Vanessa Kuentz (Institut de Mathématiques à l'Université de Bordeaux), “Clustering of variables around latent variables”, Statistics Seminar, Toulouse : TSE, September 29, 2009, 15:30–16:30, room MF 323.
Clustering of variables is studied as a way to arrange variables into homogeneous clusters, thereby organizing data into meaningful structures. Once the variables are clustered into groups such that variables are similar to the other variables belonging to their cluster, the selection of a subset of variables is possible. Several specific methods have been developed for the clustering of numerical variables. However concerning categorical variables, much less methods have been proposed. In this paper we extend the criterion used by Vigneau and Qannari (2003) in their Clustering around Latent Variables approach for numerical variables to the case of categorical data. The homogeneity criterion of a cluster of categorical variables is defined as the sum of the correlation ratio between the categorical variables and a latent variable, which is in this case a numerical variable. We show that the latent variable maximizing the homogeneity of a cluster can be obtained with Multiple Correspondence Analysis. Different algorithms for the clustering of categorical variables are proposed: iterative relocation algorithm, ascendant and divisive hierarchical clustering. The proposed methodology is illustrated by a real data application to satisfaction of pleasure craft operators.
clustering of categorical variables; correlation ratio; iterative relocation algorithm; hierarchical clustering