Procrustes Alignment in Individual-level Analyses of Functional Gradients

Abstract Functional connectivity (FC) gradients provide valuable insights into individual differences in brain organization, yet aligning these gradients across individuals poses challenges. Procrustes alignment is often employed to standardize gradients across multiple subjects, but the choice of the number of gradients used in alignment introduces complexities that may impact individual-level analyses. In this study, we systematically investigate the impact of varying gradient counts in Procrustes alignment on the principal FC gradient, using data from four resting state fMRI datasets, including the Human Connectome Project (HCP-YA), Amsterdam Open MRI Collection (AOMIC) PIOP1 and PIOP2, and Cambridge Centre for Ageing and Neuroscience (Cam-CAN). We find that increasing the number of gradients used in alignment enhances identification accuracy but can reduce differential identifiability, as additional gradients risk introducing nuisance signals such as motion back into the principal gradient. To further probe these effects, machine learning to predict fluid intelligence and age, and a motion prediction analysis, revealing that higher alignment gradient counts may leak information from lower gradients into the principal gradient for individual-level analyses. These findings highlight the trade-off between alignment precision and the potential reintroduction of noise. Key Points Gradient count used in Procrustes alignment impacts identification accuracy and differential identifiability obtained using the principal gradient The magnitude of the Procrustes transformation correlates with motion measures, and this correlation increases with higher gradient count used in alignment. Gradient count used in Procrustes alignment impacts prediction of fluid intelligence and age