plkernel {TDAkit}R Documentation

Persistence Landscape Kernel

Description

Given multiple persistence landscapes Λ1(t),Λ2(t),,ΛN(t)\Lambda_1 (t), \Lambda_2 (t), \ldots, \Lambda_N (t), compute the persistence landscape kernel under the L2L_2 sense.

Usage

plkernel(landlist)

Arguments

landlist

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

Value

an (N×N)(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)



[Package TDAkit version 0.1.2 Index]