getWFmean {fdadensity}

Wasserstein Frechet Mean Computation

Description

Function for computing the Wasserstein Frechet mean through quantile density averaging

Usage

getWFmean(
  dmatrix,
  dSup,
  N = length(dSup),
  qdSup = seq(0, 1, length.out = N),
  useAlpha = FALSE,
  alpha = 0.01
)

Arguments

dmatrix

matrix of density values on dSup - must be strictly positive and each row must integrate to 1

dSup

support (grid) for Density domain

N

desired number of points on a [0,1] grid for quantile density functions; default length(dSup)

qdSup

support for LQ domain - must begin at 0 and end at 1; default [0,1] with N-equidistant support points

useAlpha

should regularisation be performed (default=FALSE)

alpha

Scalar to regularise the supports with (default=0.01)

Value

wfmean the Wasserstein-Frechet mean density

References

Functional Data Analysis for Density Functions by Transformation to a Hilbert space, Alexander Petersen and Hans-Georg Mueller, 2016

Examples

x <- seq(0,1,length.out = 101)
# linear densities on (0, 1)
y <- t(sapply(seq(0.5, 1.5, length.out = 10), function(b) b + 2*(1 - b)*x)) 
wfmean = getWFmean(y, x)

# Plot WF mean with Euclidean Mean
matplot(x, t(y), ylab = 'Density', type = 'l', lty = 1, col = 'black')
lines(x, wfmean, lwd = 2, col = 'red')
lines(x, colMeans(y), lwd = 2, col = 'blue')
legend('topright', col = c('black', 'red', 'blue'), lwd = c(1, 2, 2), 
           legend = c('Densities', 'WF Mean', 'Euclidean Mean'))