A training algorithm for optimal margin classifiers
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Making large-scale support vector machine learning practical
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Fast training of support vector machines using sequential minimal optimization
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A Simple Decomposition Method for Support Vector Machines
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CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
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Improvements to Platt's SMO Algorithm for SVM Classifier Design
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LIBSVM: A library for support vector machines
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Successive overrelaxation for support vector machines
IEEE Transactions on Neural Networks
The analysis of decomposition methods for support vector machines
IEEE Transactions on Neural Networks
Improvements to the SMO algorithm for SVM regression
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On the convergence of the decomposition method for support vector machines
IEEE Transactions on Neural Networks
Asymptotic convergence of an SMO algorithm without any assumptions
IEEE Transactions on Neural Networks
A formal analysis of stopping criteria of decomposition methods for support vector machines
IEEE Transactions on Neural Networks
A study on SMO-type decomposition methods for support vector machines
IEEE Transactions on Neural Networks
QP Algorithms with Guaranteed Accuracy and Run Time for Support Vector Machines
The Journal of Machine Learning Research
Maximum-Gain Working Set Selection for SVMs
The Journal of Machine Learning Research
On the complexity of working set selection
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Gaps in support vector optimization
COLT'07 Proceedings of the 20th annual conference on Learning theory
Computational Optimization and Applications
The Journal of Machine Learning Research
Computational Optimization and Applications
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We present a general decomposition algorithm that is uniformly applicable to every (suitably normalized) instance of Convex Quadratic Optimization and efficiently approaches the optimal solution. The number of iterations required to be within ε of optimality grows linearly with 1/ε and quadratically with the number m of variables. The working set selection can be performed in polynomial time. If we restrict our considerations to instances of Convex Quadratic Optimization with at most k0 equality constraints for some fixed constant k0 plus some so-called box-constraints (conditions that hold for most variants of SVM-optimization), the working set is found in linear time. Our analysis builds on a generalization of the concept of rate certifying pairs that was introduced by Hush and Scovel. In order to extend their results to arbitrary instances of Convex Quadratic Optimization, we introduce the general notion of a rate certifying q-set. We improve on the results of Hush and Scovel [8] in several ways. First our result holds for Convex Quadratic Optimization whereas the results of Hush and Scovel are specialized to SVM-optimization. Second, we achieve a higher rate of convergence even for the special case of SVM-optimization (despite the generality of our approach). Third, our analysis is technically simpler.