Functional alignment by the "light" approach of the von Mises-Fisher-Procrustes model.

Procrustes-based methods involve the singular value decomposition of a square matrix, leading to polynomial time complexity, and requiring a considerable memory for large-scale problems. Procrustes-based methods are used as functional alignment for fMRI data in the multi-subjects analysis. A high-dimensional matrix expresses the subject’s neural activation, and Procrustes-based methods are infeasible (computationally). The alignment can be conducted only on regions of interest of the brain. We proposed a “light” version of the Procrustes-based methods. A semi-orthogonal transformation reduces the matrices’ dimension before applying the Procrustes alignment, maintaining the variability of the matrix that enters in the decomposition step. fMRI application shows a low decrease in predictive performance.