Regularized Multivariate Analysis Framework for Interpretable High-Dimensional Variable Selection
This work addresses the need for interpretable feature extraction in high-dimensional data, representing an incremental improvement over existing regularized MVA methods.
The paper tackles the problem of interpretable high-dimensional variable selection by proposing a regularized multivariate analysis framework that preserves uncorrelated features and uses an l-21 norm for variable selection, with experimental results showing advantages over state-of-the-art methods.
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.