estats (version 1.0)

Energy distance between matrices: Energy distance between matrices

Description

Energy distance between matrices.

Usage

edist(x, y = NULL)

Value

If "x" is matrix, a numerical value, the energy distance. If "x" is list, a matrix with all pairwsie distances of the matrices.

Arguments

x

A matrix with numbers or a list with matrices.

y

A second matrix with data. The number of columns of x and y must match. The number of rows can be different.

Author

Manos Papadakis

R implementation and documentation: Manos Papadakis <[e-mail]>.

Details

This calculates the energy distance between two matrices. It will work even for tens of thousands of rows, it will just take some time. See the references for more information. If you have many matrices and want to calculate the distance matrix, then put them in a list and use the function.

References

Szekely G. J. and Rizzo M. L. (2004) Testing for Equal Distributions in High Dimension, InterStat, November (5).

Szekely G. J. (2000) Technical Report 03-05, E-statistics: Energy of Statistical Samples, Department of Mathematics and Statistics, Bowling Green State University.

Sejdinovic D., Sriperumbudur B., Gretton A. and Fukumizu, K. (2013). Equivalence of distance-based and RKHS-based statistics in hypothesis testing. The Annals of Statistics, 41(5): 2263--2291.

Szekely G. J. and Rizzo M. L. (2023). The Energy of Data and Distance Correlation. Chapman and Hall/CRC.

Tsagris M. and Papadakis M. (2025). Fast and light-weight energy statistics using the R package Rfast. https://arxiv.org/abs/2501.02849

See Also

dcov

Examples

x <- as.matrix( iris[1:50, 1:4] )
y <- as.matrix( iris[51:100, 1:4] )
res<-edist(x, y)
z <- as.matrix(iris[101:150, 1:4])
a <- list()
a[[ 1 ]] <- x
a[[ 2 ]] <- y
a[[ 3 ]] <- z
res<-edist(a)

x<-y<-z<-a<-NULL