4.5 Ward’s Minimum Variance Clustering
This method is based on the linear model criterion of least squares. The objective is
to define groups in such a way that the within-group sum of squares (i.e., the squared
error of ANOVA) is minimized. The within-cluster sum of squared errors can be
computed as the sum of the squared distances among members of a cluster divided
by the number of objects. Note also that although the computation of within-group
sums-of-squares is based on a Euclidean model, the Ward method will produce
meaningful results from dissimilarities that are Euclidean or not.
In the literature, two different algorithms are found for Ward clustering; one
implements Ward’s (1963) minimum variance clustering criterion, the other does not
(Murtagh and Legendre 2014). Function hclust() was modified in R 3.1.1;
method ¼ "ward.D2" now implements the Ward (1963) criterion where dissimilarities are squared before cluster updating, whereas method ¼ "ward.D" does
not implement that criterion. The latter was implemented by hclust() with
method ¼ "ward" in R versions up to 3.0.3. Fig. 4.5 shows the dendrogram
resulting from a ward.D2 clustering.
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Chord - Ward
spe.ch
hclust (*, "ward.D2")
Height
3.5
3.0
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Fig. 4.5 Ward clustering of a matrix of chord distance among sites (species data)
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4 Cluster Analysis