Interpretable principal component analysis for multilevel multivariate functional data.

Area of Science:

• Neuroscience
• Statistics
• Signal Processing

Background:

• Multilevel and multivariate functional data are common in neuroscience, particularly from electroencephalography (EEG) recordings.
• Analyzing joint variation across frequency bands and locations is crucial for understanding neural responses to stimuli.
• Existing methods may not adequately capture both subject-level and within-subject (electrode-level) variation in functional brain data.

Purpose of the Study:

• To develop a novel, interpretable principal component analysis (PCA) method for multilevel multivariate functional data.
• To decompose total variation into subject-level and electrode-level components.
• To provide interpretable components that are sparse across frequency bands and localized in time.

Main Methods:

• Introduced a novel interpretable principal component analysis (PCA) approach for multilevel multivariate functional data.
• Decomposed variation into subject-level and electrode-level components.
• Employed a roughness penalty for smoothness and a rank-one based convex optimization problem with block Frobenius and matrix L1-norm penalties for sparsity and localization.

Main Results:

• Developed a method that decomposes functional data variation into subject and electrode levels.
• Achieved interpretable principal components that are sparse across frequency bands and localized in time.
• Applied the method to analyze brain activity in individuals with trauma history and dissociation.

Conclusions:

• The novel PCA method offers interpretable components for multilevel multivariate functional data.
• The analysis revealed neurophysiological insights into brain activity associated with trauma and dissociation.
• The approach enhances understanding of subject- and electrode-level brain activity in specific clinical populations.