Kernel-Based Anomaly Detection Using Generalized Hyperbolic Processes

Pauline Bourigault; Danilo P. Mandic

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arXiv · 2501.15265

Kernel-Based Anomaly Detection Using Generalized Hyperbolic Processes

Pauline Bourigault·Danilo P. Mandic

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Abstract

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

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Pauline Bourigault, Danilo P. Mandic. 2025-01-25. Kernel-Based Anomaly Detection Using Generalized Hyperbolic Processes. https://arxiv.org/abs/2501.15265

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