Classification tree algorithms for grouped variables
Résumé
The problem of predicting a binary variable is considered when a p-dimensional vector of inputs is available. These inputs are structured in a number of known groups. The objective is to take this structure into account to build a classification tree. Two tree-based approaches are proposed: the Tree Linear Discriminant Analysis algorithm (TLDA) and the Tree Penalized Linear Discriminant Analysis algorithm (TPLDA). They consist in splitting a node by repeatedly selecting a group of inputs and then applying a linear dis-criminant method based on this group. This process is iterated until some stopping criterion is satisfied. A pruning strategy is proposed to select an optimal tree. The two algorithms differ in the discriminant method used in the splitting process: TLDA applies a linear discriminant analysis (LDA) while TPLDA performs a regularized linear discriminant analysis. These two proposed methods are computationally less demanding than classical existing multivariate classification tree methods. Moreover, the resulting trees are more easily interpretable. The good performances of the proposed algorithms and the interest of using them in terms of classification accuracy and interpretation are demonstrated in comparison with alternative reference methods (CART, group-lasso logistic regression) though applications on simulated and real gene expression data.
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