The CLUSTER Procedure

Example 30.1 Cluster Analysis of Flying Mileages between 10 American Cities

This example clusters 10 American cities based on the flying mileages between them. Six clustering methods are shown with corresponding dendrograms. The EML method cannot be used because it requires coordinate data. The other omitted methods produce the same clusters, although not the same distances between clusters, as one of the illustrated methods: complete linkage and the flexible-beta method yield the same clusters as Ward’s method, McQuitty’s similarity analysis produces the same clusters as average linkage, and the median method corresponds to the centroid method.

All of the methods suggest a division of the cities into two clusters along the east-west dimension. There is disagreement, however, about which cluster Denver should belong to. Some of the methods indicate a possible third cluster that contains Denver and Houston.

The following step displays the city mileage SAS data set, which is available in the Sashelp library and is designated as a TYPE=DISTANCE data set when it is used by PROC CLUSTER:

proc print noobs data=sashelp.mileages; 
run;

A partial listing from the following statements include Output 30.1.2 and Output 30.1.3:

title 'Cluster Analysis of Flying Mileages Between 10 American Cities';
ods graphics on;

title2 'Using METHOD=AVERAGE';
proc cluster data=sashelp.mileages(type=distance) method=average pseudo;
  id City;
run;

Output 30.1.3 Dendrogram Using METHOD=AVERAGE

A partial listing from the following statements include Output 30.1.4 and Output 30.1.5:

title2 'Using METHOD=CENTROID';
proc cluster data=sashelp.mileages(type=distance) method=centroid pseudo;
   id City;
run;

Output 30.1.5 Dendrogram Using METHOD=CENTROID

A partial listing from the following statements include Output 30.1.6 and Output 30.1.7:

title2 'Using METHOD=DENSITY K=3';
proc cluster data=sashelp.mileages(type=distance) method=density k=3;
   id City;
run;

Output 30.1.7 Dendrogram Using METHOD=DENSITY K=3

A partial listing from the following statements include Output 30.1.8 and Output 30.1.9:

title2 'Using METHOD=SINGLE';
proc cluster data=sashelp.mileages(type=distance) method=single;
   id City;
run;

Output 30.1.9 Dendrogram Using METHOD=SINGLE

A partial listing from the following statements include Output 30.1.10 and Output 30.1.11:

title2 'Using METHOD=TWOSTAGE K=3';
proc cluster data=sashelp.mileages(type=distance) method=twostage k=3;
   id City;
run;

Output 30.1.11 Dendrogram Using METHOD=TWOSTAGE K=3

A partial listing from the following statements include Output 30.1.12 and Output 30.1.13:

title2 'Using METHOD=WARD';
proc cluster data=sashelp.mileages(type=distance) method=ward pseudo;
   id City;
run;

Output 30.1.13 Dendrogram Using METHOD=WARD