# Neighbor Embeddings Using Unbalanced Optimal Transport Metrics

arXiv: https://arxiv.org/abs/2509.19226 · HTML: https://mlsanity.com/paper/2509.19226/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 22 references that are in the map.
- First posted on arXiv 23 Sep 2025.

## Builds on (most cited first, 7 of 7)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Manifold learning: what, how, and why](https://mlsanity.com/paper/2311.03757/) (2023)
- [Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning](https://mlsanity.com/paper/2204.06645/) (2022)
- [The Linearized Hellinger--Kantorovich Distance](https://mlsanity.com/paper/2102.08807/) (2021)
- [Heuristic Framework for Multi-Scale Testing of the Multi-Manifold Hypothesis](https://mlsanity.com/paper/1807.00349/) (2018)
- [Hellinger-Kantorovich barycenter between Dirac measures](https://mlsanity.com/paper/2206.11211/) (2022)

## Abstract (arXiv)

This paper proposes the use of the Hellinger--Kantorovich metric from unbalanced optimal transport (UOT) in a dimensionality reduction and learning (supervised and unsupervised) pipeline. The performance of UOT is compared to that of regular OT and Euclidean-based dimensionality reduction methods on several benchmark datasets including MedMNIST. The experimental results demonstrate that, on average, UOT shows improvement over both Euclidean and OT-based methods as verified by statistical hypothesis tests. In particular, on the MedMNIST datasets, UOT outperforms OT in classification 81% of the time. For clustering MedMNIST, UOT outperforms OT 83% of the time and outperforms both other metrics 58% of the time.