Bicriterion Cluster Analysis as an Exploration Tool

Abstract

Let O denote a set of N entities and D = (d_kl) a matrix of dissimilarities defined on OxO. The diameter of a partition of O into M clusters is defined as the maximum dissimilarity between entities in the same cluster, and the split of such a partition as the minimum dissimilarity between entities in different clusters. A partition of O into M clusters is called efficient if and only if there is no partition of O into not more clusters with smaller diameter and not smaller split or with larger split and not larger diameter. A graph-theoretic algorithm which allows to obtain a complete set of efficient partitions is described. Then are presented some experiments, designed to evaluate the potential of bicriterion cluster analysis as a tool for the exploration of data sets, i.e. for detecting the underlying structure of O, if and when it exists. Both real data sets on psychological tests and on stock prices, and artificial data sets are considered. The ability of bicriterion cluster analysis to detect the best clusterings in many cases and to show whether or not there are some natural clusterings is clearly evidenced.