Arithmetic averaging attempts to avoid the extremes of the single-link and complete-link methods.
When measuring the dissimilarity between an existing cluster and a prospective cluster, the single-link method finds the closest pair of objects in the two clusters, the complete-link methods finds the most distant pair
The UPGMA (Unweighted pair group method using arithmetic averages) and WPGMA (Weighted pair group method using arithmetic averages) methods use arithmetic averages of the dissimilarities. The arithmetic averaging methods have no simple geometric interpretation.
In contrast, the UPGMC (unweighted pair group method using centroids) and WPGMC (weighted pair group method using centroids) methods have direct geometric interpretations when the objects are represented as patterns in a d-dimensional space. The centroid method assess the dissimilarity between two clusters by the distance between centroids. The UPGMC method measures distance in terms of the centroid computed from all patterns in each cluster. The WPGMC method computes centroids from the centroids of the two clusters that merge to form a new cluster.