Marquette University
Department of Mathematical and Statistical Science
Colloquium Series
Time: Friday, November 19, 2021, 1:00-2:00pm
Location: Cudahy Hall Rm 401 (Live Strem on Teams at https://bit.ly/3qk0Bk1)
Topic: Interpretable PCA for Multilevel Multivariate Functional Data
Speaker: Robert Krafty
Professor and Chair of Biostatistics and Bioinformatics
Emory University
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 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 L1-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.
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Mehdi Maadooliat
Associate Professor of Computational Mathematical and Statistical Sciences
co-Director of Bioinformatics Program
Marquette University
http://www.mssc.mu.edu/~mehdi------------------------------