2-Sided Best Fitting Hyperplane Classifier

In this paper, we propose a novel method that is more appropriate than classical large-margin classifiers for open set recognition and object detection problems. The proposed method uses the best fitting hyper planes approach, and the main idea is to find the best fitting hyper planes such that each hyper plane is close to the samples of one of the two classes and as far as possible from the other class samples. As opposed to the most common hyper plane fitting classifiers in the literature, the proposed classifier allows the negative samples to lie on both sides of the fitting hyper plane and hence it is based on a non-convex optimization problem. We use concave-convex procedure to solve this non-convex problem. Then, the method is extended to the nonlinear case by using the kernel trick. The proposed method is also suitable for large-scale problems, and it returns sparse solutions in contrast to the other hyper plane fitting methods in the literature. The experiments on several databases show that our proposed method typically outperforms other hyper plane fitting classifiers in term of classification accuracy, and it performs as good as the SVM classifier if not any better.