Complete Linkage Clustering:
The complete linkage clustering (or the farthest neighbor method) 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 maximal object-to-object distance 
, where objects 
belong to the first cluster, and objects 
belong to the second cluster. In other words, the distance between two clusters is computed as the distance between the two farthest objects in the two clusters.
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)
is the distance between objects 
and 
;