Spatio-temporal process monitoring using exponentially weighted spatial LASSO

Spatio-temporal process monitoring (STPM) has received a considerable attention recently due to its broad applications in environment monitoring, disease surveillance, streaming image processing, and more. Because spatio-temporal data often have complicated structure, including latent spatio-temporal data correlation, complex spatio-temporal mean structure, and nonparametric data distribution, STPM is a challenging research problem. In practice, if a spatio-temporal process has a distributional shift (e.g., mean shift) started at a specific time point, then the spatial locations with the shift are usually clustered in small regions. This kind of spatial feature of the shift has not been considered in the existing STPM literature yet. In this paper, we develop a new STPM method that takes into account the spatial feature of the shift in its construction. The new method combines the ideas of exponentially weighted moving average in the temporal domain for online process monitoring and spatial LASSO in the spatial domain for accommodating the spatial feature of a future shift. It can also accommodate the complicated spatio-temporal data structure well. Both simulation studies and a real-data application show that it can provide a reliable and effective tool for different STPM applications.时空过程监测（Spatio-temporal process monitoring，STPM）近年来因其在环境监测、疾病监测、流式图像处理等诸多领域的广泛应用，受到了学界的广泛关注。由于时空数据往往具备复杂结构，涵盖潜在时空相关性、复杂时空均值结构与非参数数据分布，因此STPM是一项极具挑战性的研究课题。实际应用中，若某一时空过程于特定时间点出现分布偏移（如均值偏移），则发生偏移的空间位置通常会聚集于小范围区域内。现有STPM相关研究尚未考虑偏移的这类空间特征。本文提出一种全新的STPM方法，在构建过程中充分纳入偏移的空间特征。该方法融合了时域在线过程监测所采用的指数加权移动平均（exponentially weighted moving average）思路，与空域中用于适配未来偏移空间特征的空间LASSO方法，同时亦可很好地适配复杂的时空数据结构。仿真实验与真实数据集应用均表明，该方法可为各类STPM应用提供可靠且高效的技术工具。