Linear and non-linear canonical correlation analysis:an exploratory tool for the analysis of group-structured data

Confronted with multivariate group-structured data, one is in fact always interested in describing differences between groups. In this paper, canonical correlation analysis (CCA) is used as an exploratory data analysis tool to detect and describe differences between groups of objects. CCA allows for the construction of Gabriel biplots, relating representations of objects and variables in the plane that best represents the distinction of the groups of object points. In the case of non-linear CCA, transformations of the original variables are suggested to achieve a better group separation compared with that obtained by linear CCA. One can detect which (transformed) variables are responsible for this separation. The separation itself might be due to several characteristics of the data (eg. distances between the centres of gravity of the original or transformed groups of object points, or differences in the structure of the original groups). Four case studies give an overview of an exploration of the possibilities offered by linear and non-linear CCA.