SlicedWasserstein.jl

SlicedWasserstein.jl is a lightweight Julia package for computations with finite discrete measures using sliced optimal transport.

The package currently provides:

• finite weighted discrete measures;
• one-dimensional optimal transport for discrete measures;
• Monte Carlo estimates of sliced Wasserstein costs;
• free-support sliced Wasserstein barycenters;
• sliced Wasserstein k-means clustering.

The package is currently in an early v0.1 stage, and the public API may still evolve.

Installation

using Pkg
Pkg.add("SlicedWasserstein")

Quick start

using SlicedWasserstein

μ = DiscreteMeasure(randn(2, 50))
ν = DiscreteMeasure(randn(2, 50) .+ 1)

sot = SOT(μ, ν; M = 100, seed = 1)

Documentation

The package includes Documenter-based documentation in the docs/ directory.

To build the documentation locally, run:

julia --project=docs docs/make.jl

The documentation contains:

• a short background section on optimal transport and sliced Wasserstein methods;
• examples for the main functionality;
• an API reference for exported functions and types.

Status

This package is under active development. It is intended for computations with finite discrete measures and currently focuses on clarity, reproducibility, and a small dependency footprint.

Use of generative AI

Some documentation and repository-maintenance changes were prepared with assistance from generative AI tools. All code, documentation, and package metadata are reviewed, edited, and validated by the human maintainer, who takes responsibility for the contents of the package.

References

• G. Peyré and M. Cuturi. Computational Optimal Transport. Foundations and Trends in Machine Learning, 2019.
• K. Nguyen. An Introduction to Sliced Optimal Transport. Foundations and Trends in Computer Graphics and Vision, 2025.
• N. Bonneel, G. Peyré, M. Cuturi, et al. Sliced and Radon Wasserstein Barycenters of Measures. Journal of Mathematical Imaging and Vision, 2015.