The majority of control charts based on scan statistics for spatio-temporal surveillance use full observation vectors. In high-dimensional applications, dimension-reduction techniques are usually applied. Typically, the dimension reduction is conducted as a post-processing step rather than in the data acquisition stage and thus, a full sample covariance matrix is required. When the dimensionality of data is high, (i) the sample covariance matrix tends to be ill-conditioned due to a limited number of samples; (ii) the inversion of such a sample covariance matrix causes numerical issues; and (iii) aggregating information from all variables may lead to high communication costs in sensor networks. In this paper, we propose a set of reduced-dimension (RD) control charts that perform dimension reduction during the data acquisition process by spatial scanning. The proposed methods avoid computational difficulties and possibly high communication costs. We derive a theoretical measure that characterizes the performance difference between the RD approach and the full observation approach. The numerical results show that the RD approach has little performance loss under several commonly used spatial models while enjoying all the benefits of implementation. A case study on water quality monitoring demonstrates the effectiveness of the proposed methods in real applications.

中文翻译：

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减少还是不减少：时空监视研究

大多数基于扫描统计信息的时空监视控制图都使用完整的观察向量。在高尺寸应用中，通常采用尺寸减小技术。通常，降维是作为后处理步骤而不是在数据获取阶段进行的，因此需要完整的样本协方差矩阵。当数据的维数很高时，（i）由于样本数量有限，样本协方差矩阵趋于病态；（ii）这样的样本协方差矩阵的倒置会引起数值问题；（iii）从所有变量汇总信息可能会导致传感器网络的通信成本较高。在本文中，我们提出了一组缩小尺寸（RD）控制图，这些图在通过空间扫描的数据采集过程中执行降维。所提出的方法避免了计算困难和可能的高通信成本。我们得出了一种理论上的测量方法，该方法表征了RD方法和完整观测方法之间的性能差异。数值结果表明，RD方法在几种常用空间模型下几乎没有性能损失，同时享有实施的所有好处。关于水质监测的案例研究证明了所提出方法在实际应用中的有效性。我们得出了一种理论上的测量方法，该方法表征了RD方法与完整观测方法之间的性能差异。数值结果表明，RD方法在几种常用空间模型下几乎没有性能损失，同时享有实施的所有好处。关于水质监测的案例研究证明了所提出方法在实际应用中的有效性。我们得出了一种理论上的测量方法，该方法表征了RD方法和完整观测方法之间的性能差异。数值结果表明，RD方法在几种常用空间模型下几乎没有性能损失，同时享有实施的所有好处。关于水质监测的案例研究证明了所提出方法在实际应用中的有效性。