Real-Time Monitoring of High-Dimensional Functional Data Streams via Spatio-Temporal Smooth Sparse Decomposition

High-dimensional data monitoring and diagnosis has recently attracted increasing attention among researchers as well as practitioners. However, existing process monitoring methods fail to fully use the information of high-dimensional data streams due to their complex characteristics including the large dimensionality, spatio-temporal correlation structure, and nonstationarity. In this article, we propose a novel process monitoring methodology for high-dimensional data streams including profiles and images that can effectively address foregoing challenges. We introduce spatio-temporal smooth sparse decomposition (ST-SSD), which serves as a dimension reduction and denoising technique by decomposing the original tensor into the functional mean, sparse anomalies, and random noises. ST-SSD is followed by a sequential likelihood ratio test on extracted anomalies for process monitoring. To enable real-time implementation of the proposed methodology, recursive estimation procedures for ST-SSD are developed. ST-SSD also provides useful diagnostics information about the location of change in the functional mean. The proposed methodology is validated through various simulations and real case studies. Supplementary materials for this article are available online.