基于邻域的广义动态主成分分析用于空间函数数据
Neighbourhood-Based Generalized Dynamic Principal Components for Spatial Functional Data
AI总结：
针对规则网格空间函数数据，提出基于邻域重构的SFGDPC降维方法，显著降低重构误差，并在印度洋海表温度应用中优于SFPCA。
AI中文摘要：
规则网格空间函数数据集在网格化的环境、海洋学、气候和遥感应用中自然产生，其中每个空间位置都与一条完整的曲线相关联。现有的谱空间函数主成分分析方法为这类数据提供了一种重要的频域方法，但它们并不直接针对从估计的潜在空间成分场进行有限邻域最小二乘重构。为解决这一问题，我们提出了空间函数广义动态主成分分析（SFGDPC），一种用于规则网格空间函数数据的基于重构的降维方法。每个函数首先由基系数表示，每个系数向量从标量潜在空间场及其在矩形网格上的切比雪夫邻域重构。空间邻域半径通过贝叶斯信息准则（BIC）类型的条件重构准则选择。在局部邻域转移模拟中，相对于空间函数主成分分析（SFPCA），SFGDPC在报告的成分数和协方差条件下将平均累积归一化均方误差（NMSE）降低了约38-53%。在印度洋海表温度（SST）应用中，一个SFGDPC成分在所有33个年度场上产生的整个网格重构误差低于边界安全和高峰值SFPCA基准。结果支持SFGDPC作为规则网格空间函数数据的谱SFPCA的基于局部重构的补充方法。
英文摘要：
Regular-grid spatial functional datasets arise naturally in gridded environmental, oceanographic, climate, and remote-sensing applications, where each spatial location is associated with an entire curve. Existing spectral spatial functional principal component analysis methods provide an important frequency-domain approach for such data, but they do not directly target finite-neighbourhood least-squares reconstruction from an estimated latent spatial component field. To address this, we propose Spatial Functional Generalized Dynamic Principal Components (SFGDPC), a reconstruction-based dimension-reduction method for regular-grid spatial functional data. Each function is first represented by basis coefficients, and each coefficient vector is reconstructed from a scalar latent spatial field and its Chebyshev neighbourhood on the rectangular grid. The spatial neighbourhood radius is selected using a Bayesian information criterion (BIC)-type conditional reconstruction criterion. In the local-neighbourhood transfer simulation, SFGDPC reduced mean cumulative normalized mean squared error (NMSE) relative to spatial functional principal component analysis (SFPCA) by approximately 38-53% across the reported component counts and covariance conditions. In the Indian Ocean sea surface temperature (SST) application, one SFGDPC component produced lower whole-grid reconstruction error than both the boundary-safe and high-cap SFPCA benchmarks across all 33 annual fields. The results support SFGDPC as a local reconstruction-based complement to spectral SFPCA for regular-grid spatial functional data.
