Hierarchical Cluster Analysis

Abstract

Hierarchical cluster analysis produces a unique set of nested categories or clusters by sequentially pairing variables, clusters, or variables and clusters. At each step, beginning with the correlation matrix, all clusters and unclustered variables are tried in all possible pairs, and that pair producing the highest average intercorrelation within the trial cluster is chosen as the new cluster. In contrast to other types of cluster analysis in which a single set of mutually exclusive and exhaustive clusters is formed, this technique proceeds sequentially from tighter, less inclusive clusters through larger more inclusive clusters and is continued until all variables are clustered in a single group. A graph, constructed like the taxonomic dendrogram of the biological systematist, shows the class-inclusive relations between clusters and the value of the clustering criterion associated with each.