In this paper, we propose an optimal rejection method for rejecting ambiguous samples by a rejection function. This rejection function is trained together with a classification function under the framework of Learning-with-Rejection (LwR). The highlights of LwR are: (1) the rejection strategy is not heuristic but has a strong background from a machine learning theory, and (2) the rejection function can be trained on an arbitrary feature space which is different from the feature space for classification. The latter suggests we can choose a feature space that is more suitable for rejection. Although the past research on LwR focused only on its theoretical aspect, we propose to utilize LwR for practical pattern classification tasks. Moreover, we propose to use features from different CNN layers for classification and rejection. Our extensive experiments of notMNIST classification and character/non-character classification demonstrate that the proposed method achieves better performance than traditional rejection strategies.
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