de.lmu.ifi.dbs.elki.algorithm.clustering.hierarchical.linkage

Class WeightedAverageLinkage

java.lang.Object

de.lmu.ifi.dbs.elki.algorithm.clustering.hierarchical.linkage.WeightedAverageLinkage

All Implemented Interfaces:

Linkage

@Reference(authors="R. R. Sokal, C. D. Michener",
           title="A statistical method for evaluating systematic relationship",
           booktitle="University of Kansas science bulletin 28",
           url="https://archive.org/details/cbarchive_33927_astatisticalmethodforevaluatin1902",
           bibkey="journals/kansas/SokalM1902")
 @Alias(value={"wpgma","WPGMA","de.lmu.ifi.dbs.elki.algorithm.clustering.hierarchical.WeightedAverageLinkageMethod"})
 @Priority(value=-1)
public class WeightedAverageLinkage
extends java.lang.Object
implements Linkage

Weighted average linkage clustering method (WPGMA).

This is somewhat a misnomer, as it actually ignores that the clusters should likely be weighted differently according to their size when computing the average linkage. See GroupAverageLinkage for the UPGMA method that uses the group size to weight the objects the same way. Because of this, it is sometimes also called "simple average".

There does not appear to be a closed form distance for this clustering, but it is only defined recursively on the previous clusters simply by \[d_{\text{WPGMA}}(A\cup B,C):=\tfrac{1}{2}d(A,C)+\tfrac{1}{2}d(B,C)\]

MedianLinkage (WPGMC) is similar in the sense that it is ignoring the cluster sizes, and therefore the weight of points decreases with the depth of the tree. The method is "weighted" in the sense that the new members get the weight adjusted to match the old cluster members.

Reference:

R. R. Sokal, C. D. Michener
A statistical method for evaluating systematic relationship
University of Kansas science bulletin, 28, 1409-1438. (1958)

Since:

0.6.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	WeightedAverageLinkage.Parameterizer Class parameterizer.

Field Summary

Fields

Modifier and Type	Field and Description
static WeightedAverageLinkage	STATIC Static instance of class.

Constructor Summary

Constructors

Constructor and Description
WeightedAverageLinkage() Deprecated. use the static instance STATIC instead.

Method Summary

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

Methods inherited from interface de.lmu.ifi.dbs.elki.algorithm.clustering.hierarchical.linkage.Linkage

initial, restore

Field Detail

STATIC

public static final WeightedAverageLinkage STATIC

Static instance of class.

Constructor Detail

WeightedAverageLinkage

@Deprecated
public WeightedAverageLinkage()

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