2017/01/20 by Agnan Kessy, Alex Lewin, Korbinian Strimmer · 1 citation
Chemistry · Environmental Science · Computer Science · #Spectroscopy and Chemometric Analyses #Soil Geostatistics and Mapping #Blind Source Separation Techniques
paper · doi:10.1080/00031305.2016.1277159
openalex publication_date 2017/01/20 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/01
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.