Two-way principal component analysis for matrix-variate data, with an application to functional magnetic resonance imaging data

Many modern neuroimaging studies acquire large spatial images of the brain observed sequentially over time. Such data are often stored in the forms of matrices. To model these matrix-variate data we introduce a class of separable processes using explicit latent process modeling. To account for the size and two-way structure of the data, we extend principal component analysis to achieve dimensionality reduction at the individual level. We introduce necessary identifiability conditions for each model and develop scalable estimationprocedures.Themethodismotivatedbyandappliedtoafunctionalmagneticresonanceimaging study designed to analyze the relationship between pain and brain activity.