Implementing bootstrap in ward´s algorithm to estimate the number of clusters

Resumen

In this paper we show how bootstrap can be implemented in hierarchical clustering algorithms as a strategy to estimate the number of clusters (k). Ward´s algorithm was chosen as an example. The estimation of k is based on a similarity coefficient and three statistical stopping rules, pseudo F, pseudo T² and CCC. The performance of the estimation procedure was evaluated through Monte Carlo simulation considering data consisting of correlated and uncorrelated variables, nonoverlapping and overlapping clusters. The estimation procedure discussed in this paper can be used with clustering algorithms other than Ward´s and also to provide initial solutions for non-hierarchical grouping methods.