Optimal rotations

May 18, 2021 — April 6, 2023

algebra
calculus
functional analysis
geometry
high d
linear algebra
optimization
probability
signal processing
sparser than thou
spheres
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.