riem.tsne: t-distributed Stochastic Neighbor Embedding In Riemann: Learning with Data on Riemannian Manifolds

 riem.tsne R Documentation

t-distributed Stochastic Neighbor Embedding

Description

Given N observations X_1, X_2, …, X_N \in \mathcal{M}, t-SNE mimicks the pattern of probability distributions over pairs of manifold-valued objects on low-dimensional target embedding space by minimizing Kullback-Leibler divergence.

Usage

riem.tsne(riemobj, ndim = 2, geometry = c("intrinsic", "extrinsic"), ...)


Arguments

 riemobj a S3 "riemdata" class for N manifold-valued data. ndim an integer-valued target dimension. geometry (case-insensitive) name of geometry; either geodesic ("intrinsic") or embedded ("extrinsic") geometry. ... extra parameters for Rtsne algorithm from Rtsne package, such as perplexity, momentum, and others.

Value

a named list containing

embed

an (N\times ndim) matrix whose rows are embedded observations.

stress

discrepancy between embedded and original distances as a measure of error.

Examples

#-------------------------------------------------------------------
#          Example on Sphere : a dataset with three types
#
# 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
mydata = list()
for (i in 1:20){
tgt = c(1, stats::rnorm(2, sd=0.1))
mydata[[i]] = tgt/sqrt(sum(tgt^2))
}
for (i in 21:40){
tgt = c(rnorm(1,sd=0.1),1,rnorm(1,sd=0.1))
mydata[[i]] = tgt/sqrt(sum(tgt^2))
}
for (i in 41:60){
tgt = c(stats::rnorm(2, sd=0.1), 1)
mydata[[i]] = tgt/sqrt(sum(tgt^2))
}
myriem = wrap.sphere(mydata)
mylabs = rep(c(1,2,3), each=20)

## RUN THE ALGORITHM IN TWO GEOMETRIES
mypx = 5
embed2int = riem.tsne(myriem, ndim=2, geometry="intrinsic", perplexity=mypx)
embed2ext = riem.tsne(myriem, ndim=2, geometry="extrinsic", perplexity=mypx)

## VISUALIZE
plot(embed2int$embed, main="intrinsic t-SNE", col=mylabs, pch=19) plot(embed2ext$embed, main="extrinsic t-SNE", col=mylabs, pch=19)