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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. Figure 10.1. Example dendrogram scaled by Wishart’s objective function and percent of information remaining.

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## Tables, Figures, and Equations

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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**Figure 10.1. Example dendrogram scaled by Wishart’s**objective function and percent of information remaining.**Hierarchical agglomerative cluster analysis**• Calculate distance matrix.**Hierarchical agglomerative cluster analysis**• Calculate distance matrix. • Merge two groups by a criterion of minimum distance.**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.**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.**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.**1**“R2” 0 Figure 10.1. Example dendrogram scaled by Wishart’s objective function and percent of information remaining.**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: xijtis 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.**The objective function can be rescaled from 0% to 100% of**information: % information remaining = 100(SST - E)/SST**Figure 10.3. A dendrogram is an inherently nondimensional**representation. Imagine the branches as free to pivot, like a child’s mobile**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

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