Individual identifiability following Procrustes alignment of functional gradients: effect of subspace dimensionality

Functional connectivity (FC) gradients derived from fMRI provide valuable insights into individual differences in brain organisation, yet aligning these gradients across individuals poses challenges for meaningful group comparisons. Procrustes alignment is often employed to standardize gradients, but the choice of the number of gradients used in alignment introduces complexities that may affect the validity of 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 high-quality 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 subject identification. To further probe these effects, we use machine learning to predict fluid intelligence and age, and a motion prediction analysis, revealing that higher alignment gradient counts may introduce information from lower gradients into the principal gradient with implications for the interpretation of individual-level analyses.