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Optimal Whitening and Decorrelation

Author

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  • Agnan Kessy
  • Alex Lewin
  • Korbinian Strimmer

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.

Suggested Citation

  • Agnan Kessy & Alex Lewin & Korbinian Strimmer, 2018. "Optimal Whitening and Decorrelation," The American Statistician, Taylor & Francis Journals, vol. 72(4), pages 309-314, October.
    • Handle: RePEc:taf:amstat:v:72:y:2018:i:4:p:309-314
    DOI: 10.1080/00031305.2016.1277159
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    Cited by:

    1. Dirk Roeder & Georgi Dimitroff, 2020. "Volatility model calibration with neural networks a comparison between direct and indirect methods," Papers 2007.03494, arXiv.org.
    2. Loperfido, Nicola, 2024. "The skewness of mean–variance normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    3. Jonathan Gillard & Emily O’Riordan & Anatoly Zhigljavsky, 2023. "Polynomial whitening for high-dimensional data," Computational Statistics, Springer, vol. 38(3), pages 1427-1461, September.
    4. Steen MAGNUSSEN, 2018. "An estimation strategy to protect against over-estimating precision in a LiDAR-based prediction of a stand mean," Journal of Forest Science, Czech Academy of Agricultural Sciences, vol. 64(12), pages 497-505.
    5. Nikita Moshkov & Michael Bornholdt & Santiago Benoit & Matthew Smith & Claire McQuin & Allen Goodman & Rebecca A. Senft & Yu Han & Mehrtash Babadi & Peter Horvath & Beth A. Cimini & Anne E. Carpenter , 2024. "Learning representations for image-based profiling of perturbations," Nature Communications, Nature, vol. 15(1), pages 1-17, December.
    6. Harold Doran, 2023. "A Collection of Numerical Recipes Useful for Building Scalable Psychometric Applications," Journal of Educational and Behavioral Statistics, , vol. 48(1), pages 37-69, February.
    7. Schosser, Josef, 2019. "Consistency between principal and agent with differing time horizons: Computing incentives under risk," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1113-1123.
    8. Damiano Brigo & Xiaoshan Huang & Andrea Pallavicini & Haitz Saez de Ocariz Borde, 2021. "Interpretability in deep learning for finance: a case study for the Heston model," Papers 2104.09476, arXiv.org.
    9. Priddle, Jacob W. & Drovandi, Christopher, 2023. "Transformations in semi-parametric Bayesian synthetic likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    10. Stan Lipovetsky, 2022. "Canonical Concordance Correlation Analysis," Mathematics, MDPI, vol. 11(1), pages 1-12, December.
    11. Minati, Ludovico & Li, Chao & Bartels, Jim & Chakraborty, Parthojit & Li, Zixuan & Yoshimura, Natsue & Frasca, Mattia & Ito, Hiroyuki, 2023. "Accelerometer time series augmentation through externally driving a non-linear dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    12. Wong, William & Tsuchiya, Naotsugu, 2020. "Evidence accumulation clustering using combinations of features," OSF Preprints epb6t, Center for Open Science.

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