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On the binary classification problem in discriminant analysis using linear programming methods

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  • Michael O. Olusola
  • Sydney I. Onyeagu

Abstract

This paper is centred on a binary classification problem in which it is desired to assign a new object with multivariate features to one of two distinct populations as based on historical sets of samples from two populations. A linear discriminant analysis framework has been proposed, called the minimised sum of deviations by proportion (MSDP) to model the binary classification problem. In the MSDP formulation, the sum of the proportion of exterior deviations is minimised subject to the group separation constraints, the normalisation constraint, the upper bound constraints on proportions of exterior deviations and the sign unrestriction vis-à-vis the non-negativity constraints. The two-phase method in linear programming is adopted as a solution technique to generate the discriminant function. The decision rule on group-membership prediction is constructed using the apparent error rate. The performance of the MSDP has been compared with some existing linear discriminant models using a previously published dataset on road casualties. The MSDP model was more promising and well suited for the imbalanced dataset on road casualties.

Suggested Citation

  • 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.
    • Handle: RePEc:wut:journl:v:1:y:2020:p:119-130:id:1436
    DOI: 10.37190/ord200107
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    References listed on IDEAS

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    1. Abramovich, Felix & Pensky, Marianna, 2019. "Classification with many classes: Challenges and pluses," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    2. Lam, Kim Fung & Choo, Eng Ung & Moy, Jane W., 1996. "Minimizing deviations from the group mean: A new linear programming approach for the two-group classification problem," European Journal of Operational Research, Elsevier, vol. 88(2), pages 358-367, January.
    3. Willy Gochet & Antonie Stam & V. Srinivasan & Shaoxiang Chen, 1997. "Multigroup Discriminant Analysis Using Linear Programming," Operations Research, INFORMS, vol. 45(2), pages 213-225, April.
    4. Houshmand A. Ziari & David J. Leatham & Paul N. Ellinger, 1997. "Development of Statistical Discriminant Mathematical Programming Model Via Resampling Estimation Techniques," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 79(4), pages 1352-1362.
    5. Gaynanova, Irina & Wang, Tianying, 2019. "Sparse quadratic classification rules via linear dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 278-299.
    6. J J Glen, 2001. "Classification accuracy in discriminant analysis: a mixed integer programming approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(3), pages 328-339, March.
    7. 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.
    8. J. M. Liittschwager & C. Wang, 1978. "Integer Programming Solution of a Classification Problem," Management Science, INFORMS, vol. 24(14), pages 1515-1525, October.
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