Abstract
This chapter discussed the formulation of multiple criteria programming. In linear discriminate analysis, data separation can be achieved by two opposite objectives. The first objective separates the observations by minimizing the sum of the deviations (MSD) among the observations. The second maximizes the minimum distances (MMD) of observations from the critical value. According to the concept of Pareto optimality, we can seek the best tradeoff of the two measurements by Multiple Criteria Linear Programming (MCLP) model, which is similar to the Support Vector Machine model, addresses more control parameters than the Support Vector Machine, and provides more flexibility for better separation of data under the framework of the mathematical programming. Then MCLP models for multiple classes and unbalanced training set are constructed separately. Furthermore, in order to ensure the existence of solution, we add regularization terms in the objective function of MCLP, and constructed regularized MCLP (RMCLP) model.
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© 2011 Springer-Verlag London Limited
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Shi, Y., Tian, Y., Kou, G., Peng, Y., Li, J. (2011). Multiple Criteria Linear Programming. In: Optimization Based Data Mining: Theory and Applications. Advanced Information and Knowledge Processing. Springer, London. https://doi.org/10.1007/978-0-85729-504-0_7
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DOI: https://doi.org/10.1007/978-0-85729-504-0_7
Publisher Name: Springer, London
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