# Clustering, factor discovery and optimal transport

arXiv: https://arxiv.org/abs/1902.10288 · HTML: https://mlsanity.com/paper/1902.10288/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2019.

## Built on by (most cited first, 4 of 4)

- [Wasserstein Distributionally Robust Optimization with Wasserstein Barycenters](https://mlsanity.com/paper/2203.12136/) (2022)
- [Discriminative Radial Domain Adaptation](https://mlsanity.com/paper/2301.00383/) (2023)
- [Ironing the Graphs: Toward a Correct Geometric Analysis of Large-Scale Graphs](https://mlsanity.com/paper/2407.21609/) (2024)
- [New Algorithmic Directions in Optimal Transport and Applications for Product Spaces](https://mlsanity.com/paper/2509.21502/) (2025)

## Abstract (arXiv)

The clustering problem, and more generally, latent factor discovery --or latent space inference-- is formulated in terms of the Wasserstein barycenter problem from optimal transport. The objective proposed is the maximization of the variability attributable to class, further characterized as the minimization of the variance of the Wasserstein barycenter. Existing theory, which constrains the transport maps to rigid translations, is extended to affine transformations. The resulting non-parametric clustering algorithms include k-means as a special case and exhibit more robust performance. A continuous version of these algorithms discovers continuous latent variables and generalizes principal curves. The strength of these algorithms is demonstrated by tests on both artificial and real-world data sets.