CLOE: Christoffel Loss Autoencoder for Anomaly Detection

• URL: http://arxiv.org/abs/2607.20530v1
• Date: Fri, 10 Jul 2026 11:58:45 GMT
• Title: CLOE: Christoffel Loss Autoencoder for Anomaly Detection
• Abstract summary: Semi-supervised anomaly detection plays a key role in diverse fields such as process monitoring, healthcare, and finance.<n>CloE is a new method that combines an autoencoder for dimensionality reduction with a Christoffel Function--based detector applied in the latent space.
• Score: 39.51104389161474
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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