One-class classification (OCC) aims to train a classifier only with the target class data and attracts great attention for its strong applicability in real-world application. Despite a lot of advances have been made in OCC, it still lacks the effective OCC loss functions for deep learning. In this paper, a novel logarithmic barrier function based OCC loss (LBL) that assigns large gradients to the margin samples and thus derives more compact hypersphere, is first proposed by approximating the OCC objective smoothly. But the optimization of LBL may be instability especially when samples lie on the boundary leading to the infinity loss. To address this issue, then, a unilateral relaxation Sigmoid function is introduced into LBL and a novel OCC loss named LBLSig is proposed. The LBLSig can be seen as the fusion of the mean square error (MSE) and the cross entropy (CE) and the optimization of LBLSig is smoother owing to the unilateral relaxation Sigmoid function. The effectiveness of the proposed LBL and LBLSig is experimentally demonstrated in comparisons with several state-of-the-art OCC algorithms on different network structures. The source code can be found at https://github.com/ML-HDU/LBL_LBLSig.

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