Robust generalized eigenvalue classifier with ellipsoidal uncertainty

Uncertainty is a concept associated with data acquisition and analysis, usually appearing in the form of noise or measure error, often due to some technological constraint. In supervised learning, uncertainty affects classification accuracy and yields low quality solutions. For this reason, it is essential to develop machine learning algorithms able to handle efficiently data with imprecision. In this paper we study this problem from a robust optimization perspective. We consider a supervised learning algorithm based on generalized eigenvalues and we provide a robust counterpart formulation and solution in case of ellipsoidal uncertainty sets. We demonstrate the performance of the proposed robust scheme on artificial and benchmark datasets from University of California Irvine (UCI) machine learning repository and we compare results against a robust implementation of Support Vector Machines.