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.
CLOE Method
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.
Furthermore, we 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.
Blogger's Review: The CLOE method effectively addresses the scalability issue in high-dimensional anomaly detection by combining autoencoders with Christoffel functions. The novel loss function provides stronger guidance for model training, making it a promising approach worthy of further exploration and validation in practical applications.