基于广义双曲过程的核异常检测
Kernel-Based Anomaly Detection Using Generalized Hyperbolic Processes
AI总结：
本文提出将广义双曲过程整合到基于核的方法中用于异常检测，设计了基于GH的核函数并应用于KDE和OCSVM构建检测框架，在重尾和不平衡数据分布场景下有效提升了检测性能。
摘要：
我们提出了一种异常检测的新方法，将广义双曲（GH）过程整合到基于核的方法中。GH分布以其在建模偏度、重尾和峰度方面的灵活性而闻名，有助于捕捉偏离高斯假设的数据中的复杂模式。我们提出了一种基于GH的核函数，并将其应用于核密度估计（KDE）和单类支持向量机（OCSVM）中，以构建异常检测框架。理论结果证实了基于GH的核的半正定性和一致性，确保了其在机器学习应用中的适用性。在合成和真实数据集上的实证评估表明，在涉及重尾和不对称或不平衡分布的场景中，我们的方法提升了检测性能。
英文摘要：
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
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
