On the regularization of generalized eigenvalues classifiers

Generalized Eigenvalues Classifiers (GEC), which originated from the GEPSVM algorithm by Mangasarian, proved to be an efficient alternative to the Support Vector Machines (SVMs) in the solution of supervised classification tasks. However real-life datasets are often characterized by a large number of redundant features and by a great number of points whose labels are difficult (or too expensive) to assign. In this work we start from the Regularized Generalized Eigenvalue Classifier (ReGEC) and show how regularization terms can be used to enable the classifier to solve two different problems, strictly connected to that of supervised classification: feature selection and semi-supervised classification. Numerical results, obtained on some standard benchmark data sets, show the efficiency of the proposed solution