# SlicedWasserstein.jl

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

The package currently provides:

• a DiscreteMeasure type for finite weighted 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.

Installation

using Pkg
Pkg.add("SlicedWasserstein")

Quick start

using SlicedWasserstein

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

SOT(μ, ν; M = 100, seed = 1)

1.230026516195585

Further reading

See Background and methodology for a short introduction to the optimal transport and sliced Wasserstein ideas used by the package.

See API Reference for the documented public interface.

Contents

• • Installation
  • Quick start
  • Further reading
  • Contents
  • Optimal transport
  • Sliced optimal transport
  • Discrete measures
  • One-dimensional optimal transport
  • Sliced Wasserstein barycenters
  • Sliced Wasserstein k-means
  • Computational notes
  • References
  • Measures
  • Projections
  • One-dimensional optimal transport
  • Sliced optimal transport
  • Barycenters
  • Clustering
  • Display helpers