Trace optimization and eigenproblems in dimension reduction methods

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Rewriting a Deep Generative Model (2020, background): “34 is an instance of the well-studied trace optimization problem [49] that arises in many dimension-reduction settings.”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives (2017, methodology): “2 illustrates the rich scope of the Generalized Eigenvalue Decomposition (GEVD), a backbone of many standard8 methods for linear dimensionality reduction, classification, and clustering (Kokiopoulou et al., 2011; Cunningham and Ghahramani, 2015; Benson et al., 2015; Gleich et al., 2015; Wu et al., 2”
On the Global Optima of Kernelized Adversarial Representation Learning (2019, background): “The optimization problem in (11) is equivalent to trace minimization on a Stiefel manifold which has closed-form solution(s) (see [14] and [5]).”