The TREE Procedure
Example 98.2 Iris Data
Fisher (1936)’s iris data give sepal and petal dimensions for three different species of iris. The data, which are available in the Sashelp library, are clustered by kth-nearest-neighbor density linkage by using the CLUSTER procedure with K=8. Observations are identified by species ('Setosa',
'Versicolor', or 'Virginica') in the tree diagram, which is oriented with the height axis horizontal.
The following statements produce the results shown in Output 98.2.1 and Output 98.2.2:
title 'Fisher (1936) Iris Data';
ods graphics on;
proc cluster data=sashelp.iris method=twostage print=10
outtree=tree k=8 noeigen;
var SepalLength SepalWidth PetalLength PetalWidth;
copy Species;
run;
proc tree data=tree horizontal lineprinter pages=1 maxh=10; id species; run;
The PAGES=1 option specifies that the tree diagram extend over one page from tree to root. Since the HORIZONTAL option is also specified, the horizontal extent of the diagram is one page. The number of vertical pages required for the diagram is dictated by the number of leaves in the tree.
The MAXH=10 limits the values displayed on the height axis to a maximum of 10. This prunes the tree diagram so that only the portion from the leaves to level 10 is displayed. You can see this pruning effect in Output 98.2.2.
Output 98.2.1: Clustering of Fisher’s Iris Data
| Fisher (1936) Iris Data |
The CLUSTER Procedure
Two-Stage Density Linkage Clustering
K = 8
| Root-Mean-Square Total-Sample Standard Deviation | 10.69224 |
|---|
| Cluster History | |||||||
|---|---|---|---|---|---|---|---|
| Number of Clusters |
Freq | Normalized Fusion Density |
Maximum Density in Each Cluster |
Tie | |||
| Clusters Joined | Lesser | Greater | |||||
| 10 | CL11 | OB79 | 48 | 0.2879 | 0.1479 | 8.3678 | |
| 9 | CL13 | OB112 | 46 | 0.2802 | 0.2005 | 3.5156 | |
| 8 | CL10 | OB113 | 49 | 0.2699 | 0.1372 | 8.3678 | |
| 7 | CL8 | OB91 | 50 | 0.2586 | 0.1372 | 8.3678 | |
| 6 | CL9 | OB120 | 47 | 0.1412 | 0.0832 | 3.5156 | |
| 5 | CL6 | OB118 | 48 | 0.107 | 0.0605 | 3.5156 | |
| 4 | CL5 | OB110 | 49 | 0.0969 | 0.0541 | 3.5156 | |
| 3 | CL4 | OB135 | 50 | 0.0715 | 0.0370 | 3.5156 | |
| 2 | CL7 | CL3 | 100 | 2.6277 | 3.5156 | 8.3678 | |
3 modal clusters have been formed.
Output 98.2.2: Horizontal Tree for Fisher’s Iris Data
| Fisher (1936) Iris Data |
The TREE Procedure
Two-Stage Density Linkage Clustering
Cluster Fusion Density
0 1 2 3 4 5 6 7 8 9 10
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
I Setosa XXXXXXXXXXX..................................................
r XXXXXXXXXXX
i Setosa XXXXXXXXXXXXXXXXXX...........................................
s XXXXXXXXXXXXXXXXXX
Setosa XXXXXXXXXXXXXXXXXXXXX........................................
S XXXXXXXXXXXXXXXXXXXXX
p Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...............................
e XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
c Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX..............................
i XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
e Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.............................
s XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX............................
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Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX........................
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Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.
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Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
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Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
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Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
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Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
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Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
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Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
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Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
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Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
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Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX..
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Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX............................
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Setosa XXXX.........................................................
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Versicolor XXXXXXXXXXXXXXXXXXXXX........................................
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Versicolor XXXXXXXXXXXXXXXXXXXX.........................................
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Versicolor XXXXXXXXXXXXXXXXXX...........................................
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Virginica XXXXXXXXXXXXXXXXXX...........................................
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Versicolor XXXXXXXXXXXXXXXX.............................................
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Virginica XXXXXXXXXX...................................................
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Virginica XXX..........................................................
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Virginica XX...........................................................
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Virginica XX...........................................................
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Virginica XXX..........................................................
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Virginica XXXX.........................................................
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Versicolor XXXXX........................................................
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Virginica XXXXXX.......................................................
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Virginica XXXXXX.......................................................
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Virginica XXXXXXXXXX...................................................
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Virginica XXXXXXXXXXXXXX...............................................
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Virginica XXXXXXXXXXXXXXX..............................................
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Versicolor XXXXXXXXXXXXXXX..............................................
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Virginica XXXXXXXXXXXXXXX..............................................
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Virginica XXXXXXXXXXXXXXXX.............................................
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Virginica XXXXXXXXXXXXXXXX.............................................
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Versicolor XXXXXXXXXXXXXXXXXXX..........................................
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Virginica XXXXXXXXXXXXXXXXXXX..........................................
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Virginica XXXXXXXXXXXXXXXXXX...........................................
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