In psychometric sciences, such as social or behavioral sciences, and, similarly, in medical sciences, it is increasingly common to deal with longitudinal data organized as high-dimensional multidimensional arrays, also known as tensors. Within this framework, the time-continuous property of longitudinal data often implies a smooth functional structure on one of the tensor modes. To help researchers investigate such data, we introduce a new tensor decomposition approach based on the PARAFAC decomposition. Our approach allows researchers to represent a high-dimensional functional tensor as a low-dimensional set of functions and feature matrices. Furthermore, to capture the underlying randomness of the statistical setting more efficiently, we introduce a probabilistic latent model in the decomposition. A covariance-based block-relaxation algorithm is derived to obtain estimates of model parameters. Thanks to the covariance formulation of the solving procedure and thanks to the probabilistic modeling, the method can be used in sparse and irregular sampling schemes, making it applicable in numerous settings. Our approach is applied in the psychometric setting to help characterize multiple neurocognitive scores observed over time in the Alzheimer’s Disease Neuroimaging Initiative study. Finally, intensive simulations show a notable advantage of our method in reconstructing tensors.

Understanding spatial navigation and memory formation is critical to exploring how humans learn and adapt in complex environments. To investigate these processes, we conducted an experiment using the Minecraft Memory and Navigation Task, collecting detailed three-dimensional (3D) path data in a virtual open-world setting. Statistically, we developed a novel methodology to convert complex high-dimensional 3D movement data into functional representations, enabling standardized comparisons and analyses across participants and environments. We applied techniques such as functional clustering and regression to identify navigation patterns and their relationships with cognitive map development and memory retention. Our analysis uncovered two significant insights: first, participants who adopted moderately exploratory behaviors during training demonstrated superior retention of object locations; second, inefficient navigation strategies were strongly linked to poorer spatial memory and navigation performance. These findings highlight the effectiveness of our methodology in advancing the study of navigation behaviors and cognitive processes in dynamic 3D environments.

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.