Average Linkage Clustering:
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.
is the distance between objects 
and 
;
and 
are the numbers of objects in clusters