发表机构
National Dong Hwa University; National Chung Hsing University（东华大学; 中兴大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出结构化协变量信息经验正交函数（SCIEOF），将协变量嵌入潜在基以改进时空环境场的低秩表示，提升预测性能并保持可解释性。
AI 中文摘要
低秩表示方法如经验正交函数（EOF）分解被广泛用于分析大规模时空环境场。然而，传统EOF仅从协方差结构中识别潜在模态，未利用观测到的环境协变量，限制了其将外部信息纳入低秩表示的能力。本研究引入了结构化协变量信息EOF（SCIEOF），这是EOF的一种协变量信息扩展，弥合了低秩降维与面向预测的时空建模之间的差距。SCIEOF将空间和时间协变量嵌入潜在基中，同时通过加性成分纳入时空协变量，从而产生由观测协变量信息驱动的潜在模态的低秩表示。通过模拟研究和应用于MERRA-2再分析的全球近地表气温数据，开发并评估了估计程序。模拟研究表明，纳入信息性协变量可改善潜在结构恢复和预测准确性，特别是在空间基函数适当指定时。这种优势在中到大规模样本量下更为显著，而在数据有限时，具有更强结构假设的方法仍具有竞争力。在MERRA-2应用中，SCIEOF相对于常用方法实现了具有竞争力或改进的预测性能，同时提供了紧凑且物理可解释的低秩表示。总体而言，SCIEOF为将结构化协变量信息整合到低秩时空表示中提供了一个灵活且计算可扩展的框架，将EOF扩展到预测性环境建模。
英文摘要
Low-rank representations such as empirical orthogonal function (EOF) decompositions are widely used for analyzing large spatio-temporal environmental fields. However, conventional EOF identifies latent modes solely from covariance structure and does not utilize observed environmental covariates, limiting its ability to incorporate external information into low-rank representations. This study introduces Structured Covariate-Informed EOF (SCIEOF), a covariate-informed extension of EOF that bridges low-rank dimension reduction and prediction-oriented spatio-temporal modeling. SCIEOF embeds spatial and temporal covariates into the latent bases while incorporating spatio-temporal covariates through an additive component, yielding low-rank representations with latent modes informed by observed covariates. Estimation procedures are developed and evaluated through simulation studies and an application to global near-surface air temperature from the MERRA-2 reanalysis. Simulation studies demonstrate that incorporating informative covariates improves latent structure recovery and predictive accuracy, particularly when the spatial basis is appropriately specified. The advantage is more pronounced at moderate-to-large sample sizes, while methods with stronger structural assumptions remain competitive when data are limited. In the MERRA-2 application, SCIEOF achieves competitive or improved predictive performance relative to commonly used methods while providing a compact and physically interpretable low-rank representation. Overall, SCIEOF provides a flexible and computationally scalable framework for integrating structural covariate information into low-rank spatio-temporal representations, extending EOF toward predictive environmental modeling.
