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2011 | OriginalPaper | Buchkapitel

5. Robust Support Vector Machines

verfasst von : Yong Shi, Yingjie Tian, Gang Kou, Yi Peng, Jianping Li

Erschienen in: Optimization Based Data Mining: Theory and Applications

Verlag: Springer London

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Abstract

In real world applications, the training data are not usually assumed to be known exactly due to measurement and statistical errors. Since the solutions to optimization problems are typically sensitive to training data perturbations, errors in the input data tend to get amplified in the decision function, often resulting in far from optimal solutions. So it will be useful to explore formulations that can yield robust discriminants to such estimation errors. In this chapter, we first established robust versions of SVORM, which are represented as a second order cone programming (SOCP). And as the theoretical foundation, we study the relationship between the solutions of the SOCP and its dual problem. Here the second order cone in Hilbert space is involved. Then, we also establish a multi-class algorithm based on the above robust SVORM for general multi-class classification problem with perturbations. Furthermore, we construct a robust unsupervised and semi-supervised SVC for the problems with uncertainty information.

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Vorheriges Kapitel Unsupervised and Semi-supervised Support Vector Machines

Nächstes Kapitel Feature Selection via l p -Norm Support Vector Machines

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Titel: Robust Support Vector Machines
verfasst von: Yong Shi
Yingjie Tian
Gang Kou
Yi Peng
Jianping Li
Verlag: Springer London
Buch: Optimization Based Data Mining: Theory and Applications
Print ISBN: 978-0-85729-503-3

Electronic ISBN: 978-0-85729-504-0

Copyright-Jahr: 2011
DOI: https://doi.org/10.1007/978-0-85729-504-0_5

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