ZC_cat: Maxtype Edge-Count Test for Discrete Data

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

Maxtype Edge-Count Test for Discrete Data

Description

Performs the maxtype edge-count two-sample test for multivariate data proposed by Zhang and Chen (2022). The implementation here uses the g.tests implementation from the gTests package.

Usage

ZC_cat(X1, X2, dist.fun, agg.type, graph.type = "mstree", K = 1, n.perm = 0, 
        maxtype.kappa = 1.14, 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).
maxtype.kappa	Parameter \kappa of the test (default: 1.14). See details.
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 and is more flexible than the generalized edge-count test of Chen and Friedman (2017). The test statistic is the maximum of two statistics. The first statistic ist the weighted edge-count statistic multiplied by a factor \kappa. The second statistic is the absolute value of the standardized difference of edge-counts within the first and within the second sample.

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

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 (2017).

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
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

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

FR_cat for the original edge-count test, CF_cat for the generalized edge-count test, CCS_cat for the weighted edge-count test, gTests_cat for performing all these edge-count tests at once, FR, CF, CCS, 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 generalized edge-count test
if(requireNamespace("gTests", quietly = TRUE)) {
  ZC_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.