rectPartition: Calculate a rectangular partition

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

Calculate a rectangular partition

Description

The function calculates a rectangular partition of the subspace spanned by the data. Used for BG.

Usage

rectPartition(X1, X2, n, p, exponent = 0.8, eps = 0.01)

Arguments

X1	First data set as matrix
X2	Second data set as matrix
n	Number of rows in the data
p	Number of columns in the data
exponent	Exponent to ensure covergence criteria, should be between 0 and 1 (default: 0.8)
eps	Small threshold to guarantee edge points are included (default: 0.01)

Value

A list with the following components:

A	A list of p elements containing the partition cutpoints for every dimension
m_n	Total number of elements in the partition
m_n_d	Number of partition elements per dimension

References

Biau G. and Gyorfi, L. (2005). On the asymptotic properties of a nonparametric L_1-test statistic of homogeneity, IEEE Transactions on Information Theory, 51(11), 3965-3973. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1109/TIT.2005.856979")}

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

BG

Examples

# Draw some data
X1 <- matrix(rnorm(1000), ncol = 5)
X2 <- matrix(rnorm(1000, mean = 0.5), ncol = 5)
# Calculate partition
rectPartition(X1, X2, n = nrow(X1), p = ncol(X1))

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