permutation_test {TDAstats}

Statistical Inference for Topological Data Analysis

Description

Conducts a permutation test for nonparametric statistical inference of persistent homology in topological data analysis.

Usage

permutation_test(data1, data2, iterations, exponent = 1, update = 0,
  ...)

Arguments

data1

first dataset

data2

second dataset

iterations

number of iterations for distribution in permutation test

exponent

parameter 'p' that returns Wasserstein-p metric

update

if greater than zero, will print a message every 'update' iterations

...

arguments for 'calculate_homology' used for each permutation; this includes the 'format', 'dim', and 'threshold' parameters

Details

The persistent homology of two point clouds are compared with the Wasserstein metric (where Wasserstein-1 is also known as the Earth Mover's Distance). However, the magnitude of the metric for a single pair of point clouds is meaningless without a reference distribution. This function uses a permutation test (permuting the points between the two clouds) as a nonparametric hypothesis test for statistical inference.

For more details on permutation tests for statistical inference in topological data analysis, see Robinson A, Turner K. Hypothesis testing for topological data analysis. J Appl Comput Topology. 2017; 1(2): 241-261.<doi:10.1007/s41468-017-0008-7>

Value

list containing results of permutation test