%0 Journal Article %1 kessy2016optimal %A Kessy, Agnan %A Lewin, Alex %A Strimmer, Korbinian %D 2016 %J The American Statistician %K preprocessing, whitening, zca pca %P 1--6 %R 10.1080/00031305.2016.1277159 %T Optimal whitening and decorrelation %U http://dx.doi.org/10.1080/00031305.2016.1277159 %X 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.

@article{kessy2016optimal, 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.}}, added-at = {2018-12-07T09:10:16.000+0100}, archiveprefix = {arXiv}, author = {Kessy, Agnan and Lewin, Alex and Strimmer, Korbinian}, biburl = {https://www.bibsonomy.org/bibtex/2bde73fe666a5e8dcdae3d115bfe95602/jpvaldes}, citeulike-article-id = {14618487}, citeulike-linkout-0 = {http://arxiv.org/abs/1512.00809}, citeulike-linkout-1 = {http://arxiv.org/pdf/1512.00809}, citeulike-linkout-2 = {http://dx.doi.org/10.1080/00031305.2016.1277159}, day = 18, doi = {10.1080/00031305.2016.1277159}, eprint = {1512.00809}, interhash = {49f6e96a90d965f7eeba101f9f7c2be0}, intrahash = {bde73fe666a5e8dcdae3d115bfe95602}, issn = {0003-1305}, journal = {The American Statistician}, keywords = {preprocessing, whitening, zca pca}, month = dec, pages = {1--6}, posted-at = {2018-07-26 10:23:37}, priority = {2}, timestamp = {2018-12-07T09:55:08.000+0100}, title = {{Optimal whitening and decorrelation}}, url = {http://dx.doi.org/10.1080/00031305.2016.1277159}, year = 2016 }