Knowledge-based Support Vector Machine Classifiers via Nearest Points

Prior knowledge in the form of multiple polyhedral sets or more general nonlinear sets was incorporated into Support Vector Machines (SVMs) as linear constraints in a linear programming by Mangasarian and his co-worker. However, these methods lead to rather complex optimization problems that require fairly sophisticated convex optimization tools, which can be a barrier for practitioners. In this paper we introduce a simple and practical method to incorporate prior knowledge in support vector machines. After transforming the prior knowledge into lots of boundary points by computing the shortest distances between the original training points and the knowledge sets, we get an augmented training set therefore standard SVMs and existing powerful SVM tools can be used directly to obtain the solution fast and exactly. Numerical experiments show the effectiveness of the proposed approach.