# Making transport more robust and interpretable by moving data through a small number of anchor points

arXiv: https://arxiv.org/abs/2012.11589 · HTML: https://mlsanity.com/paper/2012.11589/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2020.

## Built on by (most cited first, 18 of 18)

- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Hierarchical Refinement: Optimal Transport to Infinity and Beyond](https://mlsanity.com/paper/2503.03025/) (2025)
- [LiveSeg: Unsupervised Multimodal Temporal Segmentation of Long Livestream Videos](https://mlsanity.com/paper/2210.05840/) (2022)
- [Your contrastive learning problem is secretly a distribution alignment problem](https://mlsanity.com/paper/2502.20141/) (2025)
- [Approximating Optimal Transport via Low-rank and Sparse Factorization](https://mlsanity.com/paper/2111.06546/) (2021)
- [Feedback Schr"odinger Bridge Matching](https://mlsanity.com/paper/2410.14055/) (2024)
- [Discriminative Radial Domain Adaptation](https://mlsanity.com/paper/2301.00383/) (2023)
- [Factored couplings in multi-marginal optimal transport via difference of convex programming](https://mlsanity.com/paper/2110.00629/) (2021)
- [Wasserstein Distances Made Explainable: Insights Into Dataset Shifts and Transport Phenomena](https://mlsanity.com/paper/2505.06123/) (2025)
- [Selective Cross-Task Distillation](https://mlsanity.com/paper/2204.11526/) (2022)
- [Budget-Constrained Bounds for Mini-Batch Estimation of Optimal Transport](https://mlsanity.com/paper/2210.13630/) (2022)
- [Keypoint-Guided Optimal Transport: Models, Algorithms, and Applications](https://mlsanity.com/paper/2303.13102/) (2023)
- [Anchor Space Optimal Transport as a Fast Solution to Multiple Optimal Transport Problems](https://mlsanity.com/paper/2310.16123/) (2023)
- [Many-to-Many Matching via Sparsity Controlled Optimal Transport](https://mlsanity.com/paper/2503.24204/) (2025)
- [Simplifying Optimal Transport through Schatten-p Regularization](https://mlsanity.com/paper/2510.11910/) (2025)
- [Transport Clustering: Solving Low-Rank Optimal Transport via Clustering](https://mlsanity.com/paper/2603.03578/) (2026)
- [Reliable Modeling of Distribution Shifts via Displacement-Reshaped Optimal Transport](https://mlsanity.com/paper/2605.04965/) (2026)
- [QDSB: Quantized Diffusion Schr"odinger Bridges](https://mlsanity.com/paper/2605.11983/) (2026)

## Abstract (arXiv)

Optimal transport (OT) is a widely used technique for distribution alignment, with applications throughout the machine learning, graphics, and vision communities. Without any additional structural assumptions on trans-port, however, OT can be fragile to outliers or noise, especially in high dimensions. Here, we introduce a new form of structured OT that simultaneously learns low-dimensional structure in data while leveraging this structure to solve the alignment task. Compared with OT, the resulting transport plan has better structural interpretability, highlighting the connections between individual data points and local geometry, and is more robust to noise and sampling. We apply the method to synthetic as well as real datasets, where we show that our method can facilitate alignment in noisy settings and can be used to both correct and interpret domain shift.