fseqdist: Multi-sample Energy Test of Equal Distributions

In kyoustat/TDAkit: Toolkit for Topological Data Analysis

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)

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.

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.

Examples

# ---------------------------------------------------------------------------
#         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")

kyoustat/TDAkit documentation built on Sept. 1, 2021, 7:22 a.m.