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Taylor and Francis Group, The American Statistician, 4(72), p. 309-314, 2018

DOI: 10.1080/00031305.2016.1277159

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Optimal Whitening and Decorrelation

Journal article published in 2017 by Agnan Kessy, Alex Lewin, Korbinian Strimmer
This paper is available in a repository.
This paper is available in a repository.

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Abstract

Whitening, or sphering, is a common preprocessing step in statistical analysis to transform random variables to orthogonality. However, due to rotational freedom there are infinitely many possible whitening procedures. Consequently, there is a diverse range of sphering methods in use, for example based on principal component analysis (PCA), Cholesky matrix decomposition and zero-phase component analysis (ZCA), among others. Here we provide an overview of the underlying theory and discuss five natural whitening procedures. Subsequently, we demonstrate that investigating the cross-covariance and the cross-correlation matrix between sphered and original variables allows to break the rotational invariance and to identify optimal whitening transformations. As a result we recommend two particular approaches: ZCA-cor whitening to produce sphered variables that are maximally similar to the original variables, and PCA-cor whitening to obtain sphered variables that maximally compress the original variables.