Generalized Procrustes analysis
 | It has been suggested that this article be merged into Procrustes analysis. (Discuss) Proposed since June 2008. |
The origin of Generalized Procrustes Analysis (GPA) has a strong basis in the comparison of research results across languages (term 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. Generalized Procrustes analysis (GPA) is a procedure applying the aforementioned Procrustes analysis method to align a population of shapes instead of only two shape instances.
GPA This is one of the methods achieving this goal, namely useful to build a Point Distribution Model or to undertake any shape study on the training set. 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 proscrustes distance between the mean shape and the reference is above a threshold, set reference to mean shape and continue to step 2.
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.