# Vector-Valued Optimal Mass Transport

arXiv: https://arxiv.org/abs/1611.09946 · HTML: https://mlsanity.com/paper/1611.09946/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2016.

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

- [Learning the temporal evolution of multivariate densities via normalizing flows](https://mlsanity.com/paper/2107.13735/) (2021)
- [Riemannian block SPD coupling manifold and its application to optimal transport](https://mlsanity.com/paper/2201.12933/) (2022)
- [Resistance Distance and Linearized Optimal Transport on Graphs](https://mlsanity.com/paper/2404.15261/) (2024)

## Abstract (arXiv)

We introduce the problem of transporting vector-valued distributions. In this, a salient feature is that mass may flow between vectorial entries as well as across space (discrete or continuous). The theory relies on a first step taken to define an appropriate notion of optimal transport on a graph. The corresponding distance between distributions is readily computable via convex optimization and provides a suitable generalization of Wasserstein-type metrics. Building on this, we define Wasserstein-type metrics on vector-valued distributions supported on continuous spaces as well as graphs. Motivation for developing vector-valued mass transport is provided by applications such as multi-color image processing, polarimetric radar, as well as network problems where resources may be vectorial.