  Multivariate Analysis (MVA) comprises a family of well-known methods for
feature extraction that exploit correlations among input variables of the data
representation. One important property that is enjoyed by most such methods is
uncorrelation among the extracted features. Recently, regularized versions of
MVA methods have appeared in the literature, mainly with the goal to gain
interpretability of the solution. In these cases, the solutions can no longer
be obtained in a closed manner, and it is frequent to recur to the iteration of
two steps, one of them being an orthogonal Procrustes problem. This letter
shows that the Procrustes solution is not optimal from the perspective of the
overall MVA method, and proposes an alternative approach based on the solution
of an eigenvalue problem. Our method ensures the preservation of several
properties of the original methods, most notably the uncorrelation of the
extracted features, as demonstrated theoretically and through a collection of
selected experiments.
