Polynomial whitening for high-dimensional data

Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X, O'Riordan, Emily and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2023. Polynomial whitening for high-dimensional data. Computational Statistics 38 , pp. 1427-1461. 10.1007/s00180-022-01277-6

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Abstract

The inverse square root of a covariance matrix is often desirable for performing data whitening in the process of applying many common multivariate data analysis methods. Direct calculation of the inverse square root is not available when the covariance matrix is either singular or nearly singular, as often occurs in high dimensions. We develop new methods, which we broadly call polynomial whitening, to construct a low-degree polynomial in the empirical covariance matrix which has similar properties to the true inverse square root of the covariance matrix (should it exist). Our method does not suffer in singular or near-singular settings, and is computationally tractable in high dimensions. We demonstrate that our construction of low-degree polynomials provides a good substitute for high-dimensional inverse square root covariance matrices, in both d

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Additional Information:	This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
Publisher:	Springer Verlag (Germany)
ISSN:	0943-4062
Date of First Compliant Deposit:	6 September 2022
Date of Acceptance:	17 August 2022
Last Modified:	02 Aug 2023 16:51
URI:	https://orca.cardiff.ac.uk/id/eprint/152375

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