Linkage Method Explorer

Single, complete, average and Ward linkage on the same points — four dendrograms, four different stories.

  • hierarchical clustering
  • linkage
  • dendrogram
  • Ward

Ward linkage (K=3)

-4-3-2-10123-2-10123PC1PC2

Single linkage (K=3)

-4-3-2-10123-2-10123PC1PC2

Complete linkage (K=3)

-4-3-2-10123-2-10123PC1PC2

Mean silhouette width by linkage

-0.500.511.522.500.10.20.30.40.50.60.7Linkage methodMean silhouette width

Orange = weak structure, green = strong structure thresholds at 0.25 / 0.50.

Cluster sizes

MethodSizesMinMaxMax/Min ratio
Ward20 / 47 / 7320.00073.0003.6
Single133 / 2 / 52.000133.00066.5
Complete8 / 36 / 968.00096.00012.0
Linkage choice is a modeling assumption
Ward favors compact, balanced clusters by minimizing within-cluster variance at each merge. Single linkage chains through nearest neighbors and can produce one large cluster plus outliers. Complete and average sit between these extremes. Each method finds the structure it is designed to find, whether or not that structure exists in the data.