# riem.kmeanspp: K-Means++ Clustering In Riemann: Learning with Data on Riemannian Manifolds

## Description

Given N observations X_1, X_2, …, X_N \in \mathcal{M}, perform k-means++ clustering algorithm using pairwise distances. The algorithm was originally designed as an efficient initialization method for k-means algorithm.

## Usage

 1 riem.kmeanspp(riemobj, k = 2, geometry = c("intrinsic", "extrinsic")) 

## Arguments

 riemobj a S3 "riemdata" class for N manifold-valued data. k the number of clusters. geometry (case-insensitive) name of geometry; either geodesic ("intrinsic") or embedded ("extrinsic") geometry.

## Value

a named list containing

centers

a length-k vector of sampled centers' indices.

cluster

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

## References

\insertRef

arthur_kmeans_2007aRiemann

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 #------------------------------------------------------------------- # 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) ## K-MEANS++ WITH K=2,3,4 clust2 = riem.kmeanspp(myriem, k=2) clust3 = riem.kmeanspp(myriem, k=3) clust4 = riem.kmeanspp(myriem, k=4) ## MDS FOR VISUALIZATION mds2d = riem.mds(myriem, ndim=2)$embed ## VISUALIZE opar <- par(no.readonly=TRUE) par(mfrow=c(2,2), pty="s") plot(mds2d, pch=19, main="true label", col=mylabs) plot(mds2d, pch=19, main="K=2", col=clust2$cluster) plot(mds2d, pch=19, main="K=3", col=clust3$cluster) plot(mds2d, pch=19, main="K=4", col=clust4$cluster) par(opar) 

Riemann documentation built on June 20, 2021, 5:07 p.m.