非平稳性存在下主成分对系统变化的敏感性
Sensitivity of principal components to system changes in the presence of non-stationarity
AI总结：
本文研究非平稳性对主成分变化检测敏感性的影响，提出多正常状态模型，通过蒙特卡罗模拟证明利用非平稳性知识可显著提升检测性能，并在真实交通数据中验证。
摘要：
非平稳性影响由一组可测量变量描述的关联系统中变化检测的敏感性。我们通过投影到不同的主成分上来研究这一点。非平稳性被建模为在变化发生之前系统中就存在的多个正常状态。所研究的变化发生在变量的均值、标准差或相关性中。执行蒙特卡罗模拟以测试在有无关于非平稳性的知识的情况下，针对不同系统维度和正常状态数量的变化检测敏感性。比较清楚地表明，关于系统非平稳性的知识极大地提高了所有主成分的变化检测敏感性。这种改进对于那些在平稳情况下已经提供最大变化检测可能性的成分最为显著。我们用一个使用真实交通流数据的示例来说明我们的结果，在该示例中，我们将周末和银行假日开始检测为异常。
英文摘要：
Non-stationarity affects the sensitivity of change detection in correlated systems described by sets of measurable variables. We study this by projecting onto different principal components. Non-stationarity is modeled as multiple normal states that exist in the system even before a change occurs. The studied changes occur in mean values, standard deviations or correlations of the variables. Monte Carlo simulations are performed to test the sensitivity for change detection with and without knowledge about the non-stationarity for different system dimensions and numbers of normal states. A comparison clearly shows that the knowledge about the non-stationarity of the system greatly improves change detection sensitivity for all principal components. This improvement is largest for those components that already provide the greatest possibility for change detection in the stationary case. We illustrate our results with an example using real traffic flow data, in which we detect a weekend and a bank holiday start as anomalies.
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