Some properties of whitening transformations in function spaces

M. Vidal, A. M. Aguilera del Pino

We extend the notion of whitening (or sphering) to infinite dimensions using the factorization of the precision operator under certain boundary conditions. Here, we provide an overview of the theory and properties of certain whitening transformations whose rotational freedom is constrained to measures of cross-covariance and cross-correlation, among others. While originally a whitening transformation was applied mostly to data with moderately low dimension, we show that the use of a high-dimensional space can enhance its application avoiding singular or near-singular settings besides preserving the underlying topological properties of the data.

Keywords: Invariant Coordinate Selection; Mahalanobis distance; Whitening operator

Scheduled

GT01.FDA1 Invited Session
November 7, 2023  3:30 PM
CC1: Audience

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