Pairwise Wasserstein-like Distance between two vMF distributions

Given a collection of von Misees-Fisher (vMF) distributions, compute the pairwise distance using the Wasserstein-like distance from an approximate Wasserstein geometry.

WLpdist(means, concentrations)

Arguments

means

An \((n \times p)\) matrix where each row represents the mean direction of one of the \(n\) vMF distributions.

concentrations

A length-\(n\) vector of nonnegative concentration parameters.

Value

An \((n \times n)\) matrix of pairwise distances.

Examples

# \donttest{
# Set seed for reproducibility
set.seed(123)

# Generate two classes of mean directions around north and south poles
means1 = array(0,c(50,2)); means1[,2] = rnorm(50, mean=1, sd=0.25)
means2 = array(0,c(50,2)); means2[,2] = rnorm(50, mean=-1, sd=0.25)
means1 = means1/sqrt(rowSums(means1^2))
means2 = means2/sqrt(rowSums(means2^2))

# Concatenate the mean directions
data_means = rbind(means1, means2)

# Generate concentration parameters
data_concentrations = rnorm(100, mean=20, sd=1)

# Compute the pairwise distance matrix
pdmat = WLpdist(data_means, data_concentrations)

# Visualise the pairwise distance matrix
opar <- par(no.readonly=TRUE)
image(pdmat, main="Pairwise Wasserstein-like Distance")

par(opar)
# }