# Optimal rotations

May 18, 2021 — April 6, 2023

algebra

calculus

functional analysis

geometry

high d

linear algebra

measure

optimization

probability

signal processing

sparser than thou

spheres

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).

A.k.a. *sphereing*.

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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*.