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 hyperplanes approach, and the main idea is to find the best fitting hyperplanes such that each hyperplane 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 hyperplane fitting classifiers in the literature, the

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... posed classifier allows the negative samples to lie on both sides of the fitting hyperplane and hence it is based on a nonconvex 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 hyperplane fitting methods in the literature. The experiments on several databases show that our proposed method typically outperforms other hyperplane fitting classifiers in term of classification accuracy, and it performs as good as the SVM classifier if not any better.