TDAkit (version 0.1.3)

fseqdist: Multi-sample Energy Test of Equal Distributions

Description

Also known as \(k\)-sample problem, it tests whether multiple functional summaries are equally distributed or not via Energy statistics.

Usage

fseqdist(fslist, label, method = c("original", "disco"), mc.iter = 999)

Value

a (list) object of S3 class htest containing:

method

name of the test.

statistic

a test statistic.

p.value

\(p\)-value under \(H_0\) of equal distributions.

Arguments

fslist

a length-\(N\) list of functional summaries of persistent diagrams.

label

a length-\(N\) vector of class labels.

method

(case-sensitive) name of methods; one of "original" or "disco".

mc.iter

number of bootstrap replicates.

Examples

# \donttest{
# ---------------------------------------------------------------------------
#         Test for Equality of Distributions via Energy Statistics
#
# We will compare dim=0's 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)
}

## Create Label and Run the Test with Different Options
list_lab = c(rep(1,ndata), rep(2,ndata), rep(3,ndata))
fseqdist(list_land0, list_lab, method="original")
fseqdist(list_land0, list_lab, method="disco")
# }