Procrustes analysis involves finding the optimal superposition of two or more "forms" via rotations, translations, and scalings. Procrustes problems arise in a wide range of scientific disciplines, especially when the geometrical shapes of objects are compared, contrasted, and analyzed. Classically, the optimal transformations are found by minimizing the sum of the squared distances between corresponding points in the forms. Despite its widespread use, the ordinary unweighted least-squares (LS) criterion can give erroneous solutions when the errors have heterogeneous variances (heteroscedasticity) or the errors are correlated, both common occurrences with real data. In contrast, maximum likelihood (ML) estimation can provide accurate and consistent statistical estimates in the presence of both heteroscedasticity and correlation. Here we provide a complete solution to the nonisotropic ML Procrustes problem assuming a matrix Gaussian distribution with factored covariances. Our analysis generalizes, simplifies, and extends results from previous discussions of the ML Procrustes problem. An iterative algorithm is presented for the simultaneous, numerical determination of the ML solutions.
This research output has an Altmetric Attention Score of 18. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 09 March 2023.
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#2,653,407
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Outputs from Proceedings of the National Academy of Sciences of the United States of America
#30,304
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Outputs of similar age
#9,020
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Outputs of similar age from Proceedings of the National Academy of Sciences of the United States of America
#97
of 696 outputs
Altmetric has tracked 34,400,738 research outputs across all sources so far. Compared to these this one has done particularly well and is in the 92nd percentile: it's in the top 10% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 118,992 research outputs from this source. They typically receive a lot more attention than average, with a mean Attention Score of 40.1. This one has gotten more attention than average, scoring higher than 74% of its peers.
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We're also able to compare this research output to 696 others from the same source and published within six weeks on either side of this one. This one has done well, scoring higher than 85% of its contemporaries.
