# LBL: Logarithmic Barrier Loss Function for One-class Classification

arXiv: https://arxiv.org/abs/2307.10753 · HTML: https://mlsanity.com/paper/2307.10753/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 48 references that are in the map.
- First posted on arXiv 20 Jul 2023.

## Builds on (most cited first, 19 of 19)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery](https://mlsanity.com/paper/1703.05921/) (2017)
- [Memorizing Normality to Detect Anomaly: Memory-augmented Deep Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/1904.02639/) (2019)
- [CFLOW-AD: Real-Time Unsupervised Anomaly Detection with Localization via Conditional Normalizing Flows](https://mlsanity.com/paper/2107.12571/) (2021)
- [Deep Anomaly Detection Using Geometric Transformations](https://mlsanity.com/paper/1805.10917/) (2018)
- [Adversarially Learned One-Class Classifier for Novelty Detection](https://mlsanity.com/paper/1802.09088/) (2018)
- [OCGAN: One-class Novelty Detection Using GANs with Constrained Latent Representations](https://mlsanity.com/paper/1903.08550/) (2019)
- [PANDA: Adapting Pretrained Features for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2010.05903/) (2020)
- [Latent Space Autoregression for Novelty Detection](https://mlsanity.com/paper/1807.01653/) (2018)
- [Old is Gold: Redefining the Adversarially Learned One-Class Classifier Training Paradigm](https://mlsanity.com/paper/2004.07657/) (2020)
- [Generative Probabilistic Novelty Detection with Adversarial Autoencoders](https://mlsanity.com/paper/1807.02588/) (2018)
- [Learning Deep Representations of Appearance and Motion for Anomalous Event Detection](https://mlsanity.com/paper/1510.01553/) (2015)
- [GODS: Generalized One-class Discriminative Subspaces for Anomaly Detection](https://mlsanity.com/paper/1908.05884/) (2019)
- [Improving Pairwise Ranking for Multi-label Image Classification](https://mlsanity.com/paper/1704.03135/) (2017)
- [MOCCA: Multi-Layer One-Class ClassificAtion for Anomaly Detection](https://mlsanity.com/paper/2012.12111/) (2020)
- [Transformaly -- Two (Feature Spaces) Are Better Than One](https://mlsanity.com/paper/2112.04185/) (2021)
- [adVAE: A self-adversarial variational autoencoder with Gaussian anomaly prior knowledge for anomaly detection](https://mlsanity.com/paper/1903.00904/) (2019)

## Abstract (arXiv)

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 popular OCC algorithms on different network structures. The source code can be found at https://github.com/ML-HDU/LBL_LBLSig.