spd.wassbary: Wasserstein Barycenter of SPD Matrices

In Riemann: Learning with Data on Riemannian Manifolds

Wasserstein Barycenter of SPD Matrices

Description

Given N observations X_1, X_2, …, X_N in SPD manifold, compute the L_2-Wasserstein barycenter that minimizes

∑_{n=1}^N λ_i \mathcal{W}_2 (N(X), N(X_i))^2

where N(X) denotes the zero-mean Gaussian measure with covariance X.

Usage

spd.wassbary(spdobj, weight = NULL, method = c("RU02", "AE16"), ...)

Arguments

spdobj	a S3 "riemdata" class of SPD-valued data of (p\times p) matrices.
weight	weight of observations; if NULL it assumes equal weights, or a nonnegative length-N vector that sums to 1 should be given.
method	name of the algortihm to be used; one of the "RU02", "AE16".
...	extra parameters including maxiter maximum number of iterations to be run (default:20). abstol tolerance level for stopping criterion (default: 1e-8).

Value

a (p\times p) Wasserstein barycenter matrix.

Examples

#-------------------------------------------------------------------
#        Covariances from standard multivariate Gaussians.
#-------------------------------------------------------------------
## GENERATE DATA
ndata = 20
pdim  = 10
mydat = array(0,c(pdim,pdim,ndata))
for (i in 1:ndata){
  mydat[,,i] = stats::cov(matrix(rnorm(100*pdim), ncol=pdim))
}
myriem = wrap.spd(mydat)

## COMPUTE BY DIFFERENT ALGORITHMS
baryRU <- spd.wassbary(myriem, method="RU02")
baryAE <- spd.wassbary(myriem, method="AE16")

## VISUALIZE
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3), pty="s")
image(diag(pdim), axes=FALSE, main="True Covariance")
image(baryRU, axes=FALSE, main="by RU02")
image(baryAE, axes=FALSE, main="by AE16")
par(opar)

Riemann documentation built on March 18, 2022, 7:55 p.m.