The MODECLUS Procedure
Example 84.2 Cluster Analysis of Flying Mileages between Ten American Cities
(View the complete code for this example.)
This example uses distance data and illustrates the use of the TRANSPOSE procedure
and the DATA step to fill in the upper triangle of the distance matrix. A data set containing a table of flying mileages between 10 U.S. cities is available in the Sashelp library. The results are displayed in Output 84.2.1 through Output 84.2.3.
The following statements produce Output 84.2.1:
title 'Modeclus Analysis of 10 American Cities';
title2 'Based on Flying Mileages';
*-----Fill in Upper Triangle of Distance Matrix---------------;
proc transpose data=sashelp.mileages out=tran;
copy city;
run;
data mileages(type=distance drop=col: _: i);
merge sashelp.mileages tran;
array var[10] atlanta--washingtondc;
array col[10];
do i = 1 to 10;
var[i] = sum(var[i], col[i]);
end;
run;
*-----Clustering with K-Nearest-Neighbor Density Estimates-----;
proc modeclus data=mileages all m=1 k=3;
id CITY;
run;
Output 84.2.1: Clustering with K-Nearest-Neighbor Density Estimates
| Modeclus Analysis of 10 American Cities |
| Based on Flying Mileages |
| Nearest Neighbor List | ||
|---|---|---|
| City | Neighbor | Distance |
| Atlanta | Washington D.C. | 543.0000000 |
| Chicago | 587.0000000 | |
| Chicago | Atlanta | 587.0000000 |
| Washington D.C. | 597.0000000 | |
| Denver | Los Angeles | 831.0000000 |
| Houston | 879.0000000 | |
| Houston | Atlanta | 701.0000000 |
| Denver | 879.0000000 | |
| Los Angeles | San Francisco | 347.0000000 |
| Denver | 831.0000000 | |
| Miami | Atlanta | 604.0000000 |
| Washington D.C. | 923.0000000 | |
| New York | Washington D.C. | 205.0000000 |
| Chicago | 713.0000000 | |
| San Francisco | Los Angeles | 347.0000000 |
| Seattle | 678.0000000 | |
| Seattle | San Francisco | 678.0000000 |
| Los Angeles | 959.0000000 | |
| Washington D.C. | New York | 205.0000000 |
| Atlanta | 543.0000000 | |
| Modeclus Analysis of 10 American Cities |
| Based on Flying Mileages |
| Sums of Density Estimates Within Neighborhood | ||||||
|---|---|---|---|---|---|---|
| Cluster | City | Estimated Density | Same Cluster | Other Clusters | Total | Cluster Proportion Same/Total |
| 1 | Atlanta | 0.00025554 | 0.0005275 | 0 | 0.0005275 | 1.000 |
| Chicago | 0.00025126 | 0.00053178 | 0 | 0.00053178 | 1.000 | |
| Houston | 0.00017065 | 0.00025554 | 0.00017065 | 0.00042619 | 0.600 | |
| Miami | 0.00016251 | 0.00053178 | 0 | 0.00053178 | 1.000 | |
| New York | 0.00021038 | 0.0005275 | 0 | 0.0005275 | 1.000 | |
| Washington D.C. | 0.00027624 | 0.00046592 | 0 | 0.00046592 | 1.000 | |
| 2 | Denver | 0.00017065 | 0.00018051 | 0.00017065 | 0.00035115 | 0.514 |
| Los Angeles | 0.00018051 | 0.00039189 | 0 | 0.00039189 | 1.000 | |
| San Francisco | 0.00022124 | 0.00033692 | 0 | 0.00033692 | 1.000 | |
| Seattle | 0.00015641 | 0.00040174 | 0 | 0.00040174 | 1.000 | |
| Boundary Objects -Cluster Proportions- | ||||
|---|---|---|---|---|
| City | Density | Cluster | 1 | 2 |
| Denver | 0.0001706485 | 2 | 0.486 | 0.514 |
| Houston | 0.0001706485 | 1 | 0.600 | 0.400 |
| Cluster Statistics | ||||
|---|---|---|---|---|
| Cluster | Frequency | Maximum Estimated Density | Boundary Frequency | Estimated Saddle Density |
| 1 | 6 | 0.00027624 | 1 | 0.00017065 |
| 2 | 4 | 0.00022124 | 1 | 0.00017065 |
| Modeclus Analysis of 10 American Cities |
| Based on Flying Mileages |
| Cluster Summary | ||
|---|---|---|
| K | Number of Clusters | Frequency of Unclassified Objects |
| 3 | 2 | 0 |
The following statements produce Output 84.2.2:
*------Clustering with Uniform-Kernel Density Estimates--------;
proc modeclus data=mileages all m=1 r=600 800;
id CITY;
run;
Output 84.2.2: Clustering with Uniform-Kernel Density Estimates
| Modeclus Analysis of 10 American Cities |
| Based on Flying Mileages |
| Nearest Neighbor List | ||
|---|---|---|
| City | Neighbor | Distance |
| Atlanta | Washington D.C. | 543.0000000 |
