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Procrustes Problems$
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John C Gower and Garmt B Dijksterhuis

Print publication date: 2004

Print ISBN-13: 9780198510581

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198510581.001.0001

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Initial transformations

Initial transformations

(p.11) 2 Initial transformations
Procrustes Problems

J. C. Gower

G. B. Dijksterhuis

Oxford University Press

This chapter discusses initial transformations that may be useful before embarking on a Procrustes analysis proper. Data-scaling and configuration-scaling are the terms adopted for the many kinds of transformations that may be deemed desirable before embarking on the actual Procrustes matching. The aim of these is to eliminate possible incommensurabilities of variables within the individual data sets (data-scaling) and size differences between data sets (configuration-scaling). Although some choices of data-scaling have clear justification, other choices are largely subjective. The form and source of the data should help decide what, if any, data-scaling is needed. Three main types of data are considered: (i) sets of coordinates derived from some form of multidimensional scaling (MDS) or, in the case of shape studies, directly measured landmark coordinates; (ii) data matrices whose columns refer to different variables; and (iii) sets of loadings derived from factor analysis.

Keywords:   Procrustes analysis, data-scaling, configuration-scaling, data sets

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