Clustering of variables via the PCAMIX method

Clustering of variables is as a way to arrange variables into homogeneous clusters i.e. groups of variables which are strongly related to each other and thus bring the same information. Clustering of variables can then be useful for dimension reduction and variable selection. Several specific methods have been developed for the clustering of numerical variables. However concerning qualitative variables or mixtures of quantitative and qualitative variables, much less methods have been proposed. The ClustOfVar package has then been developped specifically for that purpose. The homogeneity criterion of a cluster is the sum of correlation ratios (for qualitative variables) and squared correlations (for quantitative variables) to a synthetic variable, summarizing as good as possible the variables in the cluster. This synthetic variable is the first principal component obtained with the PCAMIX method. Two algorithms for the clustering of variables are proposed: iterative relocation algorithm, ascendant hierarchical clustering. We also propose a bootstrap approach to determine suitable numbers of clusters. The proposed methodologies are illustrated on real datasets