plkernel {TDAkit}

Persistence Landscape Kernel

Description

Given multiple persistence landscapes \Lambda_1 (t), \Lambda_2 (t), \ldots, \Lambda_N (t), compute the persistence landscape kernel under the L_2 sense.

Usage

plkernel(landlist)

Arguments

landlist

a length-N list of "landscape" objects, which can be obtained from diag2landscape function.

Value

an (N\times N) kernel matrix.

References

Jan Reininghaus, Stefan Huber, Ulrich Bauer, and Roland Kwitt (2015). “A stable multi-scale kernel for topological machine learning.” Proc. 2015 IEEE Conf. Comp. Vision & Pat. Rec. (CVPR ’15).

Examples

# ---------------------------------------------------------------------------
#      Persistence Landscape Kernel in Dimension 0 and 1
#
# We will compare dim=0,1 with top-20 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 Persistence Landscape Kernel Matrix
plk0 <- plkernel(list_land0)
plk1 <- plkernel(list_land1)

## Visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,2), pty="s")
image(plk0[,(3*(ndata)):1], axes=FALSE, main="Kernel : dim=0")
image(plk1[,(3*(ndata)):1], axes=FALSE, main="Kernel : dim=1")
par(opar)