fshclust {TDAkit}

Hierarchical Agglomerative Clustering

Description

Given multiple functional summaries \Lambda_1 (t), \Lambda_2 (t), \ldots, \Lambda_N (t), perform hierarchical agglomerative clustering with L_2 distance.

Usage

fshclust(
  fslist,
  method = c("single", "complete", "average", "mcquitty", "ward.D", "ward.D2",
    "centroid", "median"),
  members = NULL
)

Arguments

fslist

a length-N list of functional summaries of persistent diagrams.

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.

Examples

# ---------------------------------------------------------------------------
#           K-Groups Clustering via Energy Distance
#
# We will cluster dim=0 under top-5 landscape functions with 
# - Class 1 : 'iris' dataset with noise
# - Class 2 : samples from 'gen2holes()'
# - Class 3 : samples from 'gen2circles()'
# ---------------------------------------------------------------------------
## Generate Data and Diagram from VR Filtration
ndata     = 10
list_rips = list()
for (i in 1:ndata){
  dat1 = as.matrix(iris[,1:4]) + matrix(rnorm(150*4), ncol=4)
  dat2 = gen2holes(n=100, sd=1)$data
  dat3 = gen2circles(n=100, sd=1)$data
  
  list_rips[[i]] = diagRips(dat1, maxdim=1)
  list_rips[[i+ndata]] = diagRips(dat2, maxdim=1)
  list_rips[[i+(2*ndata)]] = diagRips(dat3, maxdim=1)
}
list_lab = c(rep(1,ndata), rep(2,ndata), rep(3,ndata))

## Compute Persistence Landscapes from Each Diagram with k=5 Functions
list_land0 = list()
for (i in 1:(3*ndata)){
  list_land0[[i]] = diag2landscape(list_rips[[i]], dimension=0, k=5)
}

## Run MDS for Visualization
embed = fsmds(list_land0, ndim=2)

## Clustering with 'single' and 'complete' linkage
hc.sing <- fshclust(list_land0, method="single")
hc.comp <- fshclust(list_land0, method="complete")

## Visualize
opar  = par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(embed, pch=19, col=list_lab, main="2-dim embedding")
plot(hc.sing, main="single linkage")
plot(hc.comp, main="complete linkage")
par(opar)