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. ,, 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. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    4. 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.
    5. 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.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Onur Şeref & Talayeh Razzaghi & Petros Xanthopoulos, 2017. "Weighted relaxed support vector machines," Annals of Operations Research, Springer, vol. 249(1), pages 235-271, February.

    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Tao Yao & Supreet Mandala & Byung Chung, 2009. "Evacuation Transportation Planning Under Uncertainty: A Robust Optimization Approach," Networks and Spatial Economics, Springer, vol. 9(2), pages 171-189, June.
    10. Cleber D. Rocco & Reinaldo Morabito, 2016. "Robust optimisation approach applied to the analysis of production / logistics and crop planning in the tomato processing industry," International Journal of Production Research, Taylor & Francis Journals, vol. 54(19), pages 5842-5861, October.
    11. Nitish Umang & Michel Bierlaire & Alan L. Erera, 2017. "Real-time management of berth allocation with stochastic arrival and handling times," Journal of Scheduling, Springer, vol. 20(1), pages 67-83, February.
    12. Henao, César Augusto & Ferrer, Juan Carlos & Muñoz, Juan Carlos & Vera, Jorge, 2016. "Multiskilling with closed chains in a service industry: A robust optimization approach," International Journal of Production Economics, Elsevier, vol. 179(C), pages 166-178.
    13. Krumke, Sven O. & Schmidt, Eva & Streicher, Manuel, 2019. "Robust multicovers with budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 274(3), pages 845-857.
    14. Ghazaleh Ahmadi & Reza Tavakkoli-Moghaddam & Armand Baboli & Mehdi Najafi, 2022. "A decision support model for robust allocation and routing of search and rescue resources after earthquake: a case study," Operational Research, Springer, vol. 22(2), pages 1039-1081, April.
    15. Lin, Jun & Ng, Tsan Sheng, 2011. "Robust multi-market newsvendor models with interval demand data," European Journal of Operational Research, Elsevier, vol. 212(2), pages 361-373, July.
    16. Somayeh Moazeni & Thomas Coleman & Yuying Li, 2013. "Regularized robust optimization: the optimal portfolio execution case," Computational Optimization and Applications, Springer, vol. 55(2), pages 341-377, June.
    17. Najafi, Mehdi & Eshghi, Kourosh & Dullaert, Wout, 2013. "A multi-objective robust optimization model for logistics planning in the earthquake response phase," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 49(1), pages 217-249.
    18. Emmanuel Kwasi Mensah, 2020. "Robust data envelopment analysis via ellipsoidal uncertainty sets with application to the Italian banking industry," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 491-518, December.
    19. Shipra Agrawal & Yichuan Ding & Amin Saberi & Yinyu Ye, 2012. "Price of Correlations in Stochastic Optimization," Operations Research, INFORMS, vol. 60(1), pages 150-162, February.
    20. Xu, Liang & Zhang, Chao & Xiao, Feng & Wang, Fan, 2017. "A robust approach to airport gate assignment with a solution-dependent uncertainty budget," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 458-478.

    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.