UPGMA

UPGMA (Unweighted Pair Group Method with Arithmetic Mean) is a simple agglomerative or hierarchical clustering method used in bioinformatics for the creation of phenetic trees (phenograms). UPGMA assumes a constant rate of evolution (molecular clock hypothesis), and is not a well-regarded method for inferring relationships unless this assumption has been tested and justified for the data set being used. UPGMA was initially designed for use in protein electrophoresis studies, but is currently most often used to produce guide trees for more sophisticated phylogenetic reconstruction algorithms.

The algorithm examines the structure present in a pairwise distance matrix (or a similarity matrix) to then construct a rooted tree (dendrogram).

At each step, the nearest two clusters are combined into a higher-level cluster. The distance between any two clusters A and B is taken to be the average of all distances between pairs of objects "x" in A and "y" in B, that is, the mean distance between elements of each cluster:

${1 \over {|\mathcal{A}|\cdot|\mathcal{B}|}}\sum_{x \in \mathcal{A}}\sum_{ y \in \mathcal{B}} d(x,y)$

The method is generally attributed to Sokal and Michener. Fionn Murtagh found a time optimal O(n²) time algorithm to construct the UPGMA tree.

See also

• Neighbor-joining
• Cluster analysis
• Single-linkage clustering
• Complete-linkage clustering
• Hierarchical clustering

External links

• UPGMA clustering algorithm implementation in Ruby (AI4R)
• Example calculation of UPGMA using a similarity matrix
• Example calculation of UPGMA using a distance matrix