whitening {fastmatrix}

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

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 \bold{Z} = \bold{X W}^T, where

\bold{W}^T\bold{W} = \bold{S}^{-1},

with \bold{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