Procrustes Analysis for High-Dimensional Data

Psychometrika. 2022 Dec;87(4):1422-1438. doi: 10.1007/s11336-022-09859-5. Epub 2022 May 18.


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.

Keywords: Procrustes analysis; Von Mises–Fisher distribution; functional alignment; functional magnetic resonance imaging; high-dimensional data.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Brain*
  • Magnetic Resonance Imaging*
  • Psychometrics