LAUSR

Functional alignment between subjects is an important assumption of functional magnetic resonance imaging (fMRI) group‐level analysis. However, it is often violated in practice, even after alignment to a standard anatomical template. Hyperalignment, based on sequential Procrustes orthogonal transformations, has been proposed as a method of aligning shared functional information into a common high‐dimensional space and thereby improving inter‐subject analysis. Though successful, current hyperalignment algorithms have a number of shortcomings, including difficulties interpreting the transformations, a lack of uniqueness of the procedure, and difficulties performing whole‐brain analysis. To resolve these issues, we propose the ProMises (Procrustes von Mises–Fisher) model. We reformulate functional alignment as a statistical model and impose a prior distribution on the orthogonal parameters (the von Mises–Fisher distribution). This allows for the embedding of anatomical information into the estimation procedure by penalizing the contribution of spatially distant voxels when creating the shared functional high‐dimensional space. Importantly, the transformations, aligned images, and related results are all unique. In addition, the proposed method allows for efficient whole‐brain functional alignment. In simulations and application to data from four fMRI studies we find that ProMises improves inter‐subject classification in terms of between‐subject accuracy and interpretability compared to standard hyperalignment algorithms.