Robust Unsupervised and Semisupervised Bounded C-Support Vector Machines

Support Vector Machines (SVMs) have been dominant learning techniques for almost ten years, and mostly ap- plied to supervised learning problems. Recently two-class unsupervised and semi-supervised classification algorithms based on Bounded C-SVMs, Bounded -SVMs and La- grangian SVMs (LSVMs) respectively, which are relaxed to Semi-definite Programming (SDP), get good classifica- tion results. These support vector methods implicitly as- sume that training data in the optimization problems to be known exactly. But in practice, the training data are usually subjected to measurement noise. In this paper we proposed robust version to unsupervised and semi-supervised classifi- cation problems based on Bounded C-Support Vector Ma- chines, which trained by convex relaxation of the training criterion: find a labeling that yield a maximum margin on the training data with perturbations. But the problem has difficulty to compute, we will find its semi-definite relaxation that can approximate it well. Numerical results confirm the robustness of the proposed method. Keywords: Bounded Support Vector Machines, Semi- definite Programming, unsupervised learning, semi- supervised learning, robust