Exploring the trade-off between generalization and empirical errors in a one-norm SVM

Haldun Aytug and Serpil Sayın

European Journal of Operational Research, 2012, vol. 218, issue 3, 667-675

Abstract: We propose a one-norm support vector machine (SVM) formulation as an alternative to the well-known formulation that uses parameter C in order to balance the two inherent objective functions of the problem. Our formulation is motivated by the ϵ-constraint approach that is used in bicriteria optimization and we propose expressing the objective of minimizing total empirical error as a constraint with a parametric right-hand-side. Using dual variables we show equivalence of this formulation to the one with the trade-off parameter. We propose an algorithm that enumerates the entire efficient frontier by systematically changing the right-hand-side parameter. We discuss the results of a detailed computational analysis that portrays the structure of the efficient frontier as well as the computational burden associated with finding it. Our results indicate that the computational effort for obtaining the efficient frontier grows linearly in problem size, and the benefit in terms of classifier performance is almost always substantial when compared to a single run of the corresponding SVM. In addition, both the run time and accuracy compare favorably to other methods that search part or all of the regularization path of SVM.

Keywords: Data mining; Multiple objective programming; Support vector machines; One-norm; Regularization path (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:218:y:2012:i:3:p:667-675

DOI: 10.1016/j.ejor.2011.11.037

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