Branch and Bound for Semi-Supervised Support Vector Machines

Part of Advances in Neural Information Processing Systems 19 (NIPS 2006)

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Olivier Chapelle, Vikas Sindhwani, S. Keerthi


Semi-supervised SVMs (S3 VM) attempt to learn low-density separators by maximizing the margin over labeled and unlabeled examples. The associated optimization problem is non-convex. To examine the full potential of S3 VMs modulo local minima problems in current implementations, we apply branch and bound techniques for obtaining exact, global ly optimal solutions. Empirical evidence suggests that the globally optimal solution can return excellent generalization performance in situations where other implementations fail completely. While our current implementation is only applicable to small datasets, we discuss variants that can potentially lead to practically useful algorithms.