riem.phate {Riemann}

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

Moon KR, van Dijk D, Wang Z, Gigante S, Burkhardt DB, Chen WS, Yim K, van den Elzen A, Hirn MJ, Coifman RR, Ivanova NB, Wolf G, Krishnaswamy S (2019). “Visualizing Structure and Transitions in High-Dimensional Biological Data.” Nature Biotechnology, 37(12), 1482–1492. ISSN 1087-0156, 1546-1696.

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)