Generalized Procrustes analysis
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The origin of generalized Procrustes analysis (GPA) has a strong basis in the comparison of research results across languages (terms from interviews, surveys, panels, etc). It was developed to permit statistical analysis of the results of free-choice profiling which allows respondents (such as sensory panelists) to develop their own terms for attributes that describe a range of products in their own wods or language (Meullenet, Xiong, and Findlay, 2007). GPA is the only way to make sense of free-choice profiling data.
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 components 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 align a pair of shape instances annotated by landmark points. GPA applies the Procrustes analysis method to align a population of shapes instead of only two shape instances.
The algorithm outline is the following:
- choose a reference shape among the training set instances
- align all other instances on current reference
- compute the mean shape of the current training set
- 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
- 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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- I.L. Dryden and K.V. Mardia (1998). Statistical Shape Analysis. John Wiley & Sons. ISBN 0471958166.