riem.coreset18B: Build Lightweight Coreset

In Riemann: Learning with Data on Riemannian Manifolds

Build Lightweight Coreset

Description

Given manifold-valued data X_1,X_2,…,X_N \in \mathcal{M}, this algorithm finds the coreset of size M that can be considered as a compressed representation according to the lightweight coreset construction scheme proposed by the reference below.

Usage

riem.coreset18B(
  riemobj,
  M = length(riemobj$data)/2,
  geometry = c("intrinsic", "extrinsic"),
  ...
)

Arguments

riemobj	a S3 "riemdata" class for N manifold-valued data.
M	the size of coreset (default: N/2).
geometry	(case-insensitive) name of geometry; either geodesic ("intrinsic") or embedded ("extrinsic") geometry.
...	extra parameters including maxiter maximum number of iterations to be run (default:50). eps tolerance level for stopping criterion (default: 1e-5).

Value

a named list containing

coreid

a length-M index vector of the coreset.

weight

a length-M vector of weights for each element.

References

\insertRef

bachem_scalable_2018aRiemann

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)

## MDS FOR VISUALIZATION
embed2 = riem.mds(myriem, ndim=2)$embed

## FIND CORESET OF SIZES 3, 6, 9
core1 = riem.coreset18B(myriem, M=3)
core2 = riem.coreset18B(myriem, M=6)
core3 = riem.coreset18B(myriem, M=9)

col1 = rep(1,30); col1[core1$coreid] = 2
col2 = rep(1,30); col2[core2$coreid] = 2
col3 = rep(1,30); col3[core3$coreid] = 2

## VISUALIZE
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3), pty="s")
plot(embed2, pch=19, col=col1, main="coreset size=3")
plot(embed2, pch=19, col=col2, main="coreset size=6")
plot(embed2, pch=19, col=col3, main="coreset size=9")
par(opar)

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