Annals of Operations Research

, Volume 216, Issue 1, pp 327–342 | Cite as

Robust generalized eigenvalue classifier with ellipsoidal uncertainty

  • Petros Xanthopoulos
  • Mario R. Guarracino
  • Panos M. PardalosEmail author


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.


Robust optimization Generalized eigenvalue classification Uncertainty 



This project was partially funded by National Science Foundation (N.S.F.) grants and Italian Flagship Project Interomics funded by MIUR and CNR.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Petros Xanthopoulos
    • 1
  • Mario R. Guarracino
    • 3
  • Panos M. Pardalos
    • 2
    Email author
  1. 1.Industrial Engineering and Management Systems DepartmentUniversity of Central FloridaOrlandUSA
  2. 2.Center for Applied Optimization, Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  3. 3.High Performance Computing and Networking InstituteNational Research Council of ItalyNaplesItaly

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