Mathematics of Operations Research
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
A Tutorial on Support Vector Machines for Pattern Recognition
Data Mining and Knowledge Discovery
Relationship between support vector set and kernel functions in SVM
Journal of Computer Science and Technology
A robust minimax approach to classification
The Journal of Machine Learning Research
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
Multiple kernel learning, conic duality, and the SMO algorithm
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Learning the Kernel with Hyperkernels
The Journal of Machine Learning Research
Large Scale Multiple Kernel Learning
The Journal of Machine Learning Research
More efficiency in multiple kernel learning
Proceedings of the 24th international conference on Machine learning
More generality in efficient multiple kernel learning
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Efficient hyperkernel learning using second-order cone programming
IEEE Transactions on Neural Networks
Learning kernels with upper bounds of leave-one-out error
Proceedings of the 20th ACM international conference on Information and knowledge management
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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.