Related to Should one remove highly correlated variables before doing PCA?, PCA is used a lot in population genetics to essentially cluster individuals into ethnic group based on their genetic markers (SNPs). These SNPs may be highly correlated (linkage disequilibrium, LD), and hence are usually thinned to make them roughly independent. They can also be regressed on each other (http://www.plosgenetics.org/article/info%3Adoi%2F10.1371%2Fjournal.pgen.0020190) to make them even more independent before doing PCA. But these regressions are slightly "suspect" since the samples are not independent, which is what we're trying to estimate in the first place!
So this "chicken and egg" problem seems to suggest an EM-like iterative approach where you first try to estimate SNP relatedness using the samples, then sample relatedness using the SNPs, and repeat. Does this approach make sense and is it already used in some areas?