Combined Procrustes analysis and PLSR for internal and external mapping of data from multiple sources

Abstract

Generalised Procrustes analysis (GPA) is a method for producing a group average from rotated versions of a set of individual data matrices followed by bi-linear approximation of this group average for graphical inspection. Partial Least Squares Regression (PLSR) is a method for relating one data matrix to another data matrix, via bi-linear low-rank regression modelling. The merger of these methods proposed aims to produce an average (e.g. a sensory group panel average), which balances an “intersubjective”, internal consensus between the individual assessors’ data against an “objective” external correspondence between the sensory data and other types of data on the same samples (e.g. design information, chemical or physical measurements or consumer data). Several ways of merging GPA with PLSR are possible, of which one is selected and applied. The proposed “GP–PLSR” method is compared to a conventional GPA followed by an independent PLSR, using a data set about milk samples assessed by a group of sensory judges with respect to a set of sensory descriptor terms, and also characterised by experimental design information about the samples. The GP–PLSR gave a more design-relevant group average than traditional GPA. The proposed algorithm was tested under artificially increased noise levels.