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Procrustes Analysis for High-Dimensional Data

Author

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  • Angela Andreella

    (CA’ Foscari University of Venice)

  • Livio Finos

    (University of Padova)

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.

Suggested Citation

  • Angela Andreella & Livio Finos, 2022. "Procrustes Analysis for High-Dimensional Data," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1422-1438, December.
    • Handle: RePEc:spr:psycho:v:87:y:2022:i:4:d:10.1007_s11336-022-09859-5
    DOI: 10.1007/s11336-022-09859-5
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    References listed on IDEAS

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    1. Bert Green, 1952. "The orthogonal approximation of an oblique structure in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 17(4), pages 429-440, December.
    2. J. Gower, 1975. "Generalized procrustes analysis," Psychometrika, Springer;The Psychometric Society, vol. 40(1), pages 33-51, March.
    3. Peter J. Green & Kanti V. Mardia, 2006. "Bayesian alignment using hierarchical models, with applications in protein bioinformatics," Biometrika, Biometrika Trust, vol. 93(2), pages 235-254, June.
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    Cited by:

    1. Angela Andreella & Riccardo Santis & Anna Vesely & Livio Finos, 2023. "Procrustes-based distances for exploring between-matrices similarity," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 867-882, September.

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