# Wasserstein t-SNE

arXiv: https://arxiv.org/abs/2205.07531 · HTML: https://mlsanity.com/paper/2205.07531/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 21 references that are in the map.
- First posted on arXiv 16 May 2022.

## Builds on (most cited first, 4 of 4)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [From Louvain to Leiden: guaranteeing well-connected communities](https://mlsanity.com/paper/1810.08473/) (2018)
- [Parallelizing the dual revised simplex method](https://mlsanity.com/paper/1503.01889/) (2015)
- [Wasserstein Discriminant Analysis](https://mlsanity.com/paper/1608.08063/) (2016)

## Built on by (most cited first, 3 of 3)

- [Wasserstein Wormhole: Scalable Optimal Transport Distance with Transformers](https://mlsanity.com/paper/2404.09411/) (2024)
- [Fast and Adaptive Questionnaires for Voting Advice Applications](https://mlsanity.com/paper/2404.01872/) (2024)
- [IXPLORE: Bounded Ideal Point Estimation with Grid-Based Uncertainty Quantification](https://mlsanity.com/paper/2609.06018/) (2026)

## Abstract (arXiv)

Scientific datasets often have hierarchical structure: for example, in surveys, individual participants (samples) might be grouped at a higher level (units) such as their geographical region. In these settings, the interest is often in exploring the structure on the unit level rather than on the sample level. Units can be compared based on the distance between their means, however this ignores the within-unit distribution of samples. Here we develop an approach for exploratory analysis of hierarchical datasets using the Wasserstein distance metric that takes into account the shapes of within-unit distributions. We use t-SNE to construct 2D embeddings of the units, based on the matrix of pairwise Wasserstein distances between them. The distance matrix can be efficiently computed by approximating each unit with a Gaussian distribution, but we also provide a scalable method to compute exact Wasserstein distances. We use synthetic data to demonstrate the effectiveness of our Wasserstein t-SNE, and apply it to data from the 2017 German parliamentary election, considering polling stations as samples and voting districts as units. The resulting embedding uncovers meaningful structure in the data.