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.

翻译：关于高维功能数据的文献侧重于长期依赖性或功能变量之间的相互关系。在本文件中,我们提出了一个要素引导功能主要组成部分分析方法(FAFPCA),以考虑变量的时间依赖性和相关性,从而使提取的特征尽可能充分。特别是,我们使用一个要素过程来考虑高维功能变量之间的相互关系,然后将功能主要组成部分分析(FPCA)应用到因子过程,以解决长期依赖性。此外,为了解决三极无限维产生的计算问题,我们创造性地构建一些瞬间方程式,以不轮换地以封闭的形式估计装载、分数和机能功能。理论上,我们建立了拟议估算天体的随机特性。广泛的模拟研究表明,我们拟议的方法在准确性和计算成本方面优于其他竞争者。拟议方法用于分析阿尔茨海默氏病神经成像倡议(ADNI)的数据集,从而导致更高的预测准确性和41个重要的ROIs,与阿尔茨海默氏病有关,其中23个已得到文献的证实。