Fast training of support vector machines using sequential minimal optimization
Advances in kernel methods
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
SMO algorithm for least-squares SVM formulations
Neural Computation
Improvements to Platt's SMO Algorithm for SVM Classifier Design
Neural Computation
Support vector machines for dyadic data
Neural Computation
LIBSVM: A library for support vector machines
ACM Transactions on Intelligent Systems and Technology (TIST)
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We describe a fast sequential minimal optimization (SMO) procedure for solving the dual optimization problem of the recently proposed potential support vector machine (P-SVM). The new SMO consists of a sequence of iteration steps in which the Lagrangian is optimized with respect to either one (single SMO) or two (dual SMO) of the Lagrange multipliers while keeping the other variables fixed. An efficient selection procedure for Lagrange multipliers is given, and two heuristics for improving the SMO procedure are described: block optimization and annealing of the regularization parameter ε. A comparison of the variants shows that the dual SMO, including block optimization and annealing, performs efficiently in terms of computation time. In contrast to standard support vector machines (SVMs), the P-SVM is applicable to arbitrary dyadic data sets, but benchmarks are provided against libSVM's ε-SVR and C-SVC implementations for problems that are also solvable by standard SVM methods. For those problems, computation time of the P-SVM is comparable to or somewhat higher than the standard SVM. The number of support vectors found by the P-SVM is usually much smaller for the same generalization performance.