The average linkage clustering is a method of calculating distance between clusters in hierarchical cluster analysis. The linkage function specifying the distance between two clusters is computed as the average distance between objects from the first cluster and objects from the second cluster. The averaging is performed over all pairs of objects, where is an object from the first cluster, is an object from the second cluster.
Mathematically the linkage function – the distance between clusters and – is described by the following expression :
where
- is the distance between objects
and 
; - and are two sets of objects (clusters);
- and are the numbers of objects in clusters and respectively.