论文标题
用于高维功能数据的因子引导的功能PCA
Factor-guided functional PCA for high-dimensional functional data
论文作者
论文摘要
有关高维功能数据的文献集中于随时间的依赖性或功能变量之间的相关性。在本文中，我们提出了一种因子引导的功能主成分分析（FAFPCA）方法，以考虑变量的时间依赖性和相关性，以便提取的特征尽可能足够。特别是，我们使用因子过程来考虑高维函数变量之间的相关性，然后将功能主成分分析（FPCA）应用于因子过程中以解决随时间的依赖性。此外，为了解决由三个限制维度引起的计算问题，我们创造性地构建了一些力矩方程，以估算封闭形式的负载，得分和本征函数，而无需旋转。从理论上讲，我们建立了所提出的估计量的渐近性能。广泛的仿真研究表明，我们提出的方法在准确性和计算成本方面优于其他竞争对手。提出的方法用于分析阿尔茨海默氏病神经影像学计划（ADNI）数据集，从而提高了与阿尔茨海默氏病有关的41个重要ROI，其中23个已得到文献证实。
The literature on high-dimensional functional data focuses on either the dependence over time or the correlation among functional variables. In this paper, we propose a factor-guided functional principal component analysis (FaFPCA) method to consider both temporal dependence and correlation of variables so that the extracted features are as sufficient as possible. In particular, we use a factor process to consider the correlation among high-dimensional functional variables and then apply functional principal component analysis (FPCA) to the factor processes to address the dependence over time. Furthermore, to solve the computational problem arising from triple-infinite dimensions, we creatively build some moment equations to estimate loading, scores and eigenfunctions in closed form without rotation. Theoretically, we establish the asymptotical properties of the proposed estimator. Extensive simulation studies demonstrate that our proposed method outperforms other competitors in terms of accuracy and computational cost. The proposed method is applied to analyze the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, resulting in higher prediction accuracy and 41 important ROIs that are associated with Alzheimer's disease, 23 of which have been confirmed by the literature.
