fssc05Z {TDAkit}

Spectral Clustering by Zelnik-Manor and Perona (2005)

Description

Given N functional summaries \Lambda_1 (t), \Lambda_2 (t), \ldots, \Lambda_N (t), perform spectral clustering proposed by Zelnik-Manor and Perona using a set of data-driven bandwidth parameters.

Usage

fssc05Z(fslist, k = 2, nnbd = 5)

Arguments

fslist

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

k

the number of cluster (default: 2).

nnbd

neighborhood size to define data-driven bandwidth parameter (default: 5).

Value

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

References

Zelnik-manor L, Perona P (2005). “Self-Tuning Spectral Clustering.” In Saul LK, Weiss Y, Bottou L (eds.), Advances in Neural Information Processing Systems 17, 1601–1608. MIT Press.

Examples

# ---------------------------------------------------------------------------
#           Spectral Clustering 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)
}

## 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 Spectral Clustering using Different K's.
label2  = fssc05Z(list_land0, k=2)
label3  = fssc05Z(list_land0, k=3)
label4  = fssc05Z(list_land0, k=4)
truelab = rep(c(1,2,3), each=ndata)

## Run MDS & Visualization
embed = fsmds(list_land0, ndim=2)
opar  = par(no.readonly=TRUE)
par(mfrow=c(2,2), pty="s")
plot(embed, col=truelab, pch=19, main="true label")
plot(embed, col=label2,  pch=19, main="k=2 label")
plot(embed, col=label3,  pch=19, main="k=3 label")
plot(embed, col=label4,  pch=19, main="k=4 label")
par(opar)