T4transport0.1.8 package

Tools for Computational Optimal Transport

ecdfbary

Barycenter of Empirical CDFs

ecdfmed

Wasserstein Median of Empirical CDFs

fbary14C

Fixed-Support Barycenter by Cuturi & Doucet (2014)

fbary15B

Fixed-Support Barycenter by Benamou et al. (2015)

fiedler

Compute the fiedler vector of a point cloud

gaussbary1d

Barycenter of Gaussian Distributions in R\mathbb{R}

gaussbarypd

Barycenter of Gaussian Distributions in Rp\mathbb{R}^p

gaussmed1d

Wasserstein Median of Gaussian Distributions in R\mathbb{R}

gaussmedpd

Wasserstein Median of Gaussian Distributions in Rp\mathbb{R}^p

gaussvis2d

Sampling from a Bivariate Gaussian Distribution for Visualization

gwbary

Gromov-Wasserstein Barycenter

gwdist

Gromov-Wasserstein Distance

histbary

Barycenter of Histograms

histbary14C

Barycenter of Histograms by Cuturi and Doucet (2014)

histbary15B

Barycenter of Histograms by Benamou et al. (2015)

histdist

Distance between Histograms

histinterp

Interpolation between Histograms

histmed

Wasserstein Median of Histograms

imagebary

Barycenter of Images

imagebary14C

Barycenter of Images according to Cuturi & Doucet (2014)

imagebary15B

Barycenter of Images according to Benamou et al. (2015)

imagedist

Wasserstein Distance between Two Images

imageinterp

Interpolation between Images

imagemed

Wasserstein Median of Images

img2measure

Extract a discrete measure from a gray-scale image matrix

ipot

Wasserstein Distance via Inexact Proximal Point Method

pwbary

Procrustes-Wasserstein Barycenter

pwdist

Procrustes-Wasserstein Distance

rbary23L

Free-Support Barycenter by von Lindheim (2023)

rbaryGD

Free-Support Barycenter by Riemannian Gradient Descent

rmedIRLS

Free-Support Median by IRLS

rmedWB

Free-Support Median by Weiszfeld Update with Barycentric Projection

sinkhorn

Wasserstein Distance via Entropic Regularization and Sinkhorn Algorith...

swdist

Sliced Wasserstein Distance

wassboot

Wasserstein Distance Estimation with Boostrapping

wasserstein

Wasserstein Distance via Linear Programming

Transport theory has seen much success in many fields of statistics and machine learning. We provide a variety of algorithms to compute Wasserstein distance, barycenter, and others. See Peyré and Cuturi (2019) <doi:10.1561/2200000073> for the general exposition to the study of computational optimal transport.