DataSimilarity (version 0.1.1)

FR: Friedman-Rafsky Test

Description

Performs the Friedman-Rafsky two-sample test (original edge-count test) for multivariate data (Friedman and Rafsky, 1979). The implementation here uses the g.tests implementation from the gTests package.

Usage

FR(X1, X2, dist.fun = stats::dist, graph.fun = MST, n.perm = 0, 
    dist.args = NULL, graph.args = NULL, seed = 42)

Value

An object of class htest with the following components:

statistic

Observed value of the test statistic

p.value

Asymptotic or permutation p value

alternative

The alternative hypothesis

method

Description of the test

data.name

The dataset names

Arguments

X1

First dataset as matrix or data.frame

X2

Second dataset as matrix or data.frame

dist.fun

Function for calculating a distance matrix on the pooled dataset (default: stats::dist, Euclidean distance).

graph.fun

Function for calculating a similarity graph using the distance matrix on the pooled sample (default: MST, Minimum Spanning Tree).

n.perm

Number of permutations for permutation test (default: 0, asymptotic test is performed).

dist.args

Named list of further arguments passed to dist.fun (default: NULL).

graph.args

Named list of further arguments passed to graph.fun (default: NULL).

seed

Random seed (default: 42)

Applicability

Target variable?	Numeric?	Categorical?	K-sample?
No	Yes	No	No

Details

The test is a multivariate extension of the univariate Wald Wolfowitz runs test. The test statistic is the number of edges connecting points from different datasets in a minimum spanning tree calculated on the pooled sample (standardized with expectation and SD under the null).

High values of the test statistic indicate similarity of the datasets. Thus, the null hypothesis of equal distributions is rejected for small values.

For n.perm = 0, an asymptotic test using the asymptotic normal approximation of the null distribution is performed. For n.perm > 0, a permutation test is performed.

This implementation is a wrapper function around the function g.tests that modifies the in- and output of that function to match the other functions provided in this package. For more details see the g.tests.

References

Friedman, J. H., and Rafsky, L. C. (1979). Multivariate Generalizations of the Wald-Wolfowitz and Smirnov Two-Sample Tests. The Annals of Statistics, 7(4), 697-717.

Chen, H., and Zhang, J. (2017). gTests: Graph-Based Two-Sample Tests. R package version 0.2, https://CRAN.R-project.org/package=gTests.

Stolte, M., Kappenberg, F., Rahnenführer, J., Bommert, A. (2024). Methods for quantifying dataset similarity: a review, taxonomy and comparison. Statist. Surv. 18, 163 - 298. tools:::Rd_expr_doi("10.1214/24-SS149")

See Also

CF for the generalized edge-count test, CCS for the weighted edge-count test, ZC for the maxtype edge-count test, gTests for performing all these edge-count tests at once, SH for performing the Schilling-Henze nearest neighbor test, CCS_cat, FR_cat, CF_cat, ZC_cat, and gTests_cat for versions of the test for categorical data

Examples

# Draw some data
X1 <- matrix(rnorm(1000), ncol = 10)
X2 <- matrix(rnorm(1000, mean = 0.5), ncol = 10)
# Perform Friedman-Rafsky test
if(requireNamespace("gTests", quietly = TRUE)) {
  FR(X1, X2)
}