Function reference

[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