fsdist {TDAkit}

Pairwise L_p Distance of Multiple Functional Summaries

Description

Given multiple functional summaries \Lambda_1 (t), \Lambda_2 (t), \ldots, \Lambda_N (t), compute L_p distance in a pairwise sense.

Usage

fsdist(fslist, p = 2, as.dist = TRUE)

Arguments

fslist

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

p

an exponent in [1,\infty) (default: 2).

as.dist

logical; if TRUE, it returns dist object, else it returns an (N\times N) symmetric matrix.

Value

a S3 dist object or (N\times N) symmetric matrix of pairwise distances according to as.dist parameter.

Examples

# ---------------------------------------------------------------------------
#      Compute L_2 Distance for 3 Types of Landscapes and Silhouettes
#
# We will compare dim=0,1 with 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
#  We try to get distance in dimensions 0 and 1.
list_land0 = list()
list_land1 = list()
for (i in 1:(3*ndata)){
  list_land0[[i]] = diag2landscape(list_rips[[i]], dimension=0, k=5)
  list_land1[[i]] = diag2landscape(list_rips[[i]], dimension=1, k=5)
}

## Compute Silhouettes
list_sil0 = list()
list_sil1 = list()
for (i in 1:(3*ndata)){
  list_sil0[[i]] = diag2silhouette(list_rips[[i]], dimension=0)
  list_sil1[[i]] = diag2silhouette(list_rips[[i]], dimension=1)
}

## Compute L2 Distance Matrices
ldmat0 = fsdist(list_land0, p=2, as.dist=FALSE)
ldmat1 = fsdist(list_land1, p=2, as.dist=FALSE)
sdmat0 = fsdist(list_sil0, p=2, as.dist=FALSE)
sdmat1 = fsdist(list_sil1, p=2, as.dist=FALSE)

## Visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(2,2), pty="s")
image(ldmat0[,(3*(ndata)):1], axes=FALSE, main="Landscape : dim=0")
image(ldmat1[,(3*(ndata)):1], axes=FALSE, main="Landscape : dim=1")
image(sdmat0[,(3*(ndata)):1], axes=FALSE, main="Silhouette : dim=0")
image(sdmat1[,(3*(ndata)):1], axes=FALSE, main="Silhouette : dim=1")
par(opar)