R: Double centering and U-centering

centering distance matrices {energy} | R Documentation

## Double centering and U-centering

### Description

Stand-alone double centering and U-centering functions that are applied in unbiased distance covariance, bias corrected distance correlation, and partial distance correlation.

### Usage

    Dcenter(x)
    Ucenter(x)
    U_center(Dx)
    D_center(Dx)

### Arguments

`x` | dist object or data matrix
`Dx` | distance or dissimilarity matrix

### Details

In `Dcenter` and `Ucenter`, `x` must be a `dist` object or a data matrix. Both functions return a doubly centered distance matrix.

Note that `pdcor`, etc. functions include the centering operations (in C), so that these stand alone versions of centering functions are not needed except in case one wants to compute just a double-centered or U-centered matrix.

`U_center` is the Rcpp export of the cpp function. `D_center` is the Rcpp export of the cpp function.

### Value

All functions return a square symmetric matrix.

`Dcenter` returns a matrix

A_{ij}=a_{ij} - \bar a_{i.} - \bar a_{.j} + \bar a_{..}

as in classical multidimensional scaling. `Ucenter` returns a matrix

\tilde A_{ij}=a_{ij} - \frac{a_{i.}}{n-2} - \frac{a_{.j}}{n-2} + \frac{a_{..}}{(n-1)(n-2)},\quad i \neq j,

with zero diagonal, and this is the double centering applied in `pdcov` and `pdcor` as well as the unbiased dCov and bias corrected dCor statistics.

### Note

The c++ versions `D_center` and `U_center` should typically be faster. R versions are retained for historical reasons.

### Author(s)

Maria L. Rizzo mrizzo @ bgsu.edu and Gabor J. Szekely

### References

Szekely, G.J. and Rizzo, M.L. (2014), Partial Distance Correlation with Methods for Dissimilarities, Annals of Statistics, Vol. 42, No. 6, pp. 2382-2412.
http://projecteuclid.org/euclid.aos/1413810731

### Examples

     x <- iris[1:10, 1:4]
     dx <- dist(x)
     Dx <- as.matrix(dx)
     M <- U_center(Dx)

     all.equal(M, U_center(M))     #idempotence
     all.equal(M, D_center(M))     #invariance

[Package energy version 1.7-6 Index]