# A Wasserstein-type Distance for Gaussian Mixtures on Vector Bundles with Applications to Shape Analysis

arXiv: https://arxiv.org/abs/2311.16988 · HTML: https://mlsanity.com/paper/2311.16988/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2023.

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

- [Slicing the Gaussian Mixture Wasserstein Distance](https://mlsanity.com/paper/2504.08544/) (2025)
- [Fused Gromov-Wasserstein Variance Decomposition with Linear Optimal Transport](https://mlsanity.com/paper/2411.10204/) (2024)
- [Entropic Partial Optimal Transport and Partial Gromov--Wasserstein Distance between Gaussian Mixtures](https://mlsanity.com/paper/2608.09265/) (2026)

## Abstract (arXiv)

This paper uses sample data to study the problem of comparing populations on finite-dimensional parallelizable Riemannian manifolds and more general trivial vector bundles. Utilizing triviality, our framework represents populations as mixtures of Gaussians on vector bundles and estimates the population parameters using a mode-based clustering algorithm. We derive a Wasserstein-type metric between Gaussian mixtures, adapted to the manifold geometry, in order to compare estimated distributions. Our contributions include an identifiability result for Gaussian mixtures on manifold domains and a convenient characterization of optimal couplings of Gaussian mixtures under the derived metric. We demonstrate these tools on some example domains, including the pre-shape space of planar closed curves, with applications to the shape space of triangles and populations of nanoparticles. In the nanoparticle application, we consider a sequence of populations of particle shapes arising from a manufacturing process, and utilize the Wasserstein-type distance to perform change-point detection.