FR_cat: Friedman-Rafsky Test for Discrete Data

In DataSimilarity: Quantifying Similarity of Datasets and Multivariate Two- And k-Sample Testing

Friedman-Rafsky Test for Discrete Data

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_cat(X1, X2, dist.fun, agg.type, graph.type = "mstree", K = 1, n.perm = 0, 
        seed = 42)

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.
agg.type	Character giving the method for aggregating over possible similarity graphs. Options are "u" for union of possible similarity graphs and "a" for averaging over test statistics calculated on possible similarity graphs.
graph.type	Character specifying which similarity graph to use. Possible options are "mstree" (default, Minimum Spanning Tree) and "nnlink" (Nearest Neighbor Graph).
K	Parameter for graph (default: 1). If graph.type = "mstree", a K-MST is constructed (K=1 is the classical MST). If graph.type = "nnlink", K gives the number of neighbors considered in the K-NN graph.
n.perm	Number of permutations for permutation test (default: 0, asymptotic test is performed).
seed	Random seed (default: 42)

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). For discrete data, the similarity graph used in the test is not necessarily unique. This can be solved by either taking a union of all optimal similarity graphs or averaging the test statistics over all optimal similarity graphs. For details, see Zhang and Chen (2022).

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.

Value

An object of class htest with the following components:

statistic	Observed value of the test statistic
parameter	Degrees of freedom for \chi^2 distribution under H_0 (only for asymptotic test)
p.value	Asymptotic or permutation p value
alternative	The alternative hypothesis
method	Description of the test
data.name	The dataset names

Applicability

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

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.

Zhang, J. and Chen, H. (2022). Graph-Based Two-Sample Tests for Data with Repeated Observations. Statistica Sinica 32, 391-415, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.5705/ss.202019.0116")}.

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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/24-SS149")}

See Also

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

Examples

# Draw some data
X1cat <- matrix(sample(1:4, 300, replace = TRUE), ncol = 3)
X2cat <- matrix(sample(1:4, 300, replace = TRUE, prob = 1:4), ncol = 3)
# Perform Friedman-Rafsky test
if(requireNamespace("gTests", quietly = TRUE)) {
  FR_cat(X1cat, X2cat, dist.fun = function(x, y) sum(x != y), agg.type = "a")
}

DataSimilarity documentation built on April 3, 2025, 9:39 p.m.