DataSimilarity (version 0.1.1)

rectPartition: 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)

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

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)

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. 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. 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))