UPGMA

Unweighted Pair Group Method with Arithmetic mean ( UPGMA short ) refers to a bottom-up clustering method. It is often used in bioinformatics for reconstructing phylogenetic trees. In contrast to other techniques such as Neighbor Joining UPGMA based on the assumption of molecular clock, ie that all taxa evolve at the same constant rate.

Given a set of objects and a distance matrix comprising the distances between the pair of objects, wherein the distance measure must have the properties of an ultra- metric. Wanted is a binary tree whose leaves represent objects, and whose edges as closely as possible reflect the distances in the distance matrix.

Initially, each object in its own cluster. In each step, the two clusters with the smallest distance are combined, and calculates the distance matrix new. The distance between two clusters is the average of the distances of all pairs of objects in two clusters. Be the new cluster was formed from the two clusters and: .

The distance to a cluster is then calculated at WPGMA as follows:

If a different number of objects in a cluster, so these do not contribute equally in WPGMA for the distance calculation of the new cluster at. The distances are so in calculating weighted differently (hence weighted PGMA ).

If one uses the improved UPGMA, then the new distances calculated with:

This causes all distances equal, ie unweighted ( unweighted ), be included in the distance calculation.

The simple average of the WPGMA gives a weighted result, while the proportional average of the unweighted UPGMA a result.