Principal Component Analysis Balancing Prediction and Approximation Accuracy for Spatial Data
针对多变量空间数据，提出一种降维算法，在保留原始数据近似程度与提升下游建模预测能力之间取得最优平衡，并通过空气污染和空间转录组学应用验证效果。
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not take the downstream modeling task into consideration when finding the lower-dimensional representation. We formalize the closeness of approximation to the original data and the utility of lower-dimensional scores for downstream modeling as two complementary, sometimes conflicting, metrics for dimension reduction. We illustrate how existing methodologies fall into this framework and propose a flexible dimension reduction algorithm that achieves the optimal tradeoff. We derive a computationally simple form for our algorithm and illustrate its performance through simulation studies, as well as two applications in air pollution modeling and spatial transcriptomics.