Please use this identifier to cite or link to this item: http://buratest.brunel.ac.uk/handle/2438/13832
Title: Optimal whitening and decorrelation
Authors: Kessey, A
Lewin, A
Strimmer, K
Keywords: Whitening;decorrelation;ZCA-Mahalanobis transformation;Principal components analysis;Cholesky decomposition;CAT score
Issue Date: 2016
Publisher: Taylor & Francis
Citation: The American Statistician, (2016)
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-correlationmatrix 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-corwhitening to obtain sphered variables thatmaximally compress the original variables.
URI: http://bura.brunel.ac.uk/handle/2438/13832
Appears in Collections:Dept of Mathematics Research Papers

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