Given \(M\) observations \(X_1, X_2, \ldots, X_M \in \mathcal{M}\) and \(N\) observations \(Y_1, Y_2, \ldots, Y_N \in \mathcal{M}\), compute pairwise distances between two sets' elements.
Usage
riem.pdist2(riemobj1, riemobj2, geometry = c("intrinsic", "extrinsic"))Arguments
- riemobj1
a S3
"riemdata"class for \(M\) manifold-valued data.- riemobj2
a S3
"riemdata"class for \(N\) manifold-valued data.- geometry
(case-insensitive) name of geometry; either geodesic (
"intrinsic") or embedded ("extrinsic") geometry.
Examples
# \donttest{
#-------------------------------------------------------------------
# Example on Sphere : a dataset with two types
#
# group1 : 10 perturbed data points near (0,0,1) on S^2 in R^3
# group2 : 10 perturbed data points near (1,0,0) on S^2 in R^3
# 10 perturbed data points near (0,1,0) on S^2 in R^3
# 10 perturbed data points near (0,0,1) on S^2 in R^3
#-------------------------------------------------------------------
## GENERATE DATA
mydata1 = list()
mydata2 = list()
for (i in 1:10){
tgt = c(stats::rnorm(2, sd=0.1), 1)
mydata1[[i]] = tgt/sqrt(sum(tgt^2))
}
for (i in 1:10){
tgt = c(1, stats::rnorm(2, sd=0.1))
mydata2[[i]] = tgt/sqrt(sum(tgt^2))
}
for (i in 11:20){
tgt = c(rnorm(1,sd=0.1),1,rnorm(1,sd=0.1))
mydata2[[i]] = tgt/sqrt(sum(tgt^2))
}
for (i in 21:30){
tgt = c(stats::rnorm(2, sd=0.1), 1)
mydata2[[i]] = tgt/sqrt(sum(tgt^2))
}
myriem1 = wrap.sphere(mydata1)
myriem2 = wrap.sphere(mydata2)
## COMPARE TWO DISTANCES
dint = riem.pdist2(myriem1, myriem2, geometry="intrinsic")
dext = riem.pdist2(myriem1, myriem2, geometry="extrinsic")
## VISUALIZE
opar = par(no.readonly=TRUE)
par(mfrow=c(1,2))
image(dint[nrow(dint):1,], main="intrinsic", axes=FALSE)
image(dext[nrow(dext):1,], main="extrinsic", axes=FALSE)
par(opar)
# }