Generalized Procrustes analysis
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Generalized Procrustes analysis (GPA) is a method of statistical analysis that can be used to compare the shapes of objects, or the results of surveys, interviews, panels. It was developed for analyising the results of free-choice profiling, a survey technique which allows respondents (such as sensory panelists) to describe a range of products in their own words or language. GPA is the one way to make sense of free-choice profiling data (Meullenet et al., 2007), other ways can be multiple factorial analysis (Escofier & Pagès, 1990), or the STATIS method (Lavit et al., 1990).
Generalized Procrustes analysis estimates the scaling factor applied to respondent scale usage, thus it generates a weighting factor that is used to compensate for individual scale usage differences. Unlike measures such as a principal component analysis, since GPA uses individual level data, a measure of variance is utilized in the analysis.
The Procrustes distance provides a metric to minimize in order to superimpose a pair of shape instances annotated by landmark points. GPA applies the Procrustes analysis method to superimpose a population of shapes instead of only two shape instances.
The algorithm outline is the following:
- arbitrarily choose a reference shape (typically by selecting it among the available instances)
- superimpose all instances to current reference shape
- compute the mean shape of the current set of superimposed shapes
- if the Procrustes distance between the mean shape and the reference is above a threshold, set reference to mean shape and continue to step 2.
See also
References
- I.L. Dryden and K.V. Mardia (1998). Statistical Shape Analysis. John Wiley & Sons. ISBN 0471958166.
- J.F. Meullenet, R. Xiong, and C.J. Findlay (2007). Multivariate and Probabilistic Analyses of Sensory Science Problems. IFT Press & Blackwell Publishing. ISBN 0813801780.
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