There are 4 sets of weight matrices that are learned - and it is not clear what the difference is between them. For instance, there is y_weights_, y_rotations_ and y_loadings_ that all have the same dimensionality.

In the traditional CCA literature, there is only 1 set of loading matrices

A', B' = argmax_A,B corr(A X, B Y)

I'd expect the sample weights U and V (which is referred to as x_scores_ and y_scores_) to be given by

U = AX
V = BY

And I'd expect the loading matrices A, B should correspond to x_loadings_ and y_loadings_.

From playing around with y_rotations_ and y_weights_ its clear that these quantities are not the same as y_loadings_.

@thomasjpfan could you clarify what these weight matrices represent? I'll be happy to submit a PR to touch up the documentation for this method.

Relevant issue: #14312