whitening

Whitening transformation

Description

Applies the whitening transformation to a data matrix based on the Cholesky decomposition of the empirical covariance matrix.

Usage

whitening(x, Scatter = NULL)

Arguments

Argument	Description
x	vector or matrix of data with, say, \(p\) columns.
Scatter	covariance (or scatter) matrix ( \(p \times p\) ) of the distribution, must be positive definite. If NULL , the covariance matrix is estimated from the data.

Value

Returns the whitened data matrix \(\mathbf{Z} = \mathbf{X W}^T\) , where

\[\mathbf{W}^T\mathbf{W} = \mathbf{S}^{-1},\]

with \(\mathbf{S}\) the empirical covariance matrix.

References

Kessy, A., Lewin, A., Strimmer, K. (2018). Optimal whitening and decorrelation. The American Statistician 72 , 309-314.

Examples

x <- iris[,1:4]
species <- iris[,5]
pairs(x, col = species) # plot of Iris

# whitened data
z <- whitening(x)
pairs(z, col = species) # plot of