Procrustes Analysis for High-Dimensional Data

Angela Andreella and Livio Finos ()
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Livio Finos: University of Padova

Psychometrika, 2022, vol. 87, issue 4, No 10, 1422-1438

Abstract: 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.

Keywords: functional alignment; functional magnetic resonance imaging; high-dimensional data; Procrustes analysis; Von Mises–Fisher distribution (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11336-022-09859-5

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