DataSimilarity (version 0.1.1)

gTestsMulti: Graph-Based Multi-Sample Test

Description

Performs both proposed graph-based multi-sample test for high-dimensional data by Song and Chen (2022). The implementation here uses the gtestsmulti implementation from the gTestsMulti package. This function is inteded to be used e.g. in comparison studies where both tests need to be calculated at the same time. Since large parts of the calculation coincide, using this function should be faster than computing all four statistics individually.

Usage

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

Value

An list with the following components:

statistic

Observed value of the test statistic

p.value

Boostrap/ permutation p value (only if n.perm > 0)

estimate

Estimated KMD 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

...

Optionally more datasets as matrices or data.frames

n.perm

Number of permutations for permutation test (default: 0, no permutation test performed)

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).

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	Yes

Details

Two multi-sample test statistics are defined by Song and Chen (2022) based on a similarity graph. The first one is defined as $$S = S_W + S_B, \text{ where}$$ $$S_W = (R_W - \text{E}(R_W))^T \Sigma_W^{-1}R_W - \text{E}(R_W)),$$ $$S_B = (R_B - \text{E}(R_B))^T \Sigma_W^{-1}R_B - \text{E}(R_B)),$$ with \(R_W\) denoting the vector of within-sample edge counts and \(R_B\) the vector of between-sample edge counts. Expectations and covariance matrix are calculated under the null.

The second statistic is defined as $$S_A = (R_A - \text{E}(R_A))^T \Sigma_W^{-1}R_A - \text{E}(R_A)), $$ where \(R_A\) is the vector of all linearly independent edge counts, i.e. the edge counts for all pairs of samples except the last pair \(k-1\) and \(k\).

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

References

Song, H. and Chen, H. (2022). New graph-based multi-sample tests for high-dimensional and non- Euclidean data. arXiv:2205.13787, tools:::Rd_expr_doi("10.48550/arXiv.2205.13787")

Song, H., Chen, H. (2023). gTestsMulti: New Graph-Based Multi-Sample Tests. R package version 0.1.1, https://CRAN.R-project.org/package=gTestsMulti.

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

SC, MST

Examples

# Draw some data
X1 <- matrix(rnorm(1000), ncol = 10)
X2 <- matrix(rnorm(1000, mean = 0.5), ncol = 10)
# Perform Song and Chen tests
if(requireNamespace("gTestsMulti", quietly = TRUE)) {
  gTestsMulti(X1, X2, n.perm = 100)
}