Machine Learning
Making large-scale support vector machine learning practical
Advances in kernel methods
Fast training of support vector machines using sequential minimal optimization
Advances in kernel methods
Optimization Software Guide
A Tutorial on Support Vector Machines for Pattern Recognition
Data Mining and Knowledge Discovery
Lagrangian support vector machines
The Journal of Machine Learning Research
Estimation of Dependences Based on Empirical Data: Springer Series in Statistics (Springer Series in Statistics)
Improvements to Platt's SMO Algorithm for SVM Classifier Design
Neural Computation
Working Set Selection Using Second Order Information for Training Support Vector Machines
The Journal of Machine Learning Research
Maximum-Gain Working Set Selection for SVMs
The Journal of Machine Learning Research
Nonlinear Optimization
A study of cross-validation and bootstrap for accuracy estimation and model selection
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Asymptotic convergence of an SMO algorithm without any assumptions
IEEE Transactions on Neural Networks
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The Sequential Minimal Optimization (SMO) algorithm is known to be one of the most efficient solutions for the Support Vector Machine training phase. It solves a quadratic programming (QP) problem by optimizing a set of coefficients whose size is the number of training examples. However, its execution time may be quite long due to its computational complexity: the algorithm executes many calculations per iteration as well as many iterations until a stop criterion is satisfied. Due to its importance, many improvements have been proposed in order to obtain faster solutions. These improvements keep unchanged the SMO basic characteristic: the optimization is always performed on one pair of coefficients per iteration. This paper presents the Multiple Pairs SMO (MP-SMO), a new solution for the SMO algorithm that consists of optimizing more than one pair of coefficients per iteration. We show that this algorithm improves the performance results obtained by other known SMO solutions. Our algorithm presents the following characteristics: a) it uses the previously adopted analytical solution; b) its working set selection heuristic has been adapted from known solutions in order to deal with multiple pairs; c) the monotonic convergence of the algorithm has been demonstrated. We applied our MP-SMO algorithm to a set of known benchmarks. We tested the algorithm optimizing two, three and four pairs per iteration. We always obtained better results than the original one pair SMO algorithm.