WPGMA

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

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

The WPGMA algorithm constructs a rooted tree (dendrogram) that reflects the structure present in a pairwise distance matrix (or a similarity matrix). At each step, the nearest two clusters, say ${\displaystyle i}$ and ${\displaystyle j}$, are combined into a higher-level cluster ${\displaystyle i\cup j}$. Then, its distance to another cluster ${\displaystyle k}$ is simply the arithmetic mean of the distances between ${\displaystyle k}$ and members of ${\displaystyle i\cup j}$ :

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