Interpretable principal component analysis for multilevel multivariate functional data.
Interpretable principal component analysis for multilevel multivariate functional data.
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DOI：
10.1093/biostatistics/kxab018
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发表时间：
2021-09
期刊：
影响因子：
2.1
通讯作者：
Jun Zhang;G. Siegle;Tao Sun;Wendy D’Andrea;R. Krafty
中科院分区：
文献类型：
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作者：
Jun Zhang;G. Siegle;Tao Sun;Wendy D’Andrea;R. Krafty
许多研究从多个具有多水平和多变量结构的受试者中收集功能数据。这种数据的一个例子来自流行的神经科学实验，其中参与者的大脑活动使用脑电图等方式记录，并总结为多个电极或大脑区域内多个时变频带内的功率。总结受试者之间的全脑变化以及受试者内的位置变化的多个频带的联合变化可以帮助解释对刺激的神经反应。本文介绍了一种新的方法来对多变量函数数据进行可解释的主成分分析，该方法将总变异分解为受试者水平和受试者内复制水平（即，电极级）变化并且提供在变量之间可以是稀疏的可解释分量（例如，频带）并且在每个频带内具有随时间的局部支持。光滑度是通过粗糙度的罚款，而稀疏性和本地化的组件是通过解决一个创新的秩为一的凸优化问题与块Frobenius和矩阵L_1 $-范数为基础的罚款。该方法用于分析研究数据，以更好地了解具有创伤史和解离症状的个体对情感信息的反应，揭示了受试者和电极水平大脑活动如何与这些现象相关的新神经生理学见解。本文的补充材料可在网上查阅。
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.