Generalized procrustes analysis
Abstract
Suppose P i ( i ) ( i = 1, 2, ..., m, j = 1, 2, ..., n ) give the locations of mn points in p -dimensional space. Collectively these may be regarded as m configurations, or scalings, each of n points in p -dimensions. The problem is investigated of translating, rotating, reflecting and scaling the m configurations to minimize the goodness-of-fit criterion Σ i=1 m Σ i=1 n Δ 2 ( P j ( i ) G i ), where G i is the centroid of the m points P i ( i ) ( i = 1, 2, ..., m ). The rotated positions of each configuration may be regarded as individual analyses with the centroid configuration representing a consensus, and this relationship with individual scaling analysis is discussed. A computational technique is given, the results of which can be summarized in analysis of variance form. The special case m = 2 corresponds to Classical Procrustes analysis but the choice of criterion that fits each configuration to the common centroid configuration avoids difficulties that arise when one set is fitted to the other, regarded as fixed.
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Generalized Procrustes Superimposition was carried out on original and reflected images to remove differences in position and orientation.
“Generalized Procrustes Superimposition [24] was carried out on both sets of images (original and reflected) to remove differences in position and orientation.”
From Investigating the case of human nose shape and climate adaptation (2017) · cites this paper as [24]
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- Authors
- Gower, J. C.
- Affiliations
- Rothamsted Research (GB)
- Corresponding author
- Gower, J. C.
- Venue
- Psychometrika
- Publisher
- Cambridge University Press (CUP)
- Published
- 1975-03
- Volume
- 40
- Issue
- 1
- Pages
- 33-51
- ISSN
- 0033-3123 (ISSN-L)
- 1860-0980
- OpenAlex
- W2032618685
- Cited by
- 3,267
- References
- 13
- Citations by year
- 2026: 154 · 2025: 186 · 2024: 177 · 2023: 179 · 2022: 172 · 2021: 204 · 2020: 180 · 2019: 184 · 2018: 162 · 2017: 137 · 2016: 150 · 2015: 108 · 2014: 124 · 2013: 118 · 2012: 110
- FWCI
- 4.68
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Psychometrika (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- generalized Procrustes analysis, translation and rotation, scaling, goodness-of-fit criteria, analysis of variance
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