Fast Multilevel Functional Principal Component Analysis

We introduce fast multilevel functional principal component analysis (fast MFPCA), which scales up to high dimensional functional data measured at multiple visits. The new approach is orders of magnitude faster than and achieves comparable estimation accuracy with the original MFPCA. Methods are motivated by the National Health and Nutritional Examination Survey (NHANES), which contains minute-level physical activity information of more than 10, 000 participants over multiple days and 1440 observations per day. While MFPCA takes more than five days to analyze these data, fast MFPCA takes less than five minutes. A theoretical study of the proposed method is also provided. The associated function mfpca.face() is available in the R package refund. Supplementary materials for this article are available online.本文提出了快速多级函数型主成分分析（fast multilevel functional principal component analysis，以下简称fast MFPCA），该方法可适配多随访时点下的高维函数型数据。该新方法的运算速度较原始MFPCA提升数个数量级，同时可达到与之相当的估计精度。本方法的提出源于美国国家健康与营养检查调查（National Health and Nutritional Examination Survey, NHANES）数据集，该数据集包含超过1万名参与者连续多日的分钟级身体活动信息，每日共含1440条观测记录。若使用原始MFPCA分析该数据集需耗时五日以上，而fast MFPCA仅需不足五分钟。本文同时对所提出的方法开展了理论研究与分析。配套的mfpca.face()函数已集成于R语言refund扩展包中。本文的补充材料可在线获取。