1. Clustering Deviance From CART Analysis and Silhouette Widths
Michael A. Lindgren
EWHALE Laboratory
Institute of Arctic Biology
University of Alaska Fairbanks
March 09, 2011

3. Clustering Level Solution
Table of Deviance Summary Statistics **The previous graph was created with this data**
Clustering Level Solution
Min
1st Quart
Median
Mean
3rd Quart
Max
clus03_Dev
clus04_Dev
clus05_Dev
0.1195
0.1214
0.1604
0.8492
0.4993
clus06_Dev
clus07_Dev
clus08_Dev
clus09_Dev
clus10_Dev
clus11_Dev
clus12_Dev
0.6806
clus13_Dev
clus14_Dev
clus15_Dev
0.1096
0.3779
0.3986
1.3743
0.64
clus16_Dev
0.1084
0.3344
0.409
1.4127
0.5554
clus17_Dev
0.1198
0.3431
0.4768
1.5284
0.9333
clus18_Dev
0.1157
0.3089
0.4171
1.4201
0.5849
clus19_Dev
0.1404
0.4873
1.565
1.0354
16.163
clus20_Dev
0.2698
clus25_Dev
clus30_Dev
clus40_Dev
1.8659
clus50_Dev
LOWEST VALUE -->

5. Average Silhouette Width
Overall Average Silhouette Widths **this is the data used in previous bar graphic**
Cluster Level
Average Silhouette Width 3
0.26 4
0.21 5
0.19 6
0.18 7 8
0.17 9 10
0.16 11 12 13 14 15 16 17 18 19 20 25 30 40
0.2 50

6. PAM Metrics Across Clustering Solutions
Michael A. Lindgren
EWHALE Laboratory
Institute of Arctic Biology
University of Alaska Fairbanks
March 02, 2011

7. Recap on PAM
The algorithm searches for k representative objects (medoids) which are centrally located in the clusters they define. The representative object of a cluster, the medoid, is the object for which the average dissimilarity to all the objects in the cluster is minimal.
Actually, the PAM algorithm minimizes the sum of dissimilarities instead of the average dissimilarity.
Average distance (dissimilarity) to a medoid - If j is the medoid of cluster C, the average distance of all objects of C to j is calculated as follows:
This measure gives an insight to the similarity of the cases that have been clustered around a given medoid are to that particular medoid. Therefore, as this number decreases in a clustering solution, the dissimilarity is minimized.

8. Red-Orange: indicates a higher dissimilarity
Clustering Solution (k) 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 40 50 1 2
0.3239
0.3564
0.3909
0.3472 21 22 23
0.289 24 26 27 28 29 31 32 33 34 35 36 37 38 39 41 42 43 44 45 46 47 48 49
Number of Returned Clusters
This graphic is a matrix of the “Average Dissimilarity ” measure for each cluster from all examined clustering levels.
Using conditional formatting, the cell color is based on the dissimilarity value of that cluster.
Cell Color Range:
Red-Orange: indicates a higher dissimilarity
Yellow-Green: indicates a lower dissimilarity

9. Red-Orange: indicates a higher average silhouette
Clustering Solution (k) 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 40 50 1 2 21 22 23 24 26 27 28 29 31 32 33 34 35 36 37 38 39 41 42 43 44 45 46 47 48
0.1534 49
Number of Returned Clusters
This graphic is a matrix of the “Average Silhouette Widths” quantified through the averaging of the silhouette widths for every sample within a given cluster. This is performed for each cluster in each of the clustering levels. The total average silhouette is the average of these values for each clustering level.
Using conditional formatting, the cell color is based on the dissimilarity value of that cluster.
Cell Color Range:
Red-Orange: indicates a higher average silhouette
Yellow-Green: indicates a lower average silhouette

10. This table is a way of interpreting the Average Silhouette Width for the entire solution, Also known as Silhouette Coefficient (SC)
Range of SC
Interpretation
A strong structure has been found
A reasonable structure has been found
The structure is weak and could be artificial
< 0.25
No substantial structure has been found