Efficient Dynamic Latent Variable Analysis for High-Dimensional Time Series Data

• Published in: IEEE transactions on industrial informatics Vol. 16; no. 6; pp. 4068 - 4076
• Main Authors: Dong, Yining, Liu, Yingxiang, Joe Qin, S.
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.06.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Autoregressive models; Canonical correlation analysis; Correlation; Correlation analysis; Covariance matrix; Data models; Dimensional analysis; dynamic feature extraction; Dynamic models; Eigenvectors; Heuristic algorithms; Hidden Markov models; high-dimensional time series; Iterative methods; latent dynamic modeling; numerical implementation; Numerical models; Principal component analysis; Singular value decomposition; Time series; Time series analysis
• ISSN: 1551-3203; 1941-0050
• DOI: 10.1109/TII.2019.2958074

Dynamic-inner canonical correlation analysis (DiCCA) extracts dynamic latent variables from high-dimensional time series data with a descending order of predictability in terms of <inline-formula><tex-math notation="LaTeX">R^2</tex-math></inline-formula>. The reduced dimensional latent variables with rank-ordered predictability capture the dynamic features in the data, leading to easy interpretation and visualization. In this article, numerically efficient algorithms for DiCCA are developed to extract dynamic latent components from high-dimensional time series data. The numerically improved DiCCA algorithms avoid repeatedly inverting a covariance matrix inside the iteration loop of the numerical DiCCA algorithms. A further improvement using singular value decomposition converts the generalized eigenvector problem into a standard eigenvector problem for the DiCCA solution. Another improvement in model efficiency in this article is the dynamic model compaction of the extracted latent scores using autoregressive integrated moving average (ARIMA) models. Integrating factors, if existed in the latent variable scores, are made explicit in the ARIMA models. Numerical tests on two industrial datasets are provided to illustrate the improvements.