On the optimal solution of primal optimization problem of one-class SVM

One-class SVM, which is a good machine learning method, has recently attracted wide interest. In this paper, we focus on the properties of the optimal solution to its primal optimization problem. We first prove that the optimal solution with respect to the normal vector of the hyperplane is unique, and then present and prove the necessary and sufficient conditions for the case where the optimal solution with respect to the bias of the hyperplane is not unique. At last, we present a method to compute the bias in the case where the optimal solution with respect to the bias is not unique.