Finding Meaningful and Stable Clusters Using Local Cluster Analysis

Abstract

Let us consider the problem of finding clusters in a heterogeneous, high-dimensional setting. Usually a (global) cluster analysis model is applied to reach this aim. As a result, often ten or more clusters are detected in a heterogeneous data set. The idea of this paper is to perform subsequent local cluster analyses. Here the following two main questions arise. Is it possible to improve the stability of some of the clusters? Are there new clusters that are not yet detected by global clustering? The paper presents a methodology for such an iterative clustering that can be a useful tool in discovering stable and meaningful clusters. The proposed methodology is used successfully in the field of archaeometry. Here, without loss of generality, it is applied to hierarchical cluster analysis. The improvements of local cluster analysis will be illustrated by means of multivariate graphics.