Cluster analysis: a further approach based on density estimation

A cluster methodology, motivated via density estimation, is proposed. It is based on the idea of estimating the population clusters, which, following Hartigan (1975), are defined as the connected parts of the substantial support of the underlying density. The empirical clusters are defined by analogy in terms of the substantial support of a convolution (kemel-type) density estimator. The sample observations are grouped into data clusters, according to the empirical cluster they belong. An algorithm to implement the method, based on resampling ideas, is proposed. It allows either to automatically choose the number of clusters or to give this number as an input. Some theoretical and practical aspects are briefly discussed and a simulation study is given. The results show a good performance of our method, in terms of efficiency and robustness, when compared with two classical cluster algorithms: k-means and single linkage. Finally, a real-data example is discussed. (C) 2001 Elsevier Science B.V. All rights reserved.