Learning with Uncertain Kernel Matrix Set |
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Authors: | Lei Jia Shi-Zhong Liao Li-Zhong Ding |
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Affiliation: | 1.School of Computer Science and Technology,Tianjin University,Tianjin,China |
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Abstract: | We study support vector machines (SVM) for which the kernel matrix is not specified exactly and it is only known to belong
to a given uncertainty set. We consider uncertainties that arise from two sources: (i) data measurement uncertainty, which
stems from the statistical errors of input samples; (ii) kernel combination uncertainty, which stems from the weight of individual
kernel that needs to be optimized in multiple kernel learning (MKL) problem. Much work has been studied, such as uncertainty
sets that allow the corresponding SVMs to be reformulated as semi-definite programs (SDPs), which is very computationally
expensive however. Our focus in this paper is to identify uncertainty sets that allow the corresponding SVMs to be reformulated
as second-order cone programs (SOCPs), since both the worst case complexity and practical computational effort required to
solve SOCPs is at least an order of magnitude less than that needed to solve SDPs of comparable size. In the main part of
the paper we propose four uncertainty sets that meet this criterion. Experimental results are presented to confirm the validity
of these SOCP reformulations. |
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