Unsupervised Energy Trees: Clustering With Complex and Mixed-Type Variables

In the spirit of the recently developed and successful Object Oriented Data Analysis, we introduce Energy Trees as a model to perform classification and regression using complex and mixed-type covariates. Energy Trees may be seen as a generalization of Conditional Trees, where the testing procedures that characterize both variable selection and stopping criterion are here performed by means of Energy Statistics. The use of Energy Statistics allows to compare variables that need not to be defined on the same space, thus permitting to simultaneously model complex and mixed-type covariates. In this contribution we show how, adapting the main scheme offered in the literature to perform unsupervised learning using treelike methods, Energy Trees can also be used to perform clustering on structured and mixed-type data, giving rise to the proposed Unsupervised Energy Trees.