gr.kmedoids: k-Medoids Clustering on Grassmann Manifold

In RiemGrassmann: Inference, Learning, and Optimization on Grassmann Manifold

Description

k-Medoids algorithm depends solely on the availability of concept that gives dissimilarity. We adopt pam algorithm from cluster package. See pam for more details.

Usage

gr.kmedoids(
  input,
  k = 2,
  type = c("Intrinsic", "Extrinsic", "Asimov", "Binet-Cauchy", "Chordal",
    "Fubini-Study", "Martin", "Procrustes", "Projection", "Spectral")
)

Arguments

input	either an array of size (n\times k\times N) or a list of length N whose elements are (n\times k) orthonormal basis (ONB) on Grassmann manifold.
k	the number of clusters
type	type of distance measure. measure. Name of each type is Case Insensitive and hyphen can be omitted.

Value

an object of class pam. See pam for details.

Author(s)

Kisung You

Examples

## generate a dataset with two types of Grassmann elements
#  group1 : first four columns of (8x8) identity matrix + noise
#  group2 : last  four columns of (8x8) identity matrix + noise

mydata = list()
sdval  = 0.25
diag8  = diag(8)
for (i in 1:10){
  mydata[[i]] = qr.Q(qr(diag8[,1:4] + matrix(rnorm(8*4,sd=sdval),ncol=4)))
}
for (i in 11:20){
  mydata[[i]] = qr.Q(qr(diag8[,5:8] + matrix(rnorm(8*4,sd=sdval),ncol=4)))
}

## do k-medoids clustering with 'intrinsic' distance
#  First, apply MDS for visualization
dmat = gr.pdist(mydata, type="intrinsic")
embd = stats::cmdscale(dmat, k=2)

#  Run 'gr.kmedoids' with different numbers of clusters
grint2 = gr.kmedoids(mydata, type="intrinsic", k=2)$clustering
grint3 = gr.kmedoids(mydata, type="intrinsic", k=3)$clustering
grint4 = gr.kmedoids(mydata, type="intrinsic", k=4)$clustering

#  Let's visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3), pty="s")
plot(embd, pch=19, col=grint2, main="k=2")
plot(embd, pch=19, col=grint3, main="k=3")
plot(embd, pch=19, col=grint4, main="k=4")
par(opar)


## perform k-medoids clustering with different distance measures
#  iterate over all distance measures
alltypes = c("intrinsic","extrinsic","asimov","binet-cauchy",
"chordal","fubini-study","martin","procrustes","projection","spectral")
ntypes   = length(alltypes)
labels   = list()
for (i in 1:ntypes){
  labels[[i]] = gr.kmedoids(mydata, k=2, type=alltypes[i])$clustering
}

## visualize
#  1. find MDS scaling for each distance measure as well
embeds = list()
for (i in 1:ntypes){
  pdmat       = gr.pdist(mydata, type=alltypes[i])
  embeds[[i]] = stats::cmdscale(pdmat, k=2)
}

#  2. plot the clustering results
opar <- par(no.readonly=TRUE)
par(mfrow=c(2,5), pty="s")
for (i in 1:ntypes){
  pm = paste0("k-medoids::",alltypes[i])
  plot(embeds[[i]], col=labels[[i]], main=pm, pch=19)
}
par(opar)

RiemGrassmann documentation built on March 25, 2020, 5:07 p.m.