstein Adversarial Networks](https://mlsanity.com/paper/2409.10499/) (2024)
- [Linear Partial Gromov-Wasserstein Embedding](https://mlsanity.com/paper/2410.16669/) (2024)
- [Geometry-Aware Dataset Condensation for Diffusion Model Training](https://mlsanity.com/paper/2606.05883/) (2026)
- [Sinkhorn algorithms and linear programming solvers for optimal partial transport problems](https://mlsanity.com/paper/2407.06481/) (2024)
- [HOT-POT: Optimal Transport for Sparse Stereo Matching](https://mlsanity.com/paper/2601.12423/) (2026)
- [Ranking vs. Assignment: The Metric Mismatch in Multi-View Object Association](https://mlsanity.com/paper/2606.02022/) (2026)
- [Partial Optimal Transport on the Circle for All Transported Masses in O(N log N)](https://mlsanity.com/paper/2608.23910/) (2026)

## Abstract (arXiv)

Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision. The core assumption in the OT problem is the equal total amount of mass in source and target measures, which limits its application. Optimal Partial Transport (OPT) is a recently proposed solution to this limitation. Similar to the OT problem, the computation of OPT relies on solving a linear programming problem (often in high dimensions), which can become computationally prohibitive. In this paper, we propose an efficient algorithm for calculating the OPT problem between two non-negative measures in one dimension. Next, following the idea of sliced OT distances, we utilize slicing to define the sliced OPT distance. Finally, we demonstrate the computational and accuracy benefits of the sliced OPT-based method in various numerical experiments. In particular, we show an application of our proposed Sliced-OPT in noisy point cloud registration.