CLOE：用于异常检测的克里斯托费尔损失自动编码器
CLOE: Christoffel Loss Autoencoder for Anomaly Detection
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中文总结 AI 辅助
研究高维数据半监督异常检测问题，核心方法是结合自动编码器与基于克里斯托费尔函数的检测器，设计新损失函数并提出相关策略。主要贡献是CLOE性能卓越，兼具轻量级和低调整优势。
中文摘要 AI 辅助
半监督异常检测在过程监控、医疗保健和金融等多个领域起着关键作用。然而，轻量级方法在处理高维数据时往往存在困难，并且通常需要仔细调整多个超参数。在现有方法中，基于克里斯托费尔函数的方法因其简单性而具有吸引力，最多只需一个超参数，且有完善的理论基础。但它们在高维设置下的扩展性较差。本文介绍了CLOE，一种将用于降维的自动编码器与在潜在空间中应用的基于克里斯托费尔函数的检测器相结合的新方法。为使表示学习与异常检测更好地对齐，设计了一种新颖的损失函数，利用克里斯托费尔函数引导自动编码器获得能更好捕捉正常数据分布支持的表示。还提出了设定检测阈值的原则性程序和调整剩余单个超参数的有效策略。在多个高维表格异常检测基准上的实验表明，CLOE与现有方法相比具有卓越性能，同时保留了基于克里斯托费尔函数方法的轻量级和低调整优势。
英文摘要
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.
