Package 'BSSprep'

Whitening Data as Preparation for Blind Source Separation

Description

Whitening is the first step of almost all blind source separation (BSS) methods. A fast implementation of whitening for BSS is implemented to serve as a lightweight dependency for packages providing BSS methods.

Details

Package:	BSSprep
Type:	Package
Version:	0.1
Date:	2021-03-25
License:	GPL (>= 2)

This package contains the single function BSSprep for whitening multivariate data as a preprocessing step for blind source separation (BSS). The package is meant as a fast and lightweight dependency for packages providing BSS methods as whitening is almost always the first step.

Author(s)

Markus Matilainen, Klaus Nordhausen

Maintainer: Markus Matilainen <[email protected]>

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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

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