Optimal Whitening and Decorrelation. Issue 4 (2nd October 2018)

• Record Type: Journal Article
• Authors: Kessy, Agnan; Lewin, Alex; Strimmer, Korbinian
• Is Part Of: American statistician. Volume 72:Issue 4(2018)
• Page Start: 309
• Page End: 314
• Publication Date: 2018-10-02
• Subjects: CAR score -- CAT score -- Cholesky decomposition -- Decorrelation -- Principal components analysis -- Whitening -- ZCA-Mahalanobis transformation; Statistics -- Periodicals; 001.42205
• DOI: 10.1080/00031305.2016.1277159
• Languages: English
• ISSNs: 0003-1305

Abstract

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.