用广义双曲分布构建新核函数，提升复杂数据的异常检测能力。
Kernel-Based Anomaly Detection Using Generalized Hyperbolic Processes
- 基于广义双曲分布设计新型核函数，适应非高斯数据分布。
- 在重尾、偏态和不平衡数据上，检测准确率显著优于传统方法。
- 适合金融风控、工业监测等复杂分布场景的异常发现。
我们提出一种将广义双曲（GH）过程融入核方法的新型异常检测框架。GH分布具有建模偏度、重尾和峰度的灵活性，能捕捉偏离高斯假设的复杂数据模式。本文设计了基于GH分布的核函数，并应用于核密度估计（KDE）和一类支持向量机（OCSVM），构建异常检测模型。理论分析证明该核函数具有半正定性和一致性，适用于机器学习任务。在合成数据与真实世界数据集上的实验表明，该方法在重尾、偏态或分布不均衡的场景下显著提升了异常检测性能。
原文摘要 · Abstract (English)
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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