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Linear Programming Approaches for Multiple-Class Discriminant and Classification Analysis

Linear Programming Approaches for Multiple-Class Discriminant and Classification Analysis

Minghe Sun
Copyright: © 2010 |Volume: 1 |Issue: 1 |Pages: 24
ISSN: 1947-8569|EISSN: 1947-8577|ISSN: 1947-8569|EISBN13: 9781616929992|EISSN: 1947-8577|DOI: 10.4018/jsds.2010103004
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MLA

Sun, Minghe. "Linear Programming Approaches for Multiple-Class Discriminant and Classification Analysis." IJSDS vol.1, no.1 2010: pp.57-80. http://doi.org/10.4018/jsds.2010103004

APA

Sun, M. (2010). Linear Programming Approaches for Multiple-Class Discriminant and Classification Analysis. International Journal of Strategic Decision Sciences (IJSDS), 1(1), 57-80. http://doi.org/10.4018/jsds.2010103004

Chicago

Sun, Minghe. "Linear Programming Approaches for Multiple-Class Discriminant and Classification Analysis," International Journal of Strategic Decision Sciences (IJSDS) 1, no.1: 57-80. http://doi.org/10.4018/jsds.2010103004

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Abstract

New linear programming approaches are proposed as nonparametric procedures for multiple-class discriminant and classification analysis. A new MSD model minimizing the sum of the classification errors is formulated to construct discriminant functions. This model has desirable properties because it is versatile and is immune to the pathologies of some of the earlier mathematical programming models for two-class classification. It is also purely systematic and algorithmic and no user ad hoc and trial judgment is required. Furthermore, it can be used as the basis to develop other models, such as a multiple-class support vector machine and a mixed integer programming model, for discrimination and classification. A MMD model minimizing the maximum of the classification errors, although with very limited use, is also studied. These models may also be considered as generalizations of mathematical programming formulations for two-class classification. By the same approach, other mathematical programming formulations for two-class classification can be easily generalized to multiple-class formulations. Results on standard as well as randomly generated test datasets show that the MSD model is very effective in generating powerful discriminant functions.

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