Vanessa Kuentz

A Partitioning Method for the Clustering of Categorical Variables

In the framework of clustering, the usual aim is to cluster observations and not variables. However the issue of clustering variables clearly appears for dimension reduction, selection of variables or in some case studies. A simple approach for the clustering of variables could be to construct a dissimilarity matrix between the variables and to apply classical clustering methods. But specific methods have been developed for the clustering of variables. In this context center-based clustering algorithms have been proposed for the clustering of quantitative variables. In this article we extend this approach to categorical variables. The homogeneity criterion of a cluster of categorical variables is based on correlation ratios and Multiple Correspondence Analysis is used to determine the latent variable of each cluster. A simulation study shows that the method recovers well the underlying simulated clusters of variables. Finally an application on a real data set also highlights the practical benefits of the proposed approach.

Bagging Versions of Sliced Inverse Regression

Sliced Inverse Regression (SIR) introduced by Li (1991) is a well-known dimension reduction method in semiparametric regression. In this article, we propose bagging versions of SIR which consist in using bootstrap replications of the data set and in aggregating the corresponding estimators. We give the asymptotic distribution of the Bagging-SIR estimator. A simulation study is used to compare the numerical performance of the proposed alternative bagging versions of SIR with the classical SIR approach. The benefits of these methods are significant for noisy models and when the sample size is small. The R codes are available from the authors.

Sliced Inverse Regression for stratified population

In this article, we consider a semiparametric single index regression model involving a real dependent variable Y, a p-dimensional quantitative covariable X, and a categorical predictor Z which defines a stratification of the population. This model includes a dimension reduction of X via an index X′β. We propose an approach based on sliced inverse regression in order to estimate the space spanned by the common dimension reduction direction β. We establish -consistency of the proposed estimator and its asymptotic normality. Simulation study shows good numerical performance of the proposed estimator in homoscedastic and heteroscedastic cases. Extensions to multiple indices models, q-dimensional response variable, and/or SIRα-based methods are also discussed. The case of unbalanced subpopulations is treated. Finally, a practical method to investigate if there is or not a common direction β is proposed.

Pollution sources detection via principal component analysis and rotation

Air pollution is a widely preoccupation which needs the development of control strategies. To reach this goal, pollution sources have to be precisely identified. Principal component analysis is a possible response to this problem. Indeed this factorial method enables to detect sources, that is to have a qualitative description of them. In this work, techniques of rotation are a useful help for the association of variables with factors. We highlight the fact that the rotation must be applied to the standardized principal components, so as to keep good interpretation properties. This methodology has then been applied to a problem of air pollution on a french site.