- All Implemented Interfaces:
- AgglomerationMethod
public final class MedianLinkage
extends Object
implements AgglomerationMethod
The "median", "weighted centroid", "weighted center of mass distance", "Gower",
or "Weighted Pair-Group Method using Centroids (WPGMC)" method is a geometric approach.
The size of the clusters is assumed to be equal and
the position of the new centroid is always between the two old centroids.
This method preserves the importance of a small cluster when it is merged with a large cluster.
[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 distance between two clusters is the Euclidean distance between their weighted centroids.
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 "median" method:
ai = 0.5
aj = 0.5
b = -0.25
g = 0
Thus:
d[(i,j),k] = 0.5*d[i,k] + 0.5*d[j,k] - 0.25*d[i,j]