Optimal rotations

2021-05-17 — 2023-04-06

Wherein an optimal rotation is treated as a linear whitening transform, and an orthonormal matrix is found by minimising a trace norm via matrix calculus, as in algorithmic practice

algebra
calculus
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Figure 1

Optional rotations, e.g. for optimal whitening. Practically, likely to involve matrix calculus e.g. to minimise a trace norm, e.g. Scott and Longuet-Higgins (1991).

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1 References

Congedo, Afsari, Barachant, et al. 2015. “Approximate Joint Diagonalization and Geometric Mean of Symmetric Positive Definite Matrices.” PLOS ONE.
de Vlaming, and Slob. 2021. “Joint Approximate Diagonalization Under Orthogonality Constraints.”
Kessy, Lewin, and Strimmer. 2018. “Optimal Whitening and Decorrelation.” The American Statistician.
Li, and Zhang. 1998. “Sphering and Its Properties.” Sankhyā: The Indian Journal of Statistics, Series A (1961-2002).
Scott, and Longuet-Higgins. 1991. “An Algorithm for Associating the Features of Two Images.” Proceedings of the Royal Society of London. Series B: Biological Sciences.