# riem.phate: PHATE In Riemann: Learning with Data on Riemannian Manifolds

 riem.phate R Documentation

## 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 nbdksize of nearest neighborhood (default: 5). alphadecay parameter for Gaussian kernel exponent (default: 2). potentialtype 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