Generalized Procrustes analysis

A powerful technique which allows to answer such questions is Generalized Procrustes Analysis (GPA). This is a generalization of the Procrustes rotation method to the case of more than two data sets. As explained in Chapter 36 Procrustes analysis applies three basic operations to each data set with the objective to optimize their similarity, i.e. to reduce their distance. Each data set can be seen as defining a configuration of its rows (objects, food samples, products) in a space defined by the columns (sensory attributes) of that data set. In geometrical terms the (squared) distance between two data sets equals the sum over the squared distances between the two positions (one for data set and one for Xg) for each object. 

S. de Jong, J. Heidema and H.C.M. van der Knaap, Generalized Procrustes analysis of coffee brands tested by five European sensory panels. Food Qual. Pref., 9 (1998) 111-114. 

Le Fur, Y, Mercurio, V., Moio, L., Blanquet, J., and Meunier, J.M. (2003). A new approach to examine the relationships between sensory and gas chromatography-olfactometry data using generalized procrustes analysis applied to Six French Chardonnay wines. J. Agric. Food Chem., 5i, 443-452. 

Endeavors have been made to find a link between two data sets (sensory versus instrumental data). The common goal of these tools is to discover the components or parameters whose variation explains the variation of sensory characteristics. The most useful statistical methods used for such purpose are partial least squares regression and generalized procrustes analysis. From a practical point of view, the models can be used to complement sensory assessment in routine quality control or in product and process development work. Regression-based statistical techniques are often used in conjunction with GC to distinguish well-known brands of alcoholic beverages from less expensive ones to detect counterfeit products. 

The main result provided by FP is a sensory map. To this end, the individual data tables can be compiled and analysed by the means of a multi-block data analysis technique, such as generalized Procrustes analysis (GPA) (Gower, 1975 Dijksterhuis, 1996), multiple factor analysis (MFA) (Escofier and Pag6s, 2008) or STATIS (Lavit, 1988 Lavit et al., 1994). Figure 6.3 shows the map of the first two principal components obtained by GPA. 

King, B. M. and Arents, P. (1991). A statistical test of consensus obtained from generalized procrustes analysis of sensory data. Journal of Sensory Studies, 6, 37—48. 

Xiong, R., Blot, K., Meullenet, J. F. and Dessirier, J. M. (2008). Permutation tests for generalized procrustes analysis. Food Quality and Preference, 19, 146-155. 

Nevertheless, data can be seen another way. If we consider the poles as metadescriptors - for the taste of water, Volvic could be a metalhc and bitteT descriptor, Evian tasteless and cool and Vittel salty and astringent - data can be encoded this way from 0 for totally different taste to 10 for same taste . We now consider the intensities of each sample on several descriptors, and classical factorial analyses such as Principal Component Analysis (PCA), Multiple Factorial Analysis (MFA), Statis or Generalized Procrustes Analysis (GPA) can be processed (Fig. 10.3). 

The data were collected on Microsoft Excel spreadsheets. Generalized Procrustes analysis (GPA) (Gower, 1975) was applied to the data from Flash Profile to assess the consensus between perfumers sensory maps. 

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