Procrustes Analysis for High-Dimensional Data

Abstract

The Procrustes-based perturbation model (Goodall in J R Stat Soc Ser B Methodol 53(2):285-321, 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 connectivity analysis because the ProMises model permits incorporation of topological brain information in the alignment’s estimation process.

Publication
Psychometrika
Click the Cite button above to demo the feature to enable visitors to import publication metadata into their reference management software.
Click the Slides button above to demo Academic’s Markdown slides feature.

Supplementary notes can be added here, including code and math.

Avatar
Angela Andreella
Assistant Professor at Ca’ Foscari University of Venice

My research interests include Multiple Testing problem and Procrustes technique, generally statistical methods in the Neuroscience field.