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Multivariate Analysis (MVA) comprises a family of well-known methods forfeature extraction that exploit correlations among input variables of the datarepresentation. One important property that is enjoyed by most such methods isuncorrelation among the extracted features. Recently, regularized versions ofMVA methods have appeared in the literature, mainly with the goal to gaininterpretability of the solution. In these cases, the solutions can no longerbe obtained in a closed manner, and it is frequent to recur to the iteration oftwo steps, one of them being an orthogonal Procrustes problem. This lettershows that the Procrustes solution is not optimal from the perspective of theoverall MVA method, and proposes an alternative approach based on the solutionof an eigenvalue problem. Our method ensures the preservation of severalproperties of the original methods, most notably the uncorrelation of theextracted features, as demonstrated theoretically and through a collection ofselected experiments.

Why (and How) Avoid Orthogonal Procrustes in Regularized Multivariate Analysis