Class CentroidLinkage
java.lang.Object
ch.usi.inf.sape.hac.agglomeration.CentroidLinkage
- All Implemented Interfaces:
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)
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Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptiondouble
computeDissimilarity
(double dik, double djk, double dij, int ci, int cj, int ck) Compute the dissimilarity between the newly formed cluster (i,j) and the existing cluster k.toString()
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Constructor Details
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CentroidLinkage
public CentroidLinkage()
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Method Details
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computeDissimilarity
public double computeDissimilarity(double dik, double djk, double dij, int ci, int cj, int ck) Description copied from interface:AgglomerationMethod
Compute the dissimilarity between the newly formed cluster (i,j) and the existing cluster k.- Specified by:
computeDissimilarity
in interfaceAgglomerationMethod
- Parameters:
dik
- dissimilarity between clusters i and kdjk
- dissimilarity between clusters j and kdij
- dissimilarity between clusters i and jci
- cardinality of cluster icj
- cardinality of cluster jck
- cardinality of cluster k- Returns:
- dissimilarity between cluster (i,j) and cluster k.
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toString
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