Comparing weighted combination of hierarchical clustering based on Cophenetic measure

Abstract

In Hierarchical Clustering (HC), a set of patterns is partitioned into a sequence of groups and the results are repre- sented by a dendrogram. The dendrogram is a tree representation where each node is associated with merging of two (or more) partitions and hence each partition is nested into the next partition. Hierarchical representation has valuable properties that are useful for visualization and interpretation of the clustering results. On one hand, it is well known that hierarchical clustering results are sensitive to the algorithms that are used, thus different dendrograms are created. On the other hand, clustering com- bination methods have demonstrated promising results. This motivated us to consider different combination method for a set of dendrograms. In this paper, we compare several weighted combination methods in which the hierarchical clustering results are used in order to derive a consensus hierarchical clustering. The Cophenetic measures are used for comparison. The results illustrate that the proposed weighing combination of hierarchical clusterings perform better than other combinations such as averaging.