Optimal Hyperplane Classi er with Adaptive Norm

The conventional optimal hyperplane classi er is de ned on Euclidean space where the norm is given a priori. In this paper, we propose a new optimal hyperplane classi er in which the norm also adapts for learning. For practical implementation, the norm is restricted to a weighted Euclidean norm and the weights are controlled in learning. The statistical properties of this classi er is analyzed via the generalization bound characterized by entropy numbers. An iterative training algorithm is designed to minimize the generalization bound while keeping the complete separation of training samples. As a result of online character recognition experiments, the optimal hyperplane classi er with adaptive norm outperformed the conventional one.