fsmds {TDAkit}

Multidimensional Scaling

Description

Given multiple functional summaries \Lambda_1 (t), \Lambda_2 (t), \ldots, \Lambda_N (t), apply multidimensional scaling to get low-dimensional representation in Euclidean space. Usually, ndim=2,3 is chosen for visualization.

Usage

fsmds(fslist, ndim = 2, method = c("classical", "metric"))

Arguments

fslist

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

ndim

an integer-valued target dimension (default: 2).

method

name of an algorithm type (default: classical).

Value

an (N\times ndim) matrix of embedding.

Examples

# ---------------------------------------------------------------------------
#     Multidimensional Scaling for Multiple Landscapes and Silhouettes
#
# We will compare dim=0 with top-5 landscape and silhouette 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 Landscape and Silhouettes of Dimension 0
list_land = list()
list_sils = list()
for (i in 1:(3*ndata)){
  list_land[[i]] = diag2landscape(list_rips[[i]], dimension=0)
  list_sils[[i]] = diag2silhouette(list_rips[[i]], dimension=0)
}
list_lab = rep(c(1,2,3), each=ndata)

## Run Classical/Metric Multidimensional Scaling
land_cmds = fsmds(list_land, method="classical")
land_mmds = fsmds(list_land, method="metric")
sils_cmds = fsmds(list_sils, method="classical")
sils_mmds = fsmds(list_sils, method="metric")

## Visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(2,2))
plot(land_cmds, pch=19, col=list_lab, main="Landscape+CMDS")
plot(land_mmds, pch=19, col=list_lab, main="Landscape+MMDS")
plot(sils_cmds, pch=19, col=list_lab, main="Silhouette+CMDS")
plot(sils_mmds, pch=19, col=list_lab, main="Silhouette+MMDS")
par(opar)