Real-Time Monitoring of High-Dimensional Functional Data Streams via Spatio-Temporal Smooth Sparse Decomposition
Hao Yan, Kamran Paynabar, Jianjun Shi · Technometrics · 2017
Hao Yana, Kamran Paynabara* & Jianjun Shiaa Georgia Institute of Technology, Atlanta, GACONTACT Kamran Paynabar [email protected] Georgia Institute of Technology, Atlanta, GA, 30332Color versions of one or more of the figures in this article are available online at www.tandfonline.com/r/TECH.Supplementary materials for this article are available online. Please go to http://www.tandfonline.com/r/TECH.ABSTRACTHigh-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.