Community Analysis Package
Also known as group average sorting (Lance & Williams, 1966). At each step, the
clusters are compared in terms of the average similarity of their members and the
two clusters that are most similar are fused.
= any distance or dissimilarity measure between clusters
The distance between two clusters can be defined either directly or
combinatorially (Lance and Williams 1967), that is, by an equation for updating a
distance matrix when two clusters are joined. In all of the following combinatorial
formulas, it is assumed that clusters
are merged to form
, and the
formula gives the distance between the new cluster
and any other cluster
The combinatorial formula is
The method was independently developed by Sokal and Michener (1958) and
At each step, the centroid of the clusters are compared and the two clusters that
are most similar are fused. The position of the centroid is calculated using the
formula of Gower(1967).
At each iteration, the clusters are compared in terms of the similarity of their most
similar samples (columns) and the two clusters that hold the most similar samples
are fused. The average of the attributes of the fused group is calculated and the
similarity between average properties are used in subsequent iterations.
Once a measure has been selected the cluster analysis will immediately be run.
Output from the analysis is presented under a number of tabbed components that
can each be viewed by clicking on the tab.
Note that, depending on the distance measure used, the dendrogram may appear
in a recursive form i.e. where parent nodes are plotted further along the similarity
gradient than their child nodes. This is caused when the combination of samples
causes a change in observed species similarity. To present the dendrogram in a
more usual format, check the Space equally box.
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