Comparing Model Selection and Regularization Approaches to Variable Selection in Model-Based Clustering

Celeux, Gilles; Martin-Magniette, Marie-Laure; Maugis-Rabusseau, Cathy; Raftery, Adrian E.

Journal de la société française de statistique, Tome 155 (2014) no. 2, pp. 57-71.

Nous considérons deux approches importantes pour la sélection de variables en classification non supervisée : la sélection par modèle et la régularisation. Parmi les procédures existantes de sélection de variables par sélection de modèles, nous choisissons la méthode de Maugis et al. (2009b), généralisation de celle de Raftery et Dean (2006). Pour les méthodes fondées sur la régularisation, nous nous intéressons à la méthode de Witten and Tibshirani (2010). Nous comparons les performances de classification et de sélection de variables de ces deux procédures sur des données simulées. Nous montrons que la sélection de variables permet d’améliorer la classification quand les classes sont bien séparées. Les deux procédures de sélection de variables étudiées donnent des classifications analogues dans le premier exemple, mais l’approche par sélection de modèles a de meilleures performances pour la sélection de variables. Dans le second exemple, les variables sont corrélées. Nous montrons que l’approche par sélection de modèles améliore globalement la classification et la sélection de variables par rapport à la régularisation, et les deux procédures donnent de meilleurs résultats que l’algorithme des $K$-means (sans sélection de variables) pour la classification. Mais, il convient de noter que la sélection par modèles est inopérante pour les très grandes dimensions. Enfin, ce travail de comparaison est également mené sur des données réelles.

We compare two major approaches to variable selection in clustering: model selection and regularization. Based on previous results, we select the method of Maugis et al. (2009b), which modified the method of Raftery and Dean (2006), as a current state of the art model selection method. We select the method of Witten and Tibshirani (2010) as a current state of the art regularization method. We compared the methods by simulation in terms of their accuracy in both classification and variable selection. In the first simulation experiment all the variables were conditionally independent given cluster membership. We found that variable selection (of either kind) yielded substantial gains in classification accuracy when the clusters were well separated, but few gains when the clusters were close together. We found that the two variable selection methods had comparable classification accuracy, but that the model selection approach had substantially better accuracy in selecting variables. In our second simulation experiment, there were correlations among the variables given the cluster memberships. We found that the model selection approach was substantially more accurate in terms of both classification and variable selection than the regularization approach, and that both gave more accurate classifications than $K$-means without variable selection. But the model selection approach is not available in a very high dimension context.

Keywords: Model-based clustering, Model selection, Regularization approach, Variable selection
Mot clés : Classification non supervisée, Mélanges gaussiens, Régularisation, Sélection de modèles, Sélection de variables

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