  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.
