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Robust generalized eigenvalue classifier with ellipsoidal uncertainty

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  • Petros Xanthopoulos
  • Mario Guarracino
  • Panos Pardalos

Abstract

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. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Petros Xanthopoulos & Mario Guarracino & Panos Pardalos, 2014. "Robust generalized eigenvalue classifier with ellipsoidal uncertainty," Annals of Operations Research, Springer, vol. 216(1), pages 327-342, May.
    • Handle: RePEc:spr:annopr:v:216:y:2014:i:1:p:327-342:10.1007/s10479-012-1303-2
    DOI: 10.1007/s10479-012-1303-2
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    References listed on IDEAS

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    1. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    2. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    3. Trafalis, Theodore B. & Gilbert, Robin C., 2006. "Robust classification and regression using support vector machines," European Journal of Operational Research, Elsevier, vol. 173(3), pages 893-909, September.
    4. Claudio Cifarelli & Mario R. Guarracino & Onur Seref & Salvatore Cuciniello & Panos M. Pardalos, 2007. "Incremental Classification with Generalized Eigenvalues," Journal of Classification, Springer;The Classification Society, vol. 24(2), pages 205-219, September.
    5. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
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    Cited by:

    1. Panagopoulos, Orestis P. & Pappu, Vijay & Xanthopoulos, Petros & Pardalos, Panos M., 2016. "Constrained subspace classifier for high dimensional datasets," Omega, Elsevier, vol. 59(PA), pages 40-46.
    2. Onur Şeref & Talayeh Razzaghi & Petros Xanthopoulos, 2017. "Weighted relaxed support vector machines," Annals of Operations Research, Springer, vol. 249(1), pages 235-271, February.
    3. Orestis P. Panagopoulos & Petros Xanthopoulos & Talayeh Razzaghi & Onur Şeref, 2019. "Relaxed support vector regression," Annals of Operations Research, Springer, vol. 276(1), pages 191-210, May.
    4. Ximing Wang & Neng Fan & Panos M. Pardalos, 2018. "Robust chance-constrained support vector machines with second-order moment information," Annals of Operations Research, Springer, vol. 263(1), pages 45-68, April.
    5. Saeed Ketabchi & Hossein Moosaei & Mohamad Razzaghi & Panos M. Pardalos, 2019. "An improvement on parametric $$\nu $$ ν -support vector algorithm for classification," Annals of Operations Research, Springer, vol. 276(1), pages 155-168, May.

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