The Last Step of a New Divisive Monothetic Clustering Method: the Gluing-Back Criterion

Pirçon and Rasson (2003) propose a divisive monothetic clustering method. In that work, the selection of relevant variables is performed simultaneously with the formation of clusters. The method treats only one variable at each stage; a single variable is chosen to split a cluster into two sub-clusters. Then the sub-clusters are successively split until a stopping criterion is satisfied. The original splitting criterion is the solution of a maximum likelihood problem conditional on the fact that data are generated by a nonhomogeneous Poisson process on two disjoint intervals. The criterion splits at the place of the maximum integrated intensity between two consecutive points.This paper extends Pirçon and Rasson (2003) by developing “gluing-back” criterion. The previous work explained the new method for combining trees and nonhomogenous Poisson processes and the splitting criterion. It was shown that the maximum likelihood criterion reduces to minimization of the integrated intensity on the domain containing all of the points. This method of clustering is indexed, divisive and monothetic hierarchical, but its performance can be improved through a gluing-back criterion. That criterion is developed in this paper, after a brief review of the main ideas.