# riem.kmeans18B: K-Means Clustering with Lightweight Coreset In Riemann: Learning with Data on Riemannian Manifolds

 riem.kmeans18B R Documentation

## 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$data)/2, geometry = c("intrinsic", "extrinsic"), ... )  ### Arguments  riemobj a S3 "riemdata" class for N manifold-valued data. k the number of clusters. M the size of coreset (default: N/2). geometry (case-insensitive) name of geometry; either geodesic ("intrinsic") or embedded ("extrinsic") geometry. ... extra parameters including maxitermaximum number of iterations to be run (default:50). nstartthe number of random starts (default: 5). ### Value a named list containing cluster a length-N vector of class labels (from 1:k). means a 3d array where each slice along 3rd dimension is a matrix representation of class mean. score within-cluster sum of squares (WCSS). ### References \insertRef bachem_scalable_2018aRiemann ### See Also riem.coreset18B ### Examples #------------------------------------------------------------------- # Example on Sphere : a dataset with three types # # class 1 : 10 perturbed data points near (1,0,0) on S^2 in R^3 # class 2 : 10 perturbed data points near (0,1,0) on S^2 in R^3 # class 3 : 10 perturbed data points near (0,0,1) on S^2 in R^3 #------------------------------------------------------------------- ## GENERATE DATA mydata = list() for (i in 1:10){ tgt = c(1, stats::rnorm(2, sd=0.1)) mydata[[i]] = tgt/sqrt(sum(tgt^2)) } for (i in 11:20){ tgt = c(rnorm(1,sd=0.1),1,rnorm(1,sd=0.1)) mydata[[i]] = tgt/sqrt(sum(tgt^2)) } for (i in 21:30){ tgt = c(stats::rnorm(2, sd=0.1), 1) mydata[[i]] = tgt/sqrt(sum(tgt^2)) } myriem = wrap.sphere(mydata) mylabs = rep(c(1,2,3), each=10) ## TRY DIFFERENT SIZES OF CORESET WITH K=4 FIXED core1 = riem.kmeans18B(myriem, k=3, M=5) core2 = riem.kmeans18B(myriem, k=3, M=10) core3 = riem.kmeans18B(myriem, k=3, M=15) ## MDS FOR VISUALIZATION mds2d = riem.mds(myriem, ndim=2)$embed

## VISUALIZE
plot(mds2d, pch=19, main="kmeans18B: M=5",  col=core1$cluster) plot(mds2d, pch=19, main="kmeans18B: M=10", col=core2$cluster)