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.
|Number of pages||6|
|Journal||The American Statistician|
|Early online date||19 Jan 2017|
|Publication status||Published - 2 Oct 2018|
- CAR score
- CAT score
- Cholesky decomposition
- Principal components analysis
- ZCA-Mahalanobis transformation
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Optimal Whitening and Decorrelation
Kessy, A. (Creator), Lewin, A. (Creator) & Strimmer, K. (Creator), figshare , 19 Jan 2017