Kernel-Based Anomaly Detection Using Generalized Hyperbolic Processes

TL;DR

This paper introduces a new kernel function based on Generalized Hyperbolic processes for anomaly detection, enhancing detection of complex, heavy-tailed, and skewed data distributions in machine learning applications.

Contribution

It develops a GH-based kernel for KDE and OCSVM, with proven theoretical properties, and demonstrates improved anomaly detection performance on various datasets.

Findings

Improved detection of heavy-tailed and skewed anomalies

The GH kernel is positive semi-definite and consistent

Enhanced performance over traditional Gaussian-based methods

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