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A generalized eigenvalues classifier with embedded feature selection


Supervised classification is one of the most used methods in machine learning. In case of data characterized by a large number of features, a critical issue is to deal with redundant or irrelevant information. To this extent, an effective algorithm needs to identify a suitable subset of features, as small as possible, for the classification. In this work we present ReGEC_L1, a classifier with embedded feature selection based on the Regularized Generalized Eigenvalue Classifier (ReGEC) and equipped with a L1-norm regularization term. We detail the mathematical formulation and the numerical algorithm. Numerical results, obtained on some de facto standard benchmark data sets, show that the approach we propose produces a remarkable selection of the features, without losing accuracy in the classification. In that respect, our algorithm seems to compare favorably with the SVM_L1 method. A MATLAB implementation of ReGEC_L1 is available at

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Mara Sangiovanni was supported by Interomics Italian Flagship Project and MIUR PON02-00612. Mario Guarracino and Gerardo Toraldo were partially supported by INdAM-GNCS, under the 2015 Project “Numerical Methods for Nonconvex/Nonsmooth Optimization and Applications”. Mario Guarracino work has been conducted at National Research University Higher School of Economics (HSE) and has been supported by the RSF Grant No. 14-41-00039. Marco Viola work was performed during his undergraduate stage at the Institute for High Performance Computing and Networking (ICAR) of the National Research Council (CNR).

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Viola, M., Sangiovanni, M., Toraldo, G. et al. A generalized eigenvalues classifier with embedded feature selection. Optim Lett 11, 299–311 (2017).

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  • Supervised classification
  • Feature selection
  • Embedded methods