• java.lang.Object
• All Implemented Interfaces:

@Alias(value={"complete","clink","complete-link","farthest-neighbor","de.lmu.ifi.dbs.elki.algorithm.clustering.hierarchical.CompleteLinkageMethod"})
@Priority(value=100)
@Reference(authors="T. S\u00f8rensen",title="A method of establishing groups of equal amplitude in plant sociology based on similarity of species and its application to analyses of the vegetation on Danish commons",booktitle="Biologiske Skrifter 5 (4)",bibkey="journals/misc/Sorensen48") @Reference(authors="P. Macnaughton-Smith",title="Some statistical and other numerical techniques for classifying individuals",booktitle="Home Office Res. Rpt. No. 6, H.M.S.O., London",bibkey="journals/misc/MacnaughtonSmith65") @Reference(authors="G. N. Lance, W. T. Williams",title="A general theory of classificatory sorting strategies 1. Hierarchical systems",booktitle="The Computer Journal 9.4",url="https://doi.org/10.1093/comjnl/9.4.373",bibkey="doi:10.1093/comjnl/9.4.373") @Reference(authors="S. C. Johnson",title="Hierarchical clustering schemes",booktitle="Psychometrika 32",url="https://doi.org/10.1007/BF02289588",bibkey="doi:10.1007/BF02289588")
extends java.lang.Object
implements Linkage

The distance of two clusters is simply the maximum of all pairwise distances between the two clusters.

The distance of two clusters is defined as: $d_{\max}(A,B):=\max_{a\in A}\max_{b\in B} d(a,b)$

This can be computed recursively using: $d_{\max}(A\cup B,C) = \max(d(A,C), d(B,C))$

Note that with similarity functions, one would need to use the minimum instead to get the same effect.

The algorithm CLINK is a faster algorithm to find such clusterings, but it is very much order dependent and tends to find worse solutions.

References:

This is attributed to different sources that are not easily verifiable. Lance and Williams (1967) attribute the idea to Macnaughton-Smith, albeit he may have suggested a divisive rather than agglomerative procedure, but Sørensen may have used this already in 1948 (and is credited, e.g., by Johnson 1967).

T. Sørensen
A method of establishing groups of equal amplitude in plant sociology based on similarity of species and its application to analyses of the vegetation on Danish commons
Biologiske Skrifter 5 (4)

P. Macnaughton-Smith
Some statistical and other numerical techniques for classifying individuals
Home Office Res. Rpt. No. 6, H.M.S.O., London

G. N. Lance, W. T. Williams
A general theory of classificatory sorting strategies
1. Hierarchical systems
The Computer Journal 9.4

S. C. Johnson
Hierarchical clustering schemes
Psychometrika 32

Since:
0.6.0
Author:
Erich Schubert
• ### Nested Class Summary

Nested Classes
Modifier and Type Class and Description
static class  CompleteLinkage.Parameterizer
Class parameterizer.
• ### Field Summary

Fields
Modifier and Type Field and Description
static CompleteLinkage STATIC
Static instance of class.
• ### Constructor Summary

Constructors
Constructor and Description
CompleteLinkage()
Deprecated.
use the static instance STATIC instead.
• ### Method Summary

All Methods
Modifier and Type Method and Description
double combine(int sizex, double dx, int sizey, double dy, int sizej, double dxy)
Compute combined linkage for two clusters.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

initial, restore
• ### Field Detail

• #### STATIC

public static final CompleteLinkage STATIC
Static instance of class.
• ### Constructor Detail

@Deprecated
public CompleteLinkage()
Deprecated. use the static instance STATIC instead.
Constructor.
• ### Method Detail

• #### combine

public double combine(int sizex,
double dx,
int sizey,
double dy,
int sizej,
double dxy)
Description copied from interface: Linkage
Compute combined linkage for two clusters.
Specified by:
combine in interface Linkage
Parameters:
sizex - Size of first cluster x before merging
dx - Distance of cluster x to j before merging
sizey - Size of second cluster y before merging
dy - Distance of cluster y to j before merging
sizej - Size of candidate cluster j
dxy - Distance between clusters x and y before merging
Returns:
Combined distance