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Multigroup Discriminant Analysis Using Linear Programming

Author

Listed:
  • Willy Gochet

    (Katholieke Universiteit Leuven, Leuven, Belgium)

  • Antonie Stam

    (The University of Georgia, Athens, Georgia, and International Institute for Applied Systems Analysis, Laxenburg, Austria)

  • V. Srinivasan

    (Stanford University, Stanford, California)

  • Shaoxiang Chen

    (Nanyang Technological University, Singapore)

Abstract

In this paper we introduce a nonparametric linear programming formulation for the general multigroup classification problem. Previous research using linear programming formulations has either been limited to the two-group case, or required complicated constraints and many zero-one variables. We develop general properties of our multigroup formulation and illustrate its use with several small example problems and previously published real data sets. A comparative analysis on the real data sets shows that our formulation may offer an interesting robust alternative to parametric statistical formulations for the multigroup discriminant problem.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:2:p:213-225
    DOI: 10.1287/opre.45.2.213
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    Citations

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    Cited by:

    1. Araz, Ceyhun & Ozkarahan, Irem, 2007. "Supplier evaluation and management system for strategic sourcing based on a new multicriteria sorting procedure," International Journal of Production Economics, Elsevier, vol. 106(2), pages 585-606, April.
    2. Emilio Carrizosa & Belén Martín-Barragán & Frank Plastria & Dolores Romero Morales, 2007. "On the Selection of the Globally Optimal Prototype Subset for Nearest-Neighbor Classification," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 470-479, August.
    3. 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.
    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. Pedro Duarte Silva, A., 2017. "Optimization approaches to Supervised Classification," European Journal of Operational Research, Elsevier, vol. 261(2), pages 772-788.
    6. 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.
    7. Adem, Jan & Gochet, Willy, 2004. "Aggregating classifiers with mathematical programming," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 791-807, November.
    8. 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.
    9. Doumpos, Michael & Zopounidis, Constantin, 2004. "A multicriteria classification approach based on pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 158(2), pages 378-389, October.
    10. 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.
    11. Loucopoulos, Constantine, 2001. "Three-group classification with unequal misclassification costs: a mathematical programming approach," Omega, Elsevier, vol. 29(3), pages 291-297, June.
    12. Dillon, Carl R., 2002. "A Mathematical Programming Model For Optimal Management Zone Delineation In Precision Agriculture," 2002 Annual meeting, July 28-31, Long Beach, CA 19672, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    13. Roe, R.A. & Smeelen, M. & Hoefeld, C., 2005. "Outsourcing and organizational change : an employee perspective," Research Memorandum 045, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    14. Carrizosa, E. & Martin-Barragán, B. & Plastria, F. & Romero Morales, M.D., 2002. "A Dissimilarity-based approach for Classification," Research Memorandum 027, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    15. Soulef Smaoui & Belaid Aouni, 2017. "Fuzzy goal programming model for classification problems," Annals of Operations Research, Springer, vol. 251(1), pages 141-160, April.
    16. Bruce Golden & Linus Schrage & Douglas Shier & Lida Anna Apergi, 2021. "The power of linear programming: some surprising and unexpected LPs," 4OR, Springer, vol. 19(1), pages 15-40, March.

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