Anomaly Detection in Streaming Nonstationary Temporal Data

This article proposes a framework that provides early detection of anomalous series within a large collection of nonstationary streaming time-series data. We define an anomaly as an observation, that is, very unlikely given the recent distribution of a given system. The proposed framework first calculates a boundary for the system’s typical behavior using extreme value theory. Then a sliding window is used to test for anomalous series within a newly arrived collection of series. The model uses time series features as inputs, and a density-based comparison to detect any significant changes in the distribution of the features. Using various synthetic and real world datasets, we demonstrate the wide applicability and usefulness of our proposed framework. We show that the proposed algorithm can work well in the presence of noisy nonstationarity data within multiple classes of time series. This framework is implemented in the open source R package <i>oddstream</i>. R code and data are available in the online supplementary materials.

本文提出一种可对大规模非平稳流式时序数据集中的异常序列开展早期检测的框架。我们将异常定义为观测值，具体而言，基于给定系统的近期分布判断，该观测值出现的概率极低。所提框架首先借助极值理论（Extreme Value Theory）计算系统正常行为的边界，随后利用滑动窗口对新抵达的序列集中的异常序列进行检测。本模型以时序特征作为输入，并采用基于密度的对比方法识别特征分布中的显著变化。通过多组合成数据集与真实世界数据集，我们验证了所提框架广泛的适用性与实用价值。实验结果表明，所提算法在多类时序数据的含噪非平稳场景下仍可保持优异性能。本框架已在开源R语言包`oddstream`中实现，相关R代码与数据集可在在线补充材料中获取。