riem.kmeans18B: K-Means Clustering with Lightweight Coreset

In Riemann: Learning with Data on Riemannian Manifolds

K-Means Clustering with Lightweight Coreset

Description

The modified version of lightweight coreset for scalable k-means computation is applied for manifold-valued data X_1,X_2,…,X_N \in \mathcal{M}. The smaller the set is, the faster the execution becomes with potentially larger quantization errors.

Usage

riem.kmeans18B(
  riemobj,
  k = 2,
  M = length(riemobj$data)/2,
  geometry = c("intrinsic", "extrinsic"),
  ...
)

Arguments

riemobj	a S3 "riemdata" class for N manifold-valued data.
k	the number of clusters.
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). nstart the number of random starts (default: 5).

Value

a named list containing

cluster

a length-N vector of class labels (from 1:k).

means

a 3d array where each slice along 3rd dimension is a matrix representation of class mean.

score

within-cluster sum of squares (WCSS).

References

\insertRef

bachem_scalable_2018aRiemann

See Also

riem.coreset18B

Examples

#-------------------------------------------------------------------
#          Example on Sphere : a dataset with three types
#
# class 1 : 10 perturbed data points near (1,0,0) on S^2 in R^3
# class 2 : 10 perturbed data points near (0,1,0) on S^2 in R^3
# class 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)

## TRY DIFFERENT SIZES OF CORESET WITH K=4 FIXED
core1 = riem.kmeans18B(myriem, k=3, M=5)
core2 = riem.kmeans18B(myriem, k=3, M=10)
core3 = riem.kmeans18B(myriem, k=3, M=15)

## MDS FOR VISUALIZATION
mds2d = riem.mds(myriem, ndim=2)$embed

## VISUALIZE
opar <- par(no.readonly=TRUE)
par(mfrow=c(2,2), pty="s")
plot(mds2d, pch=19, main="true label", col=mylabs)
plot(mds2d, pch=19, main="kmeans18B: M=5",  col=core1$cluster)
plot(mds2d, pch=19, main="kmeans18B: M=10", col=core2$cluster)
plot(mds2d, pch=19, main="kmeans18B: M=15", col=core3$cluster)
par(opar)

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