IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v216y2014i1p327-34210.1007-s10479-012-1303-2.html
   My bibliography  Save this article

Robust generalized eigenvalue classifier with ellipsoidal uncertainty

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-012-1303-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-012-1303-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. 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.
    3. 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.
    4. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    5. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
    2. Stefan Mišković, 2017. "A VNS-LP algorithm for the robust dynamic maximal covering location problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1011-1033, October.
    3. M. J. Naderi & M. S. Pishvaee, 2017. "Robust bi-objective macroscopic municipal water supply network redesign and rehabilitation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(9), pages 2689-2711, July.
    4. Mínguez, R. & García-Bertrand, R., 2016. "Robust transmission network expansion planning in energy systems: Improving computational performance," European Journal of Operational Research, Elsevier, vol. 248(1), pages 21-32.
    5. Antonio G. Martín & Manuel Díaz-Madroñero & Josefa Mula, 2020. "Master production schedule using robust optimization approaches in an automobile second-tier supplier," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 143-166, March.
    6. Hamed Mamani & Shima Nassiri & Michael R. Wagner, 2017. "Closed-Form Solutions for Robust Inventory Management," Management Science, INFORMS, vol. 63(5), pages 1625-1643, May.
    7. Shunichi Ohmori, 2021. "A Predictive Prescription Using Minimum Volume k -Nearest Neighbor Enclosing Ellipsoid and Robust Optimization," Mathematics, MDPI, vol. 9(2), pages 1-16, January.
    8. Hanks, Robert W. & Weir, Jeffery D. & Lunday, Brian J., 2017. "Robust goal programming using different robustness echelons via norm-based and ellipsoidal uncertainty sets," European Journal of Operational Research, Elsevier, vol. 262(2), pages 636-646.
    9. Roberto Gomes de Mattos & Fabricio Oliveira & Adriana Leiras & Abdon Baptista de Paula Filho & Paulo Gonçalves, 2019. "Robust optimization of the insecticide-treated bed nets procurement and distribution planning under uncertainty for malaria prevention and control," Annals of Operations Research, Springer, vol. 283(1), pages 1045-1078, December.
    10. Soyster, A.L. & Murphy, F.H., 2013. "A unifying framework for duality and modeling in robust linear programs," Omega, Elsevier, vol. 41(6), pages 984-997.
    11. Li, Ping & Han, Yingwei & Xia, Yong, 2016. "Portfolio optimization using asymmetry robust mean absolute deviation model," Finance Research Letters, Elsevier, vol. 18(C), pages 353-362.
    12. Wang, Tian & Deng, Shiming, 2019. "Multi-Period energy procurement policies for smart-grid communities with deferrable demand and supplementary uncertain power supplies," Omega, Elsevier, vol. 89(C), pages 212-226.
    13. Kuhn, K. & Raith, A. & Schmidt, M. & Schöbel, A., 2016. "Bi-objective robust optimisation," European Journal of Operational Research, Elsevier, vol. 252(2), pages 418-431.
    14. Hamarat, Caner & Kwakkel, Jan H. & Pruyt, Erik, 2013. "Adaptive Robust Design under deep uncertainty," Technological Forecasting and Social Change, Elsevier, vol. 80(3), pages 408-418.
    15. Oğuz Solyalı & Jean-François Cordeau & Gilbert Laporte, 2016. "The Impact of Modeling on Robust Inventory Management Under Demand Uncertainty," Management Science, INFORMS, vol. 62(4), pages 1188-1201, April.
    16. Xie, Chen & Wang, Liangquan & Yang, Chaolin, 2021. "Robust inventory management with multiple supply sources," European Journal of Operational Research, Elsevier, vol. 295(2), pages 463-474.
    17. Mavrotas, George & Figueira, José Rui & Siskos, Eleftherios, 2015. "Robustness analysis methodology for multi-objective combinatorial optimization problems and application to project selection," Omega, Elsevier, vol. 52(C), pages 142-155.
    18. Zhang, Bo & Yao, Tao & Friesz, Terry L. & Sun, Yuqi, 2015. "A tractable two-stage robust winner determination model for truckload service procurement via combinatorial auctions," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 16-31.
    19. Gülpinar, Nalan & Pachamanova, Dessislava, 2013. "A robust optimization approach to asset-liability management under time-varying investment opportunities," Journal of Banking & Finance, Elsevier, vol. 37(6), pages 2031-2041.
    20. Donya Rahmani & Arash Zandi & Sara Behdad & Arezou Entezaminia, 2021. "A light robust model for aggregate production planning with consideration of environmental impacts of machines," Operational Research, Springer, vol. 21(1), pages 273-297, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:216:y:2014:i:1:p:327-342:10.1007/s10479-012-1303-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.