BSSprep {BSSprep}

Whitening of Multivariate Data

Description

A function for data whitening.

Usage

BSSprep(X)

Arguments

X

A numeric matrix. Missing values are not allowed.

Details

A p-variate {\bf Y} with T observations is whitened, i.e. {\bf Y}={\bf S}^{-1/2}({\bf X}_t - \frac{1}{T}\sum_{t=1}^T {\bf X}_{t}), for t = 1, \ldots, T, where {\bf S} is the sample covariance matrix of {\bf X}.

This is often need as a preprocessing step like in almost all blind source separation (BSS) methods. The function is implemented using C++ and returns the whitened data matrix as well as the ingredients to back transform.

Value

A list containing the following components:

Y

The whitened data matrix.

X.C

The mean-centered data matrix.

COV.sqrt.i

The inverse square root of the covariance matrix of X.

MEAN

Mean vector of X.

Author(s)

Markus Matilainen, Klaus Nordhausen

Examples

n <- 100
X <- matrix(rnorm(10*n) - 1, nrow = n, ncol = 10)

res1 <- BSSprep(X)
res1$Y # The whitened matrix
colMeans(res1$Y) # should be close to zero
cov(res1$Y) # should be close to the identity matrix
res1$MEAN # Should hover around -1 for all 10 columns