CF: Generalized Edge-Count Test

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

Generalized Edge-Count Test

Description

Performs the generalized edge-count two-sample test for multivariate data proposed by Chen and Friedman (2017). The implementation here uses the g.tests implementation from the gTests package.

Usage

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

Details

The test is an enhancement of the Friedman-Rafsky test (original edge-count test) that aims at detecting both location and scale alternatives. The test statistic is given as

S = (R_1 - \mu_1, R_2 - \mu_2)\Sigma^{-1} \binom{R_1 - \mu_1}{R_2 - \mu_2}, \text{ where}

R_1 and R_2 denote the number of edges in the similarity graph connecting points within the first and second sample X_1 and X_2, respectively, \mu_1 = \text{E}_{H_0}(R_1), \mu_2 = \text{E}_{H_0}(R_2) and \Sigma is the covariance matrix of R_1 and R_2 under the null.

High values of the test statistic indicate dissimilarity of the datasets as the number of edges connecting points within the same sample is high meaning that points are more similar within the datasets than between the datasets.

For n.perm = 0, an asymptotic test using the asymptotic \chi^2 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	Yes	No	No

References

Chen, H. and Friedman, J.H. (2017). A New Graph-Based Two-Sample Test for Multivariate and Object Data. Journal of the American Statistical Association, 112(517), 397-409. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.2016.1147356")}

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

FR for the original 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 generalized edge-count test
if(requireNamespace("gTests", quietly = TRUE)) {
  CF(X1, X2)
}

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