Clustering using Unsupervised Binary Trees: CUBT

We introduce a new clustering method based on unsupervised binary trees. It is a three stages procedure, which performs on a first stage recursive binary splits reducing the heterogeneity of the data within the new subsamples. On the second stage (pruning) adjacent nodes are considered to be aggregated. Finally, on the third stage (joining) similar clusters are joined even if they do not descend from the same node. Consistency results are obtained and the procedure is tested on simulated and real data sets.