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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
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    Citations

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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Pedro Duarte Silva, A., 2017. "Optimization approaches to Supervised Classification," European Journal of Operational Research, Elsevier, vol. 261(2), pages 772-788.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.

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