Cross-validation of component models: A critical look at current methods

By Rasmus Bro, K. Kjeldahl, Age K. Smilde, Henk A. L. Kiers. Analytical and Bioanalytical Chemistry, 2008

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Multiple imputation for continuous variables using a Bayesian principal component analysis† (2014, methodology): “Cross-validation (Bro et al., 2008) or an approximation of cross-validation such as generalized cross-validation (Josse and Husson, 2011b) perform well.”
Noise2Self: Blind Denoising by Self-Supervision (2019, background): “Cross-validation for choosing the rank of a PCA requires some care, since adding more principal components will always produce a better fit, even on held-out samples (Bro et al., 2008).”
Bootstrap based confidence limits in principal component analysis: a case study (2013, methodology): “The practical rank is determined beforehand based on the stability of the PCA subspace [17–21], by using techniques such as cross-validation [41], some reported alternative methods [40,42,43], or knowledge of the user about the data; this rank will be fixed from here on.”