{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/optimal-whitening-and-decorrelation","title":"Optimal whitening and decorrelation","arxiv_id":"1512.00809","date":"2015-12-02","proceeding":null,"authors":["Agnan Kessy","Alex Lewin","Korbinian Strimmer"],"abstract":"Whitening, or sphering, is a common preprocessing step in statistical\nanalysis to transform random variables to orthogonality. However, due to\nrotational freedom there are infinitely many possible whitening procedures.\nConsequently, there is a diverse range of sphering methods in use, for example\nbased on principal component analysis (PCA), Cholesky matrix decomposition and\nzero-phase component analysis (ZCA), among others.\n  Here we provide an overview of the underlying theory and discuss five natural\nwhitening procedures. Subsequently, we demonstrate that investigating the\ncross-covariance and the cross-correlation matrix between sphered and original\nvariables allows to break the rotational invariance and to identify optimal\nwhitening transformations. As a result we recommend two particular approaches:\nZCA-cor whitening to produce sphered variables that are maximally similar to\nthe original variables, and PCA-cor whitening to obtain sphered variables that\nmaximally compress the original variables.","url_abs":"http://arxiv.org/abs/1512.00809v4","url_pdf":"http://arxiv.org/pdf/1512.00809v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"optimal-whitening-and-decorrelation","repo_url":"https://github.com/Yijunmaverick/UniversalStyleTransfer","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1512.00809","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}