This paper is concerned with data science and analytics as applied to data from dynamic systems for the purpose of monitoring, prediction, and inference. Collinearity is inevitable in industrial operation data. Therefore, we focus on latent variable methods that achieve dimension reduction and collinearity removal. We present a new dimension reduction expression of state space framework to unify dynamic latent variable analytics for process data, dynamic factor models for econometrics, subspace identification of multivariate dynamic systems, and machine learning algorithms for dynamic feature analysis. We unify or differentiate them in terms of model structure, objectives with constraints, and parsimony of parameterization. The Kalman filter theory in the latent space is used to give a system theory foundation to some empirical treatments in data analytics. We provide a unifying review of the connections among the dynamic latent variable methods, dynamic factor models, subspace identification methods, dynamic feature extractions, and their uses for prediction and process monitoring. Both unsupervised dynamic latent variable analytics and the supervised counterparts are reviewed. Illustrative examples are presented to show the similarities and differences among the analytics in extracting features for prediction and monitoring.

本文关注的是数据科学和分析，这些数据应用于动态系统的数据以进行监视，预测和推理。工业操作数据中共线性是不可避免的。因此，我们专注于实现降维和共线性去除的潜在变量方法。我们提出了一种新的状态空间框架降维表达式，以统一过程数据的动态潜在变量分析，计量经济学的动态因子模型，多元动态系统的子空间标识以及动态特征分析的机器学习算法。我们根据模型结构，具有约束的目标以及对参数化的简化来统一或区分它们。潜在空间中的卡尔曼滤波理论用于为数据分析中的一些经验处理提供系统理论基础。我们对动态潜在变量方法，动态因子模型，子空间识别方法，动态特征提取及其在预测和过程监控中的用途之间的联系进行了统一的回顾。审查了无监督的动态潜在变量分析和有监督的对应变量。给出了说明性示例，以显示在提取特征以进行预测和监视时分析之间的异同。审查了无监督的动态潜在变量分析和有监督的对应变量。给出了说明性示例，以显示在提取特征以进行预测和监视时分析之间的异同。审查了无监督的动态潜在变量分析和有监督的对应变量。给出了说明性示例，以显示在提取特征以进行预测和监视时分析之间的异同。