Procrustes analysis for high-dimensional data

TL;DR

This paper introduces the ProMises model, an extension of Procrustes analysis tailored for high-dimensional data like neuroimaging, improving interpretability and estimation speed by using a von Mises-Fisher prior.

Contribution

The paper develops the ProMises model with a conjugate prior to address non-identifiability and interpretability issues in high-dimensional Procrustes analysis, and introduces an efficient version for neuroimaging applications.

Findings

Enhanced fMRI connectivity analysis using ProMises.

Incorporation of topological brain information improves alignment.

Fast estimation process for high-dimensional data.

Abstract

The Procrustes-based perturbation model (Goodall, 1991) allows minimization of the Frobenius distance between matrices by similarity transformation. However, it suffers from non-identifiability, critical interpretation of the transformed matrices, and inapplicability in high-dimensional data. We provide an extension of the perturbation model focused on the high-dimensional data framework, called the ProMises (Procrustes von Mises-Fisher) model. The ill-posed and interpretability problems are solved by imposing a proper prior distribution for the orthogonal matrix parameter (i.e., the von Mises-Fisher distribution) which is a conjugate prior, resulting in a fast estimation process. Furthermore, we present the Efficient ProMises model for the high-dimensional framework, useful in neuroimaging, where the problem has much more than three dimensions. We found a great improvement in functional magnetic resonance imaging (fMRI) connectivity analysis because the ProMises model permits incorporation of topological brain information in the alignment's estimation process.