riem.phate: PHATE

In Riemann: Learning with Data on Riemannian Manifolds

PHATE

Description

PHATE is a nonlinear manifold learning method that is specifically targeted at improving diffusion maps by incorporating data-adaptive kernel construction, detection of optimal time scale, and information-theoretic metric measures.

Usage

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

Arguments

riemobj	a S3 "riemdata" class for N manifold-valued data.
ndim	an integer-valued target dimension (default: 2).
geometry	(case-insensitive) name of geometry; either geodesic ("intrinsic") or embedded ("extrinsic") geometry.
...	extra parameters for PHATE including nbdk size of nearest neighborhood (default: 5). alpha decay parameter for Gaussian kernel exponent (default: 2). potential type of potential distance transformation; "log" or "sqrt" (default: "log").

Value

a named list containing

embed

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

References

\insertRef

moon_visualizing_2019Riemann

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 1:10){
  tgt = c(1, stats::rnorm(2, sd=0.1))
  mydata[[i]] = tgt/sqrt(sum(tgt^2))
}
for (i in 11:20){
  tgt = c(rnorm(1,sd=0.1),1,rnorm(1,sd=0.1))
  mydata[[i]] = tgt/sqrt(sum(tgt^2))
}
for (i in 21:30){
  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=10)

## PHATE EMBEDDING WITH LOG & SQRT POTENTIAL 
phate_log  = riem.phate(myriem, potential="log")$embed
phate_sqrt = riem.phate(myriem, potential="sqrt")$embed
embed_mds  = riem.mds(myriem)$embed

## VISUALIZE
opar = par(no.readonly=TRUE)
par(mfrow=c(1,3), pty="s")
plot(embed_mds,  col=mylabs, pch=19, main="MDS" )
plot(phate_log,  col=mylabs, pch=19, main="PHATE+Log")
plot(phate_sqrt, col=mylabs, pch=19, main="PHATE+Sqrt")
par(opar)

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