基于几何熵最小化的在线非参数异常检测
Online Nonparametric Anomaly Detection based on Geometric Entropy Minimization
摘要：
我们考虑在线和非参数检测突然和持续的异常，例如由于异常事件（例如，故障、恶意活动）。结合简单的非参数几何熵最小化（GEM）的方法与及时检测能力的累积和（Cumulative Sum）算法，我们提出了一种计算效率高的在线异常检测方法，适用于高维数据集，并在同一时间实现了一个接近最佳的平均检测延迟性能为给定的虚警约束。我们提供了新的见解，GEM和EQUUM，包括新的渐近分析GEM，使软决策离群值检测，和一个新的解释EQUUM的差异理论，这有助于我们推广到非参数GEM统计。我们数值计算表明，使用模拟和真实的数据集，所提出的非参数算法达到了接近的性能千里眼参数的CRAMUM测试。
英文摘要：
We consider the online and nonparametric detection of abrupt and persistent anomalies, such as a change in the regular system dynamics at a time instance due to an anomalous event (e.g., a failure, a malicious activity). Combining the simplicity of the nonparametric Geometric Entropy Minimization (GEM) method with the timely detection capability of the Cumulative Sum (CUSUM) algorithm we propose a computationally efficient online anomaly detection method that is applicable to high-dimensional datasets, and at the same time achieve a near-optimum average detection delay performance for a given false alarm constraint. We provide new insights to both GEM and CUSUM, including new asymptotic analysis for GEM, which enables soft decisions for outlier detection, and a novel interpretation of CUSUM in terms of the discrepancy theory, which helps us generalize it to the nonparametric GEM statistic. We numerically show, using both simulated and real datasets, that the proposed nonparametric algorithm attains a close performance to the clairvoyant parametric CUSUM test.
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