Performs the graph-based multi-sample test for high-dimensional data proposed by Song and Chen (2022). The implementation here uses the gtestsmulti implementation from the gTestsMulti package.
SC(X1, X2, ..., n.perm = 0, dist.fun = stats::dist, graph.fun = MST,
dist.args = NULL, graph.args = NULL, type = "S", seed = 42)An object of class htest with the following components:
Observed value of the test statistic
Permutation p value (only if n.perm > 0)
Estimated KMD value
The alternative hypothesis
Description of the test
The dataset names
First dataset as matrix or data.frame
Second dataset as matrix or data.frame
Optionally more datasets as matrices or data.frames
Number of permutations for permutation test (default: 0, no permutation test performed)
Function for calculating a distance matrix on the pooled dataset (default: stats::dist, Euclidean distance).
Function for calculating a similarity graph using the distance matrix on the pooled sample (default: MST, Minimum Spanning Tree).
Named list of further arguments passed to dist.fun (default: NULL).
Named list of further arguments passed to graph.fun (default: NULL).
Character specifying the test statistic to use. Possible options are "S" (default) and "SA". See details.
Random seed (default: 42)
| Target variable? | Numeric? | Categorical? | K-sample? |
| No | Yes | No | Yes |
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.
Song, H. and Chen, H. (2022). New graph-based multi-sample tests for high-dimensional and non- Euclidean data. tools:::Rd_expr_doi("10.48550/arXiv.2205.13787")
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")
gTestsMulti for performing both tests at once, MST
# Draw some data
X1 <- matrix(rnorm(1000), ncol = 10)
X2 <- matrix(rnorm(1000, mean = 0.5), ncol = 10)
# Perform Song and Chen test
if(requireNamespace("gTestsMulti", quietly = TRUE)) {
SC(X1, X2, n.perm = 100)
SC(X1, X2, n.perm = 100, type = "SA")
}
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