. 2017 Jun 14;12(6):e0179180. doi: 10.1371/journal.pone.0179180

Table 1. Parameters of various hierarchical clustering methods.

β, ɣ: corrections based on the triangle ijk; Dissimilarity [E2: Euclidean distance; E2′: half of the squared Euclidean distance]; Monotony [monotonically increasing lengths (We note that this is not true in the centroid and median methods. The value of a monotonic increase depends on the particular situation.); T: true; F: false;]; Metric [expansion & reduction: renewal of ongoing clustering by increasing or reducing the distance between data points].

method	α_i	α_j	β	ɣ	Dissimilarity	Monotony	Metric
single	1/2	1/2	0	−1/2	no restriction	T	reduction
complete	1/2	1/2	0	1/2	no restriction	T	expansion
group average	$\frac{n_{i}}{n_{i} + n_{j}}$	$\frac{n_{j}}{n_{i} + n_{j}}$	0	0	no restriction	T	conserved
weighted average	1/2	1/2	0	0	no restriction	T	conserved
centroid	$\frac{n_{i}}{n_{i} + n_{j}}$	$\frac{n_{j}}{n_{i} + n_{j}}$	$\frac{{- n}_{i} n_{j}}{{{(n}_{i} + n_{j})}^{2}}$	0	E2	F	conserved & reduction
median	1/2	1/2	−1/4	0	E2	F	conserved & reduction
Ward	$\frac{n_{i} + n_{k}}{n_{i} + n_{j} + n_{k}}$	$\frac{n_{j} + n_{k}}{n_{i} + n_{j} + n_{k}}$	$\frac{- n_{k}}{n_{i} + n_{j} + n_{k}}$	0	E2′	T	conserved & expansion