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Dimensionality representation of linear discriminant function space for the multiple-group problem: An MIP approach

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  • Robert Pavur

Abstract

This paper proposes a new mathematical programming approach to represent the dimensions of the discriminant space for the multiple-group classification problem. Few papers have investigated generalizations of two-group mathematical programming approaches for the classification of multiple groups. While several papers have proposed mathematical programming models for separating groups of observations, the issue of considering the classification problem by finding discriminant linear functions to describe the groups in fewer dimensions has not been addressed. The new mathematical programming approach proposed in this paper first solves the multiple-group problem using a single discriminant function, which essentially represents the separation of the groups in one dimension. Then the multiple-group problem is successively solved using single discriminant functions with the requirement that successive linear discriminant functions have a sample covariance equal to zero. An algorithm is proposed to classify observations from multiple groups using the linear discriminant functions from the mathematical programming approach in a reduced number of dimensions. Copyright Kluwer Academic Publishers 1997

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  • Robert Pavur, 1997. "Dimensionality representation of linear discriminant function space for the multiple-group problem: An MIP approach," Annals of Operations Research, Springer, vol. 74(0), pages 37-50, November.
    • Handle: RePEc:spr:annopr:v:74:y:1997:i:0:p:37-50:10.1023/a:1018938925084
    DOI: 10.1023/A:1018938925084
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    Cited by:

    1. Mingue Sun, 2009. "Liquidity Risk and Financial Competition: A Mixed Integer Programming Model for Multiple-Class Discriminant Analysis," Working Papers 0102, College of Business, University of Texas at San Antonio.
    2. Mingue Sun, 2009. "Liquidity Risk and Financial Competition: A Mixed Integer Programming Model for Multiple-Class Discriminant Analysis," Working Papers 0102, College of Business, University of Texas at San Antonio.

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