用自编码器+克里斯托弗尔函数,轻量高效检测高维异常。
CLOE: Christoffel Loss Autoencoder for Anomaly Detection

- 先降维再检测:在潜在空间用克里斯托弗尔函数做异常判定。
- 仅需调一个超参数,在多个高维数据集上表现最优。
- 自动设阈值,适合工业、医疗等需低维护的异常检测场景。
半监督异常检测在流程监控、医疗和金融等领域至关重要。然而,轻量级方法常难以处理高维数据,且需精细调参。现有基于克里斯托弗尔函数的方法虽只需单个超参数且理论基础扎实,但难以扩展至高维场景。本文提出CLOE,将自编码器用于降维,并在潜在空间应用克里斯托弗尔函数检测器。设计新型损失函数,利用克里斯托弗尔函数引导自编码器学习更贴近正常数据分布的支持表示。提出合理阈值设定方法与高效超参数调优策略。在多个高维表格型异常检测基准上,CLOE性能优于现有方法,同时保持轻量与低调参优势。
原文摘要 · Abstract (English)
Semi-supervised anomaly detection plays a key role in diverse fields such as process monitoring, healthcare, and finance. However, lightweight methods often struggle with high-dimensional data and typically require careful tuning of multiple hyperparameters. Among existing approaches, Christoffel Function--based methods are attractive due to their simplicity, requiring at most a single hyperparameter. They also benefit from a well-established theoretical foundation that yields several interesting results for data science. However, their main limitation is poor scalability to high-dimensional settings. In this paper, we introduce CLOE, a new method that combines an autoencoder for dimensionality reduction with a Christoffel Function--based detector applied in the latent space. To better align representation learning with anomaly detection, we design a novel loss function that leverages the Christoffel Function to guide the autoencoder toward representations that better capture the support of the normal data distribution. We further propose a principled procedure to set the detection threshold and an efficient strategy to tune the single remaining hyperparameter. Experiments on multiple high-dimensional tabular anomaly detection benchmarks demonstrate that CLOE achieves superior performance compared to existing methods, while preserving the lightweight and low-tuning advantages of Christoffel Function--based approaches.
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