Function reference • T4transport

[1] Distance

Wasserstein Distance

ipot() ipotD(): Wasserstein Distance by Inexact Proximal Point Method

sinkhorn() sinkhornD(): Wasserstein Distance by Entropic Regularization

wasserstein() wassersteinD(): Wasserstein Distance between Empirical Measures

Others

swdist(): Sliced Wasserstein Distance

[2] Wasserstein Barycenter

Fixed Support

bary14C() bary14Cdist(): Barycenter by Cuturi & Doucet (2014)

bary15B() bary15Bdist(): Barycenter by Benamou et al. (2015)

[3] Special Cases

Cumulative Distribution Functions

ecdfbary(): Barycenter of Empirical CDFs

ecdfmed(): Wasserstein Median of Empirical CDFs

Gaussian Distributions

gaussbary1d(): Barycenter of Gaussian Distributions in \(\mathbf{R}\)

gaussbarypd(): Barycenter of Gaussian Distributions in \(\mathbf{R}^p\)

gaussmed1d(): Wasserstein Median of Gaussian Distributions in \(\mathbf{R}\)

gaussmedpd(): Wasserstein Median of Gaussian Distributions in \(\mathbf{R}^p\)

Histograms

histbary14C(): Barycenter of Histograms by Cuturi & Doucet (2014)

histbary15B(): Barycenter of Histograms by Benamou et al. (2015)

histmed22Y(): Wasserstein Median of Histograms by You et al. (2022)

Images

imagebary14C(): Barycenter of Images according to Cuturi & Doucet (2014)

imagebary15B(): Barycenter of Images according to Benamou et al. (2015)

imagemed22Y(): Wasserstein Median of Images by You et al. (2022)

[4] Data

digit3: MNIST Images of Digit 3

digits: MNIST Images of All Digits

[5] Others

gaussvis2d(): Sampling from a Bivariate Gaussian Distribution for Visualization