IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v218y2012i3p667-675.html
   My bibliography  Save this article

Exploring the trade-off between generalization and empirical errors in a one-norm SVM

Author

Listed:
  • Aytug, Haldun
  • Sayın, Serpil

Abstract

We propose a one-norm support vector machine (SVM) formulation as an alternative to the well-known formulation that uses parameter C in order to balance the two inherent objective functions of the problem. Our formulation is motivated by the ϵ-constraint approach that is used in bicriteria optimization and we propose expressing the objective of minimizing total empirical error as a constraint with a parametric right-hand-side. Using dual variables we show equivalence of this formulation to the one with the trade-off parameter. We propose an algorithm that enumerates the entire efficient frontier by systematically changing the right-hand-side parameter. We discuss the results of a detailed computational analysis that portrays the structure of the efficient frontier as well as the computational burden associated with finding it. Our results indicate that the computational effort for obtaining the efficient frontier grows linearly in problem size, and the benefit in terms of classifier performance is almost always substantial when compared to a single run of the corresponding SVM. In addition, both the run time and accuracy compare favorably to other methods that search part or all of the regularization path of SVM.

Suggested Citation

  • Aytug, Haldun & Sayın, Serpil, 2012. "Exploring the trade-off between generalization and empirical errors in a one-norm SVM," European Journal of Operational Research, Elsevier, vol. 218(3), pages 667-675.
  • Handle: RePEc:eee:ejores:v:218:y:2012:i:3:p:667-675
    DOI: 10.1016/j.ejor.2011.11.037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711010460
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108.
    2. Khemchandani, Reshma & Jayadeva & Chandra, Suresh, 2009. "Knowledge based proximal support vector machines," European Journal of Operational Research, Elsevier, vol. 195(3), pages 914-923, June.
    3. Serpil Say{i}n & Panos Kouvelis, 2005. "The Multiobjective Discrete Optimization Problem: A Weighted Min-Max Two-Stage Optimization Approach and a Bicriteria Algorithm," Management Science, INFORMS, vol. 51(10), pages 1572-1581, October.
    Full references (including those not matched with items on IDEAS)

    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:eee:ejores:v:218:y:2012:i:3:p:667-675. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/eor .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.