Procrustes problem

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 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 semiorthogonal 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.

A Statistical Approach to the Alignment of fMRI Data

Multi-subject functional Magnetic Resonance Image studies are critical. The anatomical and functional structure varies across subjects, so the image alignment is necessary. We define a probabilistic model to describe functional alignment. Imposing a prior distribution, as the matrix Fisher Von Mises distribution, of the orthogonal transformation parameter, the anatomical information is embedded in the estimation of the parameters, i.e., penalizing the combination of spatially distant voxels. Real applications show an improvement in the classification and interpretability of the results comparing to various functional alignment methods.