Kessy, A, Lewin, A and Strimmer, K. 2017. Optimal Whitening and Decorrelation. [Online]. Figshare. Available from: https://doi.org/10.6084/m9.figshare.4568002.v1
Kessy, A, Lewin, A and Strimmer, K. Optimal Whitening and Decorrelation [Internet]. Figshare; 2017. Available from: https://doi.org/10.6084/m9.figshare.4568002.v1
Kessy, A, Lewin, A and Strimmer, K (2017). Optimal Whitening and Decorrelation. [Data Collection]. Figshare. https://doi.org/10.6084/m9.figshare.4568002.v1
Description
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.
Data capture method | Simulation |
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Date (Date published in a 3rd party system) | 19 January 2017 |
Language(s) of written materials | English |
Data Creators | Kessy, A, Lewin, A and Strimmer, K |
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LSHTM Faculty/Department | Faculty of Epidemiology and Population Health > Dept of Medical Statistics |
Participating Institutions | London School of Hygiene & Tropical Medicine, London, United Kingdom, Brunel University, London, United Kingdom, Imperial College, London, United Kingdom |
Date Deposited | 05 Oct 2018 09:45 |
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Last Modified | 09 Jul 2021 11:22 |
Publisher | Figshare |