# Linearized optimal transport on manifolds

arXiv: https://arxiv.org/abs/2303.13901 · HTML: https://mlsanity.com/paper/2303.13901/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2023.

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

- [Manifold learning in Wasserstein space](https://mlsanity.com/paper/2311.08549/) (2023)
- [LCOT: Linear circular optimal transport](https://mlsanity.com/paper/2310.06002/) (2023)
- [Generalized Wasserstein Flow Matching: Transport Plans, Everywhere, All at Once](https://mlsanity.com/paper/2605.08424/) (2026)
- [Resistance Distance and Linearized Optimal Transport on Graphs](https://mlsanity.com/paper/2404.15261/) (2024)
- [Barycentric Projections of Optimal Transport Plans on Riemannian Manifolds](https://mlsanity.com/paper/2606.07926/) (2026)
- [Fused Gromov-Wasserstein Variance Decomposition with Linear Optimal Transport](https://mlsanity.com/paper/2411.10204/) (2024)

## Abstract (arXiv)

Optimal transport is a geometrically intuitive, robust and flexible metric for sample comparison in data analysis and machine learning. Its formal Riemannian structure allows for a local linearization via a tangent space approximation. This in turn leads to a reduction of computational complexity and simplifies combination with other methods that require a linear structure. Recently this approach has been extended to the unbalanced Hellinger--Kantorovich (HK) distance. In this article we further extend the framework in various ways, including measures on manifolds, the spherical HK distance, a study of the consistency of discretization via the barycentric projection, and the continuity properties of the logarithmic map for the HK distance.