# Variational Wasserstein Barycenters for Geometric Clustering

arXiv: https://arxiv.org/abs/2002.10543 · HTML: https://mlsanity.com/paper/2002.10543/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2020.

## Built on by (most cited first, 1 of 1)

- [Tree-Based Diffusion Schr"odinger Bridge with Applications to Wasserstein Barycenters](https://mlsanity.com/paper/2305.16557/) (2023)

## Abstract (arXiv)

We propose to compute Wasserstein barycenters (WBs) by solving for Monge maps with variational principle. We discuss the metric properties of WBs and explore their connections, especially the connections of Monge WBs, to K-means clustering and co-clustering. We also discuss the feasibility of Monge WBs on unbalanced measures and spherical domains. We propose two new problems -- regularized K-means and Wasserstein barycenter compression. We demonstrate the use of VWBs in solving these clustering-related problems.