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A Fractional Programming Framework for Support Vector Machine-type Formulations

Vovsha, Ilia

We develop a theoretical framework for relating various formulations of regularization problems through fractional programming. We focus on problems with objective functions of the type L + λ · P , where the parameter λ lacks intuitive interpretation. We observe that fractional programming is an elegant approach to obtain bounds on the range of the parameter, and then generalize this approach to show that different forms can be obtained from a common fractional program. Furthermore, we apply the proposed framework in two concrete settings; we consider support vector machines (SVMs), where the framework clarifies the relation between various existing soft-margin dual forms for classification, and the SVM+ algorithm (Vapnik and Vashist, 2009), where we use this methodology to derive a new dual formulation, and obtain bounds on the cost parameter.

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Academic Units
Center for Computational Learning Systems
Publisher
Center for Computational Learning Systems, Columbia University
Series
CCLS Technical Report, CCLS-14-02
Published Here
October 13, 2014
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