dipro.fun: Direction-Projection Functions for DiProPerm Test

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

Direction-Projection Functions for DiProPerm Test

Description

Helper functions performing the direction and projection step using different classifiers for the Direction-Projection-Permutation (DiProPerm) two-sample test for high-dimensional data (Wei et al., 2016)

Usage

dwdProj(X1, X2)
svmProj(X1, X2)

Arguments

X1	First dataset as matrix or data.frame
X2	Second dataset as matrix or data.frame

Details

The DiProPerm test works by first combining the datasets into a pooled dataset and creating a target variable with the dataset membership of each observation. A binary linear classifier is then trained on the class labels and the normal vector of the separating hyperplane is calculated. The data from both samples is projected onto this normal vector. This gives a scalar score for each observation. On these projection scores, a univariate two-sample statistic is calculated. The permutation null distribution of this statistic is calculated by permuting the dataset labels and repeating the whole procedure with the permuted labels. The functions here correspond to the direction and projection step for either the DWD or SVM classifier as proposed by Wei et al., 2016.

The DWD model implementation genDWD in the DWDLargeR package is used with the penalty parameter C calculated with penaltyParameter using the recommended default values. More details on the algorithm can be found in Lam et al. (2018).

For the SVM, the implementation svm in the e1071 package is used with default parameters.

Value

A numeric vector containing the projected values for each observation in the pooled sample

References

Lam, X. Y., Marron, J. S., Sun, D., & Toh, K.-C. (2018). Fast Algorithms for Large-Scale Generalized Distance Weighted Discrimination. Journal of Computational and Graphical Statistics, 27(2), 368-379. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/10618600.2017.1366915")}

Wei, S., Lee, C., Wichers, L., & Marron, J. S. (2016). Direction-Projection-Permutation for High-Dimensional Hypothesis Tests. Journal of Computational and Graphical Statistics, 25(2), 549-569. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/10618600.2015.1027773")}

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

DiProPerm

Examples

# Draw some data
X1 <- matrix(rnorm(1000), ncol = 10)
X2 <- matrix(rnorm(1000, mean = 0.5), ncol = 10)

# calculate projections separately (only for demonstration)

dwdProj(X1, X2)

svmProj(X1, X2)

# Use within DiProPerm test 
# Note: For real applications, n.perm should be set considerably higher
# No permutations chosen for demonstration due to runtime

if(requireNamespace("DWDLargeR", quietly = TRUE)) {
  DiProPerm(X1, X2, n.perm = 10, dipro.fun = dwdProj)
}
if(requireNamespace("e1071", quietly = TRUE)) {
  DiProPerm(X1, X2, n.perm = 10, dipro.fun = svmProj)
}

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