Title: Interpretable principal components analysis for multilevel multivariate functional data
Authors: Jun Zhang - University of Pittsburgh (United States)
Robert Krafty - University of Pittsburgh (United States) [presenting]
Greg Siegle - University of Pittsburgh (United States)
Abstract: 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 EEG or fMRI and summarized as power within multiple time-varying frequency bands at multiple brain regions. An important question is summarizing the joint variation across multiple frequency bands for both whole-brain variability between subjects, as well as location-variation within subjects. We discuss 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. The sparsity and localization of components is 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 blunted affect, revealing new neurophysiological insights into how subject- and electrode-level brain activity are connected to the phenomenon of trauma patients ``shutting down'' when presented with emotional information.