Clustering of Variables Around Latent Components

Clustering of variables around latent components is investigated as a means to organize multivariate data into meaningful structures. The coverage includes (i) the case where it is desirable to lump together correlated variables no matter whether the correlation coefficient is positive or negative; (ii) the case where negative correlation shows high disagreement among variables; (iii) an extension of the clustering techniques which makes it possible to explain the clustering of variables taking account of external data. The strategy basically consists in performing a hierarchical cluster analysis, followed by a partitioning algorithm. Both algorithms aim at maximizing the same criterion which reflects the extent to which variables in each cluster are related to the latent variable associated with this cluster. Illustrations are outlined using real data sets from sensory studies.