Hybrid Latent Variable Modeling of High Dimensional Time Series Data

This paper is concerned with high dimensional time series data analytics based on hybrid dynamic and static latent variable modeling. Application areas can include industrial data analytics, dynamic feature extraction, econometric data modeling, image sequence modeling, and other high dimensional time-correlated data analytic problems. As collinearity is typical in these high-dimensional data, the interest is to extract the latent driving factors which are concentrated in a reduced subspace. Furthermore, in the latent subspace, variations in some dimensions are auto-correlated, while those in other dimensions are not auto-correlated. We present in this paper several latent dynamic variable modeling methods to extract the principal variations in the data, either dynamic or static, in a low dimensional latent subspace. The approaches effectively distill and separate latent features in the data for easy interpretation, prediction, and visualization. The dynamic latent variables are extracted to have maximized predictability, in terms of correlation or covariance between the latent variables scores and the predicted values from the past scores. A simulation data case study is presented to illustrate how these latent dynamic analytics extract important features from the data.