Package index • T4transport

[1] Distance

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

sinkhorn() sinkhornD(): Wasserstein Distance via Entropic Regularization and Sinkhorn Algorithm

swdist(): Sliced Wasserstein Distance

wasserstein() wassersteinD(): Wasserstein Distance via Linear Programming

[2] Centroid

Fixed-Support Barycenter

fbary14C() fbary14Cdist(): Fixed-Support Barycenter by Cuturi & Doucet (2014)

fbary15B() fbary15Bdist(): Fixed-Support Barycenter by Benamou et al. (2015)

Free-Support Barycenter

rbary23L(): Free-Support Barycenter by von Lindheim (2023)

rbaryGD(): Free-Support Barycenter by Riemannian gradient descent

Free-Support Median

rmedGD(): Free-Support Wasserstein Median by Riemannian gradient descent

[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 \(\mathbb{R}\)

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

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

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

Histograms

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

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

Images

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

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

[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