Robust Solutions to Least-Squares Problems with Uncertain Data
SIAM Journal on Matrix Analysis and Applications
Mathematics of Operations Research
Clustering Algorithms
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Robust Solutions to Uncertain Semidefinite Programs
SIAM Journal on Optimization
Lagrangian support vector machines
The Journal of Machine Learning Research
Operations Research
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
Unsupervised and Semi-Supervised Two-class Support Vector Machines
ICDMW '06 Proceedings of the Sixth IEEE International Conference on Data Mining - Workshops
Robust Unsupervised and Semisupervised Bounded C-Support Vector Machines
ICDMW '07 Proceedings of the Seventh IEEE International Conference on Data Mining Workshops
Unsupervised and Semi-supervised Lagrangian Support Vector Machines
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part III: ICCS 2007
Robust solutions of uncertain linear programs
Operations Research Letters
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Support Vector Machines (SVMs) have been dominant learning techniques for more than ten years, and mostly applied to supervised learning problems. These years two-class unsupervised and semi-supervised classification algorithms based on Bounded C-SVMs, Bounded ν-SVMs and Lagrangian SVMs (LSVMs) respectively, which are relaxed to Semi-definite Programming (SDP), get good classification results. These support vector methods implicitly assume that training data in the optimization problems to be known exactly. But in practice, the training data are usually subjected to measurement noise. Zhao et al proposed robust version to Bounded C- SVMs, Bounded ν-SVMs and Lagrangian SVMs (LSVMs) respectively with perturbations in convex polyhedrons and ellipsoids. The region of perturbation in the methods mentioned above is not general, and there are many perturbations in non-convex regions in practice. Therefore we proposed unsupervised and semi-supervised classification problems based on Lagrangian Support Vector Machines with general polyhedral perturbations. But the problem has difficulty to compute, we will find its semidefinite relaxation that can approximate it well. Numerical results confirm the robustness of the proposed method.