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Table 2 Description of common agglomerative metrics used as cluster merging criteria

From: A reference guide for tree analysis and visualization

   Agglomerative Methods
Abbreviation Full Name Description
single Single Linkage Merge those clusters for which the minimum distance between their elements is the least one.
complete Complete Linkage Merge those clusters for which the maximum distance between their elements is the least one.
average Average Linkage Merge those clusters for which the mean distance between their elements is the least one.
centroid Centroid Method Merge those clusters for which the (squared) Euclidean distance between their centroids or means is the least one.
median Median Method Merge those clusters for which the Euclidean distance between their weighted centroids is the least one; called median because the centre of each new cluster is based on the combination of the centroids of the merged groups.
ward Ward's Criterion, or else Ward's Minimum-Variance Method Merge those clusters for which the increase in variance for the resulting group is the least one.
EML EML Merge those clusters that maximize the likelihood at each level of the resulted hierarchy; similar to Ward's method but removes the bias toward equal-sized clusters.
density Density Linkage Merge those clusters for which the probability density estimate for the resulting group is maximized; consists of two steps: 1. the dissimilarity measure is based on reciprocals of the estimates of the density midway between the members of each cluster within a defined area or otherwise is infinite, 2. a single linkage cluster analysis follows. (Examples of different types of density methods are the kth-nearest-neighbor, the uniform kernel and the Wong's hybrid ones which among others differ with respect to the neighbourhood within which the density is measured)
mcquitty McQuitty's Similarity Analysis Merge those clusters for which the average of their distances, or else the distance of the resulting group, from the remaining ones is minimal.