CLOE: Christoffel Loss Autoencoder for Anomaly Detection

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.