UnbalancedOptimalTransport

This package provides an MIT license, dependency-free implementation of Algorithm 1 of "Sinkhorn Divergences for Unbalanced Optimal Transport" [SFVTP19], which allows calculation of the optimal transport and Sinkhorn divergence between two positive measures (with possibly different total mass), where mass creation and destruction is penalized by one of several possible φ-divergences.

See the documentation for a quick tutorial as well as a mathematical description of the quantities computed by this package.

While the code is generic, it is not currently written to dispatch to BLAS or non-scalar GPU operations, although such contributions would be welcomed.

This package was motivated by a desire to compare bitmaps corresponding to printed strings in VisualStringDistances.jl.

Related packages

https://github.com/JuliaOptimalTransport/OptimalTransport.jl provides many optimal transport methods, including the unbalanced case treated here. See also #9.

Other packages (warning, this list may become outdated):

• https://github.com/mirkobunse/EarthMoversDistance.jl (wrapper of C library)
• https://github.com/mark-fangzhou-xie/JOT-Julia-Optimal-Transport (balanced only, I think)
• https://github.com/niladridas/OT_Julia (balanced only, I think)
• https://www.numerical-tours.com/julia/ (tutorials)
• https://github.com/lchizat/optimal-transport (not maintained)
• https://github.com/baggepinnen/SpectralDistances.jl (uses this package for the unbalanced case!)
• https://github.com/devmotion/OptimalTransport.jl (balanced only; exact algorithm via the network simplex method)