We propose a new fast generalized functional principal components analysis (fast-GFPCA) algorithm for dimension reduction of non-Gaussian functional data. The method consists of: (1) binning the data within the functional domain; (2) fitting local random intercept generalized linear mixed models in every bin to obtain the initial estimates of the person-specific functional linear predictors; (3) using fast functional principal component analysis to smooth the linear predictors and obtain their eigenfunctions; and (4) estimating the global model conditional on the eigenfunctions of the linear predictors. An extensive simulation study shows that fast-GFPCA performs as well or better than existing state-of-the-art approaches, it is orders of magnitude faster than existing general purpose GFPCA methods, and scales up well with both the number of observed curves and observations per curve. Methods were motivated by and applied to a study of active/inactive physical activity profiles obtained from wearable accelerometers in the NHANES 2011-2014 study. The method can be implemented by any user familiar with mixed model software, though the R package fastGFPCA is provided for convenience.

翻译：本文提出一种新的快速广义函数主成分分析（fast-GFPCA）算法，用于非高斯函数型数据的降维。该方法包括：（1）在函数域内对数据进行分箱；（2）在每个分箱内拟合局部随机截距广义线性混合模型，以获取个体特定函数线性预测量的初始估计；（3）使用快速函数主成分分析对线性预测量进行平滑并提取其特征函数；（4）基于线性预测量的特征函数估计全局模型。广泛的仿真研究表明，fast-GFPCA的性能与现有最先进方法相当或更优，其计算速度比现有通用GFPCA方法快数个数量级，并且对观测曲线数量及每条曲线的观测值具有良好的可扩展性。该方法受美国国家健康与营养调查（NHANES）2011-2014研究中可穿戴加速度计获取的活跃/非活跃体力活动特征研究的启发，并应用于该数据集。任何熟悉混合模型软件的用户均可实现该方法，同时本文提供R包fastGFPCA以方便使用。