# Wasserstein K-Means for Clustering Tomographic Projections

arXiv: https://arxiv.org/abs/2010.09989 · HTML: https://mlsanity.com/paper/2010.09989/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2020.

## Built on by (most cited first, 6 of 6)

- [Alignment of Density Maps in Wasserstein Distance](https://mlsanity.com/paper/2305.12310/) (2023)
- [Asymptotic Theory of Geometric and Adaptive k-Means Clustering](https://mlsanity.com/paper/2202.13423/) (2022)
- [Fast rigid alignment of heterogeneous images in sliced Wasserstein distance](https://mlsanity.com/paper/2503.13756/) (2025)
- [Quantization-based Bounds on the Wasserstein Metric](https://mlsanity.com/paper/2506.00976/) (2025)
- [Quantifying the noise sensitivity of the Wasserstein metric for images](https://mlsanity.com/paper/2510.01015/) (2025)
- [On the stability of scale-space metrics](https://mlsanity.com/paper/2606.27605/) (2026)

## Abstract (arXiv)

Motivated by the 2D class averaging problem in single-particle cryo-electron microscopy (cryo-EM), we present a k-means algorithm based on a rotationally-invariant Wasserstein metric for images. Unlike existing methods that are based on Euclidean (L2) distances, we prove that the Wasserstein metric better accommodates for the out-of-plane angular differences between different particle views. We demonstrate on a synthetic dataset that our method gives superior results compared to an L2 baseline. Furthermore, there is little computational overhead, thanks to the use of a fast linear-time approximation to the Wasserstein-1 metric, also known as the Earthmover's distance.