Unsupervised Support Vector Machines with Perturbations

Support vector machines (SVMs) have been dominant learning techniques for almost ten years, and mostly applied to supervised learning problems. Recently nice results are obtained by two-class unsupervised and semi-supervised classification algorithms where the optimization problems based on bounded C-SVMs, bounded v-SVMs and Lagrangian SVMs respectively are relaxed to semi-definite programming (SDP). These support vector methods implicitly assume that training data in the optimization problems are known exactly. But in practice, the training data are usually subjected to measurement noise. Zhao et al proposed robust version to unsupervised and semi-supervised classification problems based on Bounded C-SVMs, which need to find the dual problem twice. In this paper we propose unsupervised classification algorithm based on primal problem of standard SVMs with perturbations, which directly relaxes it with label variables to a semi-definite programming. Numerical results confirm the robustness of the proposed method.