Hierarchical Agglomerative Clustering

Given \(N\) observations \(X_1, X_2, \ldots, X_M \in \mathcal{M}\), perform hierarchical agglomerative clustering with fastcluster package's implementation.

Usage

riem.hclust(
  riemobj,
  geometry = c("intrinsic", "extrinsic"),
  method = c("single", "complete", "average", "mcquitty", "ward.D", "ward.D2",
    "centroid", "median"),
  members = NULL
)

Arguments

riemobj

a S3 "riemdata" class for \(N\) manifold-valued data.

geometry

(case-insensitive) name of geometry; either geodesic ("intrinsic") or embedded ("extrinsic") geometry.

method

agglomeration method to be used. This must be one of "single", "complete", "average", "mcquitty", "ward.D", "ward.D2", "centroid" or "median".

members

NULL or a vector whose length equals the number of observations. See hclust for details.

Value

an object of class hclust. See hclust for details.

References

Müllner D (2013). “fastcluster : Fast Hierarchical, Agglomerative Clustering Routines for R and Python.” Journal of Statistical Software, 53(9). ISSN 1548-7660.

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)

## COMPUTE SINGLE AND COMPLETE LINKAGE
hc.sing <- riem.hclust(myriem, method="single")
hc.comp <- riem.hclust(myriem, method="complete")

## VISUALIZE
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,2))
plot(hc.sing, main="single linkage")
plot(hc.comp, main="complete linkage")

par(opar)