CLOE: Christoffel Loss Autoencoder for Anomaly Detection

arXiv cs.LG Papers

Summary

CLOE is a new semi-supervised anomaly detection method combining an autoencoder with a Christoffel Function-based detector, using a novel loss function to improve representation learning. It achieves state-of-the-art results on high-dimensional tabular data while maintaining simplicity.

arXiv:2607.20530v1 Announce Type: new 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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# CLOE: Christoffel Loss Autoencoder for Anomaly Detection
Source: [https://arxiv.org/abs/2607.20530](https://arxiv.org/abs/2607.20530)
[View PDF](https://arxiv.org/pdf/2607.20530)

> 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\.

## Submission history

From: Lea Billet \[[view email](https://arxiv.org/show-email/1bd5e380/2607.20530)\] \[via CCSD proxy\] **\[v1\]**Fri, 10 Jul 2026 11:58:45 UTC \(734 KB\)

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