Approximation of Wasserstein distance with Transshipment

TL;DR

This paper introduces a scalable algorithm for approximating the p-Wasserstein distance between histograms on unstructured grids, utilizing barycenter computation constrained to low-dimensional subspaces and a multi-scale approach.

Contribution

It presents a novel transshipment-based method with a multi-scale strategy for efficient Wasserstein distance approximation on large, unstructured datasets.

Findings

Provides sparse transport matrices for efficiency

Applicable to large-scale, non-structured data

Achieves accurate approximations with reduced computational complexity

Abstract

An algorithm for approximating the p-Wasserstein distance between histograms defined on unstructured discrete grids is presented. It is based on the computation of a barycenter constrained to be supported on a low dimensional subspace, which corresponds to a transshipment problem. A multi-scale strategy is also considered. The method provides sparse transport matrices and can be applied to large scale and non structured data.