IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v24y1978i14p1515-1525.html
   My bibliography  Save this article

Integer Programming Solution of a Classification Problem

Author

Listed:
  • J. M. Liittschwager

    (University of Iowa)

  • C. Wang

    (University of Iowa)

Abstract

A classification problem is presented in which it is desired to assign a new individual or observation with k characteristics to one of two distinct populations based upon historical sets of samples from the two populations. The resulting classification problem is formulated as a mixed-integer programming problem. The solution, which can be obtained through use of a partitioning algorithm based on Benders decomposition, provides a nonparametric classification statistic which minimizes the expected total cost of misclassification. Also, an enumeration algorithm is developed for the special case of k = 2. Monte Carlo studies are reported which compare the results of the enumeration algorithm with Anderson's "normal" procedure for different underlying distributions. The performance of the enumeration algorithm is shown to be significantly better than Anderson's normal procedure for distributions with uncorrelated normal populations with unequal covariance matrices and for uncorrelated skewed populations with equal covariances.

Suggested Citation

  • J. M. Liittschwager & C. Wang, 1978. "Integer Programming Solution of a Classification Problem," Management Science, INFORMS, vol. 24(14), pages 1515-1525, October.
  • Handle: RePEc:inm:ormnsc:v:24:y:1978:i:14:p:1515-1525
    DOI: 10.1287/mnsc.24.14.1515
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.24.14.1515
    Download Restriction: no

    File URL: https://libkey.io/10.1287/mnsc.24.14.1515?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
    ---><---

    Citations

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


    Cited by:

    1. Michael O. Olusola & Sydney I. Onyeagu, 2020. "On the binary classification problem in discriminant analysis using linear programming methods," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 30(1), pages 119-130.
    2. Eva K. Lee & Richard J. Gallagher & David A. Patterson, 2003. "A Linear Programming Approach to Discriminant Analysis with a Reserved-Judgment Region," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 23-41, February.
    3. Uney, Fadime & Turkay, Metin, 2006. "A mixed-integer programming approach to multi-class data classification problem," European Journal of Operational Research, Elsevier, vol. 173(3), pages 910-920, September.
    4. Stef Buuren & Willem Heiser, 1989. "Clusteringn objects intok groups under optimal scaling of variables," Psychometrika, Springer;The Psychometric Society, vol. 54(4), pages 699-706, September.
    5. Pedro Duarte Silva, A., 2017. "Optimization approaches to Supervised Classification," European Journal of Operational Research, Elsevier, vol. 261(2), pages 772-788.
    6. 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.
    7. Adem, Jan & Gochet, Willy, 2006. "Mathematical programming based heuristics for improving LP-generated classifiers for the multiclass supervised classification problem," European Journal of Operational Research, Elsevier, vol. 168(1), pages 181-199, January.
    8. Stam, Antonie & Ungar, David R., 1995. "RAGNU: A microcomputer package for two-group mathematical programming-based nonparametric classification," European Journal of Operational Research, Elsevier, vol. 86(2), pages 374-388, October.
    9. Wayne DeSarbo & Vijay Mahajan, 1984. "Constrained classification: The use of a priori information in cluster analysis," Psychometrika, Springer;The Psychometric Society, vol. 49(2), pages 187-215, June.
    10. 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.
    11. Zopounidis, Constantin & Doumpos, Michael, 2002. "Multicriteria classification and sorting methods: A literature review," European Journal of Operational Research, Elsevier, vol. 138(2), pages 229-246, April.
    12. Wojtek Krzanowski & Glenn Milligan & Stanley Wasserman & Joseph Galaskiewicz & Joel Levine & Elke Weber & Peter Fishburn & Theodore Crovello & Bernard Baum & Wayne DeSarbo, 1987. "Book reviews," Journal of Classification, Springer;The Classification Society, vol. 4(1), pages 111-141, 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:inm:ormnsc:v:24:y:1978:i:14:p:1515-1525. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.