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An additive utility mixed integer programming model for nonlinear discriminant analysis

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  • J J Glen

    (University of Edinburgh)

Abstract

Mathematical programming (MP) discriminant analysis models can be used to develop classification models for assigning observations of unknown class membership to one of a number of specified classes using values of a set of features associated with each observation. Since most MP discriminant analysis models generate linear discriminant functions, these MP models are generally used to develop linear classification models. Nonlinear classifiers may, however, have better classification performance than linear classifiers. In this paper, a mixed integer programming model is developed to generate nonlinear discriminant functions composed of monotone piecewise-linear marginal utility functions for each feature and the cut-off value for class membership. It is also shown that this model can be extended for feature selection. The performance of this new MP model for two-group discriminant analysis is compared with statistical discriminant analysis and other MP discriminant analysis models using a real problem and a number of simulated problem sets.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:59:y:2008:i:11:d:10.1057_palgrave.jors.2602485
    DOI: 10.1057/palgrave.jors.2602485
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    References listed on IDEAS

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    1. Antonie Stam, 1997. "Nontraditional approaches to statistical classification: Some perspectives on L_p-norm methods," Annals of Operations Research, Springer, vol. 74(0), pages 1-36, November.
    2. 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.
    3. Silva, Antonio Pedro Duarte & Stam, Antonie, 1994. "Second order mathematical programming formulations for discriminant analysis," European Journal of Operational Research, Elsevier, vol. 72(1), pages 4-22, January.
    4. Stam, Antonie & Joachimsthaler, Erich A., 1990. "A comparison of a robust mixed-integer approach to existing methods for establishing classification rules for the discriminant problem," European Journal of Operational Research, Elsevier, vol. 46(1), pages 113-122, May.
    5. Pavur, Robert, 2002. "A comparative study of the effect of the position of outliers on classical and nontraditional approaches to the two-group classification problem," European Journal of Operational Research, Elsevier, vol. 136(3), pages 603-615, February.
    6. 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.
    7. Keeney,Ralph L. & Raiffa,Howard, 1993. "Decisions with Multiple Objectives," Cambridge Books, Cambridge University Press, number 9780521438834, September.
    8. 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.
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    Cited by:

    1. Pedro Duarte Silva, A., 2017. "Optimization approaches to Supervised Classification," European Journal of Operational Research, Elsevier, vol. 261(2), pages 772-788.

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