IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v50y1999i10d10.1057_palgrave.jors.2600804.html
   My bibliography  Save this article

Integer programming methods for normalisation and variable selection in mathematical programming discriminant analysis models

Author

Listed:
  • J J Glen

    (The University of Edinburgh)

Abstract

Mathematical programming discriminant analysis models must be normalised to prevent the generation of discriminant functions in which the variable coefficients and the constant term are zero. This normalisation requirement can cause difficulties, and unlike statistical discriminant analysis, variables cannot be selected in a computationally efficient way with mathematical programming discriminant analysis models. Two new integer programming normalisations are proposed in this paper. In the first, binary variables are used to represent the constant term, but with this normalisation functions with a zero constant term cannot be generated and the variable coefficients are not invariant under origin shifts. These limitations are overcome by using integer programming methods to constrain the sum of the absolute values of the variable coefficients to a constant. These new normalisations are extended to allow variable selection with mathematical programming discriminant analysis models. The use of these new applications of integer programming is illustrated using published data.

Suggested Citation

  • J J Glen, 1999. "Integer programming methods for normalisation and variable selection in mathematical programming discriminant analysis models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(10), pages 1043-1053, October.
    • Handle: RePEc:pal:jorsoc:v:50:y:1999:i:10:d:10.1057_palgrave.jors.2600804
    DOI: 10.1057/palgrave.jors.2600804
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/palgrave.jors.2600804
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1057/palgrave.jors.2600804?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.

    Citations

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


    Cited by:

    1. Soulef Smaoui & Belaid Aouni, 2017. "Fuzzy goal programming model for classification problems," Annals of Operations Research, Springer, vol. 251(1), pages 141-160, April.
    2. Mingue Sun, 2009. "Liquidity Risk and Financial Competition: A Mixed Integer Programming Model for Multiple-Class Discriminant Analysis," Working Papers 0102, College of Business, University of Texas at San Antonio.
    3. Crook, Jonathan N. & Edelman, David B. & Thomas, Lyn C., 2007. "Recent developments in consumer credit risk assessment," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1447-1465, December.
    4. J J Glen, 2008. "An additive utility mixed integer programming model for nonlinear discriminant analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(11), pages 1492-1505, November.
    5. J J Glen, 2005. "Mathematical programming models for piecewise-linear discriminant analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(3), pages 331-341, March.
    6. Glen, J.J., 2006. "A comparison of standard and two-stage mathematical programming discriminant analysis methods," European Journal of Operational Research, Elsevier, vol. 171(2), pages 496-515, June.
    7. Pedro Duarte Silva, A., 2017. "Optimization approaches to Supervised Classification," European Journal of Operational Research, Elsevier, vol. 261(2), pages 772-788.
    8. J. J. Glen, 2004. "Dichotomous categorical variable formation in mathematical programming discriminant analysis models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 575-596, June.
    9. K Falangis & J J Glen, 2010. "Heuristics for feature selection in mathematical programming discriminant analysis models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(5), pages 804-812, May.
    10. Fadime Üney-Yüksektepe, 2014. "A novel approach to cutting decision trees," 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. 22(3), pages 553-565, September.

    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:pal:jorsoc:v:50:y:1999:i:10:d:10.1057_palgrave.jors.2600804. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.palgrave-journals.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.