Generalized Procrustes analysis

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 only way to make sense of free-choice profiling data (Meullenet et al., 2007).

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 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:

1. choose a reference shape among the training set instances
2. align all other instances on current reference
3. compute the mean shape of the current training set
4. 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

• Procrustes analysis
• Orthogonal Procrustes problem

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.{{cite book}}: CS1 maint: multiple names: authors list (link)

• I.L. Dryden and K.V. Mardia (1998). Statistical Shape Analysis. John Wiley & Sons. ISBN 0471958166.