Generalized Procrustes Analysis

Generalized Procrustes Analysis (GPA) is a multivariate exploratory technique that involves transformations (i.e., translation, rotation, reflection, isotropic rescaling, Figure 1) of individual data matrices to provide optimal comparability. The average of the individual matrices is called the consensus matrix. Procrustes Analysis (GPA) is a multivariate technique used to analyze data from different panelists1. It was initially developed for use in analyzing data generated from Free Choice Profiling (FCP). GPA equalizes the terms/attributes and scale usage used in the panelist-specific vocabularies from FCP. Instead of using mean values like PCA, GPA uses individual scores to account for any variance. Since all panelists evaluate the same samples, the samples remain constant and do not vary3.

The individual and consensus matrices are typically submitted to Principal Components Analysis (PCA) and projected onto a lower dimensional space. This space provides a vantage point to compare individual data and to visualize the consensus. In theory, the matrix transformation processes can be assumed to help hone in on underlying perceptual phenomena independent of scaling artefacts.Generalized Analysis of variance (ANOVA) may be run on the data to identify significant attributes. Subsequent GPA can demonstrate the product/attribute and the panelist scores in the sensory space. Combined with ANOVA, recognizing singular panelists is straightforward. The graphical representation of GPA is easy to interpret as vectors illustrate the distance of panelist responses from the origin. This also indicates relationships between panelists and products, including product differences and panelist agreement (indicating outliers, etc). PCA by attribute may be conducted on the data as well. However, it is not as visually pleasing or easy to interpret with regard to panelist agreement2. GPA is popular among sensory professionals as a way to combine data from different individual assessors. GPA is especially useful for free choice profiling or flash profiling, because it can accommodate different numbers and kinds of attributes among assessors. Moreover, GPA can be used to visually describe different effects, such as product differences, assessor agreement, and repeatability. Significance of these different effects can actually be tested with GPA permutation tests.

Figure 1. Procrustes analysis: translation, rotation and reflection, and isotropic scaling

References

1 Gower, JC. 1975. Generalized procrustes analysis. Psychometrika, 40, 33-51.

2 Meullenet, JF, Xiong, R, and Findlay, C. 2007. Multivariate and Probabilistic Analyses of Sensory Science Problems. Iowa: Blackwell Publishing Professional.

3 Xiong, R, Meullenet, J-F, and Dessirier, JM. 2008. Permutation tests for Generalized Procrustes Analysis. Food Quality and Preference, 19, 146-155.