fi/fj & wfi/wfj

[derekbeaton]

this is a very to-be-considered idea but would greatly benefit CCA and correlation PCA by way of geigen when using a covariance matrix...

I should consider introducing the idea of fi/fj and a "weighted" one. The "weighted" one should be perhaps an "unweighted" one, so that fi/fj are in the correct metric.

So either fi/fj = W[P/Q]D (as it is) or just [U/V]D But perhaps an unweighted or "standard scores" approach should be [U/V]D and then W[P/Q]D remains as the "correct metric" scores

if I introduce them as weighted then fi/fj become [U/V]D where wfi/wfj become W[P/Q]D

but if I flip that, then fi/fj remain W[P/Q]D and then maybe "ufi/ufj" or perhaps something as simple as "ud/vd" for [U/V]D

[derekbeaton]

infact, RRR (and the correlation PCA via covariance) makes a compelling argument for this

[derekbeaton]

thinking much more about it: this should be something at the analysis level, not the decomposition level.

If PCA, CCA, or RRR benefit from different sets of scores, then those methods should produce those for the user. But the GSVD package should only produce the key elements

[derekbeaton]

actually I may consider bringing these in because then we have two distinct concepts: "component scores" and "generalized component scores"

but that could ultimately be kind of confusing