Department of Biostatistics, University of Pittsburgh, 130 De Soto Street, Pittsburgh, PA, 15261, USA.
Department of Psychiatry, University of Pittsburgh, 3811 O'Hara Street, Pittsburgh, PA, 15213, USA.
Biostatistics. 2023 Apr 14;24(2):227-243. doi: 10.1093/biostatistics/kxab018.
Many studies collect functional data from multiple subjects that have both multilevel and multivariate structures. An example of such data comes from popular neuroscience experiments where participants' brain activity is recorded using modalities such as electroencephalography and summarized as power within multiple time-varying frequency bands within multiple electrodes, or brain regions. Summarizing the joint variation across multiple frequency bands for both whole-brain variability between subjects, as well as location-variation within subjects, can help to explain neural reactions to stimuli. This article introduces a novel approach to conducting interpretable principal components analysis on multilevel multivariate functional data that decomposes total variation into subject-level and replicate-within-subject-level (i.e., electrode-level) variation and provides interpretable components that can be both sparse among variates (e.g., frequency bands) and have localized support over time within each frequency band. Smoothness is achieved through a roughness penalty, while sparsity and localization of components are achieved by solving an innovative rank-one based convex optimization problem with block Frobenius and matrix $L_1$-norm-based penalties. The method is used to analyze data from a study to better understand reactions to emotional information in individuals with histories of trauma and the symptom of dissociation, revealing new neurophysiological insights into how subject- and electrode-level brain activity are associated with these phenomena. Supplementary materials for this article are available online.
许多研究从具有多层次和多变量结构的多个主体收集功能数据。这样的数据示例来自流行的神经科学实验，其中参与者的大脑活动通过诸如脑电图等模式记录，并在多个电极或脑区的多个时变频带内概括为功率。总结多个频带之间的联合变化，无论是在主体之间的全脑变异性方面，还是在主体内的位置变异性方面，都有助于解释对刺激的神经反应。本文介绍了一种对多层次多变量功能数据进行可解释主成分分析的新方法，该方法将总变差分解为主体水平和主体内重复水平（即电极水平）的变差，并提供了可解释的成分，这些成分在变量（例如频带）之间可以稀疏，并且在每个频带内的时间上具有局部支持。通过粗糙度惩罚来实现平滑性，而通过求解具有块 Frobenius 和矩阵$L_1$-范数惩罚的创新基于秩一的凸优化问题来实现成分的稀疏性和局部性。该方法用于分析一项研究的数据，以更好地了解创伤史和分离症状个体对情绪信息的反应，揭示了这些现象与主体和电极水平大脑活动之间关联的新神经生理学见解。本文的补充材料可在线获取。
