# A Relaxed Wasserstein Distance Formulation for Mixtures of Radially Contoured Distributions

arXiv: https://arxiv.org/abs/2503.13893 · HTML: https://mlsanity.com/paper/2503.13893/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 18 Mar 2025.

## Builds on (most cited first, 10 of 10)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [A Wasserstein-type distance in the space of Gaussian Mixture Models](https://mlsanity.com/paper/1907.05254/) (2019)
- [On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithms](https://mlsanity.com/paper/1901.06482/) (2019)
- [Diffeomorphic density matching by optimal information transport](https://mlsanity.com/paper/1501.07635/) (2015)
- [Generalized Sinkhorn iterations for regularizing inverse problems using optimal mass transport](https://mlsanity.com/paper/1612.02273/) (2016)
- [Optimal Transport and Wasserstein Barycenter for Radially Contoured Distributions](https://mlsanity.com/paper/2404.08383/) (2024)

## Abstract (arXiv)

Recently, a Wasserstein-type distance for Gaussian mixture models has been proposed. However, that framework can only be generalized to identifiable mixtures of general elliptically contoured distributions whose components come from the same family and satisfy marginal consistency. In this paper, we propose a simple relaxed Wasserstein distance for identifiable mixtures of radially contoured distributions whose components can come from different families. We show some properties of this distance and that its definition does not require marginal consistency. We apply this distance in color transfer tasks and compare its performance with the Wasserstein-type distance for Gaussian mixture models in an experiment. The error of our method is more stable and the color distribution of our output image is more desirable.