2025/01/25 by Pauline Bourigault, Bourigault, Pauline, Danilo P. Mandic +1
Computer Science · Engineering · Physics and Astronomy · #Anomaly Detection Techniques and Applications #FOS: Computer and information sciences #Fault Detection and Control Systems #Machine Learning (cs.LG) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2501.15265
openalex publication_date 2025/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a novel approach to anomaly detection by integrating Generalized Hyperbolic (GH) processes into kernel-based methods. The GH distribution, known for its flexibility in modeling skewness, heavy tails, and kurtosis, helps to capture complex patterns in data that deviate from Gaussian assumptions. We propose a GH-based kernel function and utilize it within Kernel Density Estimation (KDE) and One-Class Support Vector Machines (OCSVM) to develop anomaly detection frameworks. Theoretical results confirmed the positive semi-definiteness and consistency of the GH-based kernel, ensuring its suitability for machine learning applications. Empirical evaluation on synthetic and real-world datasets showed that our method improves detection performance in scenarios involving heavy-tailed and asymmetric or imbalanced distributions. https://github.com/paulinebourigault/GHKernelAnomalyDetect