From: McCune, B'

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Tables, Figures, and Equations
From McCune, B. J. B. Grace. 2002. Analysis
of Ecological Communities. MjM Software Design,
Gleneden Beach, Oregon http//www.pcord.com
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Figure 10.1. Example dendrogram scaled by
Wisharts objective function and percent of
information remaining.
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Hierarchical agglomerative cluster analysis

• Calculate distance matrix.

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Hierarchical agglomerative cluster analysis

• Calculate distance matrix.
• Merge two groups by a criterion of minimum
  distance.

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Hierarchical agglomerative cluster analysis

• Calculate distance matrix.
• Merge two groups by a criterion of minimum
  distance.
• Combine the attributes of the entities in the two
  groups that were fused.

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Hierarchical agglomerative cluster analysis

• Calculate distance matrix.
• Merge two groups by a criterion of minimum
  distance.
• Combine the attributes of the entities in the two
  groups that were fused.
• Merge the next two groups, then go to step 3,
  until one group remains.

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Hierarchical agglomerative cluster analysis

• Calculate distance matrix.
• Merge two groups by a criterion of minimum
  distance.
• Combine the attributes of the entities in the two
  groups that were fused.
• Merge the next two groups, then go to step 3,
  until one group remains.
• Display the results as a dendrogram.

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R2
0
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Figure 10.1. Example dendrogram scaled by
Wisharts objective function and percent of
information remaining.
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The objective function (E) is the sum of the
error sum of squares from each centroid to the
items in that group
where t indexes the T clusters Et is the error
sum of squares for cluster t. Each Et is found
by
xijt is the value of the jth variable for the
ith point of cluster t containing kt points
is the mean of the jth variable for cluster t.
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The objective function can be rescaled from 0 to
100 of information information remaining
100(SST - E)/SST
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Figure 10.2. Reversal in a dendrogram.
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Figure 10.3. A dendrogram is an inherently
nondimensional representation. Imagine the
branches as free to pivot, like a childs mobile
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Complete chaining
Figure 10.4. Use of average path length to
measure percent chaining in cluster analysis.
Path length is the number of nodes between the
tip of a branch and the trunk.
No chaining