# Procrustes analysis for high-dimensional data

arXiv: https://arxiv.org/abs/2008.04631 · HTML: https://mlsanity.com/paper/2008.04631/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Aug 2020.

## Built on by (most cited first, 3 of 3)

- [Resampling and averaging coordinates on data](https://mlsanity.com/paper/2408.01379/) (2024)
- [Are Video Generation Models Geographically Fair? An Attraction-Centric Evaluation of Global Visual Knowledge](https://mlsanity.com/paper/2601.18698/) (2026)
- [Fast Whole-Brain, Geometry-Aware Functional Alignment for Cross-Subject Decoding](https://mlsanity.com/paper/2607.10931/) (2026)

## Abstract (arXiv)

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.