Unweighted Multiple Group Method with Arithmetic Mean

The traditional UPGMA (Unweighted Pair Group Method with Arithmetic Mean) sometimes derives two or more topologies of “tie trees” from a single data set, depending on the order of data entry. This paper presents an improved algorithm for UPGMA, namely, UMGMA (Unweighted Multiple Group Method with Arithmetic Mean), which can produce a unique multifurcating tree from any distance matrix. Moreover, a UMGMA tree has the same topology as its corresponding UPGMA tree if it is actually bifurcating. UMGMA is different from UPGMA in that it repeatedly merges multiple groups into one by the vertices of a maximal θ-distant subtree until only one group is left, so the UMGMA tree is always unique even in the case that the UPGMA tree is not unique.