Optimal Whitening and Decorrelation

Agnan Kessy, Alex Lewin, Korbinian Strimmer

    Research output: Contribution to journalArticlepeer-review


    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.
    Original languageEnglish
    Pages (from-to)309-314
    Number of pages6
    JournalThe American Statistician
    Issue number4
    Early online date19 Jan 2017
    Publication statusPublished - 2 Oct 2018


    • CAR score
    • CAT score
    • Cholesky decomposition
    • Decorrelation
    • Principal components analysis
    • Whitening
    • ZCA-Mahalanobis transformation


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