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A Fractional Programming Framework for Support Vector Machine-type Formulations

Ilia Vovsha

Title:
A Fractional Programming Framework for Support Vector Machine-type Formulations
Author(s):
Vovsha, Ilia
Date:
Type:
Reports
Department(s):
Center for Computational Learning Systems
Persistent URL:
Series:
CCLS Technical Report
Part Number:
CCLS-14-02
Publisher:
Center for Computational Learning Systems, Columbia University
Publisher Location:
New York
Abstract:
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.
Subject(s):
Computer science
Item views
164
Metadata:
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Suggested Citation:
Ilia Vovsha, , A Fractional Programming Framework for Support Vector Machine-type Formulations, Columbia University Academic Commons, .

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