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A Mixed Integer Programming Model For Multiple-Class Discriminant Analysis

Author

Listed:
  • MINGHE SUN

    (Department of Management Science and Statistics, College of Business, The University of Texas at San Antonio, San Antonio, TX 78249-0632, USA)

Abstract

A mixed integer programming model is proposed for multiple-class discriminant and classification analysis. When multiple discriminant functions, one for each class, are constructed with the mixed integer programming model, the number of misclassified observations in the sample is minimized. This model is an extension of the linear programming models for multiple-class discriminant analysis but may be considered as a generalization of mixed integer programming formulations for two-class classification analysis. Properties of the model are studied. The model is immune from any difficulties of many mathematical programming formulations for two-class classification analysis, such as nonexistence of optimal solutions, improper solutions, and instability under linear data transformation. In addition, meaningful discriminant functions can be generated under conditions where other techniques fail. Examples are provided. Results on publically accessible datasets show that this model is very effective in generating powerful discriminant functions.

Suggested Citation

  • Minghe Sun, 2011. "A Mixed Integer Programming Model For Multiple-Class Discriminant Analysis," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 589-612.
    • Handle: RePEc:wsi:ijitdm:v:10:y:2011:i:04:n:s0219622011004476
    DOI: 10.1142/S0219622011004476
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    Cited by:

    1. Stan Lipovetsky & Igor Mandel, 2017. "Coefficients of Structural Association," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 285-313, March.
    2. 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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