A simultaneous non-symmetrical principal component analysis with a group structure

The aim of this paper is to propose an extension of Principal Component Analysis onto a Reference Subspace (PCAR) to the case where the same dependent variables have been measured on the same statistical units under two, or more, different observational conditions. As the units belong to the same multidimensional space, we profitably apply the orthogonal Procrustean rotations, jointly with PCAR, so as to enrich the interpretability of patterns on factorial planes. The proposed technique is applied to a problem of agreement in the area of sensory data analysis for representing evaluation gaps between the perception of quality by wine experts and ordinary consumers. The proposed approach allows to explain the eventually detected gaps in terms of the physical-chemical characteristics of wines