One-class classification (OCC) aims to train a classifier solely on target data and attracts increasing attention due to its applicability in practice. Despite OCC has obtained many advances, 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 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 value. To address this issue, a smoother LBLSig loss is further proposed by utilizing a unilateral relaxation Sigmoid function. Experiments on different networks demonstrate the effectiveness of the proposed LBL and LBLSig. The source code can be found at https://github.com/ML-HDU/LBL_LBLSig.

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