Procrustes analysis 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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2020
- DOI:
- 10.48550/arXiv.2008.04631
- arXiv:
- arXiv:2008.04631
- Bibcode:
- 2020arXiv200804631A
- Keywords:
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- Statistics - Methodology
- E-Print:
- 22 pages, 7 figures