Robust functional principal component analysis via a functional pairwise spatial sign operator.
Robust functional principal component analysis via a functional pairwise spatial sign operator.
复制标题
通过函数成对空间符号算子进行稳健的函数主成分分析。
DOI：
10.1111/biom.13695
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发表时间：
2023
期刊：
影响因子：
1.9
通讯作者：
Di,Chong-Zhi
中科院分区：
文献类型：
--
作者：
Wang,Guangxing;Liu,Sisheng;Han,Fang;Di,Chong-Zhi
函数主成分分析(FPCA)在函数数据分析中被广泛应用于捕捉主要变异模式和降维。然而，如果数据表现出重尾或异常值，基于样本协方差估计的标准FPCA就不能很好地工作。为了解决这一问题，提出了一种新的基于函数成对空间符号(PASS)算子的稳健FPCA方法，称为PASS FPCA。我们提出了特征函数和特征值的稳健估计方法。建立了PASS算子的理论性质，表明它采用与标准协方差算子相同的特征函数，并允许恢复特征值之间的比率。我们还将所提出的程序扩展到处理有噪声测量的函数数据。与现有的稳健FPCA方法相比，所提出的PASS FPCA方法需要更弱的分布假设来保持协方差函数的特征空间。具体地说，现有的工作通常建立在一类泛函椭圆分布上，这内在地需要对称性。相反，我们引入了一类称为弱函数坐标对称性的分布，它允许严重的非对称性，并且比泛函椭圆分布族灵活得多。通过大量的仿真研究，证明了PASS FPCA的稳健性，特别是在具有非椭圆分布的场景中的优势。建议的方法是受到客观体力活动和心血管健康研究的加速测量数据的启发并应用于分析，这是一项大规模的流行病学研究，旨在调查客观测量的体力活动与老年女性心血管健康的关系。
Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well if the data exhibits heavy‐tailedness or outliers. To address this challenge, a new robust FPCA approach based on a functional pairwise spatial sign (PASS) operator, termed PASS FPCA, is introduced. We propose robust estimation procedures for eigenfunctions and eigenvalues. Theoretical properties of the PASS operator are established, showing that it adopts the same eigenfunctions as the standard covariance operator and also allows recovering ratios between eigenvalues. We also extend the proposed procedure to handle functional data measured with noise. Compared to existing robust FPCA approaches, the proposed PASS FPCA requires weaker distributional assumptions to conserve the eigenspace of the covariance function. Specifically, existing work are often built upon a class of functional elliptical distributions, which requires inherently symmetry. In contrast, we introduce a class of distributions called the weakly functional coordinate symmetry (weakly FCS), which allows for severe asymmetry and is much more flexible than the functional elliptical distribution family. The robustness of the PASS FPCA is demonstrated via extensive simulation studies, especially its advantages in scenarios with nonelliptical distributions. The proposed method was motivated by and applied to analysis of accelerometry data from the Objective Physical Activity and Cardiovascular Health Study, a large‐scale epidemiological study to investigate the relationship between objectively measured physical activity and cardiovascular health among older women.