UPGMA

UPGMA (Unweighted Pair Group Method with Arithmetic Mean) is a simple agglomerative (bottom-up) hierarchical clustering method. The method is generally attributed to Sokal and Michener.

The UPGMA method is similar to its weighted variant, the WPGMA method.

Note that the unweighted term indicates that all distances contribute equally to each average that is computed and does not refer to the math by which it is achieved. Thus the simple averaging in WPGMA produces a weighted result and the proportional averaging in UPGMA produces an unweighted result (see the working example).

The UPGMA algorithm constructs a rooted tree (dendrogram) that reflects the structure present in a pairwise similarity matrix (or a dissimilarity matrix). At each step, the nearest two clusters are combined into a higher-level cluster. The distance between any two clusters A and B, each of size (i.e., cardinality) ${\displaystyle {|{\mathcal {A}}|}}$ and ${\displaystyle {|{\mathcal {B}}|}}$, is taken to be the average of all distances ${\displaystyle d(x,y)}$ between pairs of objects ${\displaystyle x}$ in ${\displaystyle {\mathcal {A}}}$ and ${\displaystyle y}$ in ${\displaystyle {\mathcal {B}}}$, that is, the mean distance between elements of each cluster:

...
Wikipedia