- All Implemented Interfaces:
AgglomerationMethod
public final class CentroidLinkage
extends Object
implements AgglomerationMethod
The "centroid" or "Unweighted Pair-Group Method using Centroids (UPGMC)"
method is a geometric approach that links the centroids of clusters.
Each cluster is represented by its centroid.
The distance between two clusters is calculated as the distance between their centriods.
This method does not distort the cluster space.
[The data analysis handbook. By Ildiko E. Frank, Roberto Todeschini]
Can produce a dendrogram that is not monotonic
(it can have so called inversions, which are hard to interpret).
This occurs when the distance from the union of two clusters, r and s,
to a third cluster is less than the distance between r and s.
Used only for Euclidean distance!
The general form of the Lance-Williams matrix-update formula:
d[(i,j),k] = ai*d[i,k] + aj*d[j,k] + b*d[i,j] + g*|d[i,k]-d[j,k]|
For the "centroid" method:
ai = ci/(ci+cj)
aj = cj/(ci+cj)
b = -ci*cj/((ci+cj)*(ci+cj))
g = 0
Thus:
d[(i,j),k] = ci/(ci+cj)*d[i,k] + cj/(ci+cj)*d[j,k] - ci*cj/((ci+cj)*(ci+cj))*d[i,j]
= ( ci*d[i,k] + cj*d[j,k] - ci*cj/(ci+cj)*d[i,j] ) / (ci+cj)