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An SMO Algorithm for the Potential Support VectorMachine

tk{at}cs.tu-berlin.de Neural Information Processing Group, Fakultät IV, Technische Universität Berlin, 10587 Berlin, Germany

Sepp Hochreiter

hochreit{at}bioinf.jku.at Institute of Bioinformatics, Johannes Kepler University Linz, 4040 Linz, Austria

Klaus Obermayer

oby{at}cs.tu-berlin.de Neural Information Processing Group, Fakultät IV and Bernstein Center for Computational Neuroscience, Technische Universität Berlin, 10587 Berlin, Germany

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 . 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 -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.