  Multivariate Analysis (MVA) comprises a family of well-known methods for
feature extraction which exploit correlations among input variables
representing the data. 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 more complex optimization methods
that rely on the iteration of two steps are frequently used. This paper recurs
to an alternative approach to solve efficiently this iterative problem. The
main novelty of this approach lies in preserving several properties of the
original methods, most notably the uncorrelation of the extracted features.
Under this framework, we propose a novel method that takes advantage of the
l-21 norm to perform variable selection during the feature extraction process.
Experimental results over different problems corroborate the advantages of the
proposed formulation in comparison to state of the art formulations.
