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[1] Core OT for Empirical Measures

Distances

hdist()
Distance between Histograms
ipot() ipotD()
Wasserstein Distance via Inexact Proximal Point Method
pwdist()
Procrustes-Wasserstein Distance
sinkhorn() sinkhornD()
Wasserstein Distance via Entropic Regularization and Sinkhorn Algorithm
swdist()
Sliced Wasserstein Distance
wassboot()
Wasserstein Distance Estimation with Boostrapping
wasserstein() wassersteinD()
Wasserstein Distance via Linear Programming

Free-Support Centroids

pwbary()
Procrustes-Wasserstein Barycenter
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

Fixed-Support Centroids

fbary14C() fbary14Cdist()
Fixed-Support Barycenter by Cuturi & Doucet (2014)
fbary15B() fbary15Bdist()
Fixed-Support Barycenter by Benamou et al. (2015)

[2] Modality-Specific

Cumulative Distribution Functions

ecdfbary()
Barycenter of Empirical CDFs
ecdfmed()
Wasserstein Median of Empirical CDFs

Gaussian Measures

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

histbary()
Barycenter of Histograms
histbary14C()
Barycenter of Histograms by Cuturi and Doucet (2014)
histbary15B()
Barycenter of Histograms by Benamou et al. (2015)
histinterp()
Interpolation between Histograms
histmed()
Wasserstein Median of Histograms

Images

imagebary14C()
Barycenter of Images according to Cuturi & Doucet (2014)
imagebary15B()
Barycenter of Images according to Benamou et al. (2015)

[3] Gromov–Wasserstein

gwbary()
Gromov-Wasserstein Barycenter
gwdist()
Gromov-Wasserstein Distance

[4] Data Sets

digit3
MNIST Images of Digit 3
digits
MNIST Images of All Digits

[5] Utilities

fiedler()
Compute the fiedler vector of a point cloud
gaussvis2d()
Sampling from a Bivariate Gaussian Distribution for Visualization
img2measure()
Extract a discrete measure from a gray-scale image matrix