A tensor-based approach for monitoring partially observed high-dimensional data stream

Abstract

With advancements in measurement equipment and communication technology, engineers in many fields now have access to high-dimensional (HD) data streams. In real-world applications, however, limited transmission bandwidth, time restrictions, and rising costs often lead to partial data observation. And practitioners have no choice but to rely on only this incomplete information to assess if their processes are functioning without anomalies. To tackle these challenges, we propose an innovative framework designed to monitor incomplete streaming HD data effectively, leveraging its inherent auto- and cross-correlation structure. To be specific, we exploit the tensor decomposition of delay-embedding transformed data which allows to extract latent relationships among features in the form of factorizing matrices while a sparse anomaly tensor is utilized not only to take the measurements deviated from regularities but also to develop a process control chart signaling if the process has been changed. Through intensive simulation experiments and a case study, we evaluate the performance and efficacy of our procedure and compare it with other approaches.