I am trying to benchmark multivariate analysis performance such as CCA or PLS and I am trying to find a common association metric for both methods.
From my understanding Stewart & Love, 1968 proposed a canonical correlation index which measures the variance explained either in X or Y by the canonical correlations. Intuitively, more the explained variance is high more we have informative associations between the two datasets.
My question is: Can we do the same for PLS ?
What I intended to do is to adapt the method using the PLS paradigm (maximization of the covariance instead of correlation for CCA). Is it correct to compute squared correlations between variates in order to compute eigen values, in the same way as in a CCA approach ? Or because of the nature of PLS we need to take covariance ? Or it’s impossible to obtain it and sorry to bother you.