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Abstract Neuroimaging studies, such as the Human Connectome Project (HCP), often collect multifaceted data to study the human brain. However, these data are often analyzed in a pairwise fashion, which can hinder our understanding of how different brain-related measures interact. In this study, we analyze the multi-block HCP data using data integration via analysis of subspaces (DIVAS). We integrate structural and functional brain connectivity, substance use, cognition, and genetics in an exhaustive five-block analysis. This gives rise to the important finding that genetics is the single data modality most predictive of brain connectivity, outside of brain connectivity itself. Nearly 14% of the variation in functional connectivity (FC) and roughly 12% of the variation in structural connectivity (SC) is attributed to shared spaces with genetics. Moreover, investigations of shared space loadings provide interpretable associations between particular brain regions and drivers of variability. Novel Jackstraw hypothesis tests are developed for the DIVAS framework to establish statistically significant loadings. For example, in the (FC, SC, and substance use) subspace, these novel hypothesis tests highlight largely negative functional and structural connections suggesting the brain’s role in physiological responses to increased substance use. Our findings are validated on genetically relevant subjects not studied in the main analysis. 

Data matrix centering is an ever-present yet under-examined aspect of data analysis. Functional data analysis (FDA) often operates with a default of centering such that the vectors in one dimension have mean zero. We find that centering along the other dimension identifies a novel useful mode of variation beyond those familiar in FDA. We explore ambiguities in both matrix orientation and nomenclature. Differences between centerings and their potential interaction can be easily misunderstood. We propose a unified framework and new terminology for centering operations. We clearly demonstrate the intuition behind and consequences of each centering choice with informative graphics. We also propose a new direction energy hypothesis test as part of a series of diagnostics for determining which choice of centering is best for a data set. We explore the application of these diagnostics in several FDA settings.