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.

翻译：摘要：单类分类旨在仅使用目标类数据训练分类器，因其在现实应用中的强适用性而备受关注。尽管单类分类已取得诸多进展，但仍缺乏适用于深度学习的有效损失函数。本文通过平滑逼近单类分类目标，首次提出一种基于对数障碍函数的单类分类损失函数——LBL，该函数为边缘样本赋予大梯度，从而推导出更紧凑的超球体。然而，LBL的优化可能存在不稳定性，尤其是当样本位于边界时会导致无穷损失。为解决此问题，本文进一步引入单边松弛Sigmoid函数，并提出一种新型单类分类损失函数LBLSig。LBLSig可视为均方误差与交叉熵的融合，且由于单边松弛Sigmoid函数的作用，其优化过程更为平滑。通过在不同网络结构上与多种现有最优单类分类算法进行实验对比，验证了所提出的LBL和LBLSig的有效性。源代码可在https://github.com/ML-HDU/LBL_LBLSig获取。