  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.