| Chicago | 587.0000000 | |
| Miami | 604.0000000 | |
| Houston | 701.0000000 | |
| New York | 748.0000000 | |
| Chicago | Atlanta | 587.0000000 |
| Washington D.C. | 597.0000000 | |
| New York | 713.0000000 | |
| Houston | Atlanta | 701.0000000 |
| Los Angeles | San Francisco | 347.0000000 |
| Miami | Atlanta | 604.0000000 |
| New York | Washington D.C. | 205.0000000 |
| Chicago | 713.0000000 | |
| Atlanta | 748.0000000 | |
| San Francisco | Los Angeles | 347.0000000 |
| Seattle | 678.0000000 | |
| Seattle | San Francisco | 678.0000000 |
| Washington D.C. | New York | 205.0000000 |
| Atlanta | 543.0000000 | |
| Chicago | 597.0000000 | |
| Modeclus Analysis of 10 American Cities |
| Based on Flying Mileages |
| Sums of Density Estimates Within Neighborhood | ||||||
|---|---|---|---|---|---|---|
| Cluster | City | Estimated Density | Same Cluster | Other Clusters | Total | Cluster Proportion Same/Total |
| 1 | Atlanta | 0.00025 | 0.00058333 | 0 | 0.00058333 | 1.000 |
| Chicago | 0.00025 | 0.00058333 | 0 | 0.00058333 | 1.000 | |
| New York | 0.00016667 | 0.00033333 | 0 | 0.00033333 | 1.000 | |
| Washington D.C. | 0.00033333 | 0.00066667 | 0 | 0.00066667 | 1.000 | |
| 2 | Los Angeles | 0.00016667 | 0.00016667 | 0 | 0.00016667 | 1.000 |
| San Francisco | 0.00016667 | 0.00016667 | 0 | 0.00016667 | 1.000 | |
| 3 | Denver | 0.00008333 | 0 | 0 | 0 | . |
| 4 | Houston | 0.00008333 | 0 | 0 | 0 | . |
| 5 | Miami | 0.00008333 | 0 | 0 | 0 | . |
| 6 | Seattle | 0.00008333 | 0 | 0 | 0 | . |
| No Boundary Objects |
| Cluster Statistics | ||||
|---|---|---|---|---|
| Cluster | Frequency | Maximum Estimated Density | Boundary Frequency | Estimated Saddle Density |
| 1 | 4 | 0.00033333 | 0 | . |
| 2 | 2 | 0.00016667 | 0 | . |
| 3 | 1 | 0.00008333 | 0 | . |
| 4 | 1 | 0.00008333 | 0 | . |
| 5 | 1 | 0.00008333 | 0 | . |
| 6 | 1 | 0.00008333 | 0 | . |
| Modeclus Analysis of 10 American Cities |
| Based on Flying Mileages |
| Sums of Density Estimates Within Neighborhood | ||||||
|---|---|---|---|---|---|---|
| Cluster | City | Estimated Density | Same Cluster | Other Clusters | Total | Cluster Proportion Same/Total |
| 1 | Atlanta | 0.000375 | 0.001 | 0 | 0.001 | 1.000 |
| Chicago | 0.00025 | 0.000875 | 0 | 0.000875 | 1.000 | |
| Houston | 0.000125 | 0.000375 | 0 | 0.000375 | 1.000 | |
| Miami | 0.000125 | 0.000375 | 0 | 0.000375 | 1.000 | |
| New York | 0.00025 | 0.000875 | 0 | 0.000875 | 1.000 | |
| Washington D.C. | 0.00025 | 0.000875 | 0 | 0.000875 | 1.000 | |
| 2 | Los Angeles | 0.000125 | 0.0001875 | 0 | 0.0001875 | 1.000 |
| San Francisco | 0.0001875 | 0.00025 | 0 | 0.00025 | 1.000 | |
| Seattle | 0.000125 | 0.0001875 | 0 | 0.0001875 | 1.000 | |
| 3 | Denver | 0.0000625 | 0 | 0 | 0 | . |
| No Boundary Objects |
| Cluster Statistics | ||||
|---|---|---|---|---|
| Cluster | Frequency | Maximum Estimated Density | Boundary Frequency | Estimated Saddle Density |
| 1 | 6 | 0.000375 | 0 | . |
| 2 | 3 | 0.0001875 | 0 | . |
| 3 | 1 | 0.0000625 | 0 | . |
| Modeclus Analysis of 10 American Cities |
| Based on Flying Mileages |
| Cluster Summary | ||
|---|---|---|
| R | Number of Clusters | Frequency of Unclassified Objects |
| 600 | 6 | 0 |
| 800 | 3 | 0 |
The following statements produce Output 84.2.3:
*------Clustering Neighborhoods Extended to Nearest Neighbor--------;
proc modeclus data=mileages list m=1 ck=2 r=600 800;
id CITY;
run;
Output 84.2.3: Uniform-Kernel Density Estimates, Clustering Neighborhoods Extended to Nearest Neighbor
| Modeclus Analysis of 10 American Cities |
| Based on Flying Mileages |
| Sums of Density Estimates Within Neighborhood | ||||||
|---|---|---|---|---|---|---|
| Cluster | City | Estimated Density | Same Cluster | Other Clusters | Total | Cluster Proportion Same/Total |
| 1 | Atlanta | 0.00025 | 0.00058333 | 0 | 0.00058333 | 1.000 |
| Chicago | 0.00025 | 0.00058333 | 0 | 0.00058333 | 1.000 | |
| Houston | 0.00008333 | 0.00025 | 0 | 0.00025 | 1.000 | |
| Miami | 0.00008333 | 0.00025 | 0 | 0.00025 | 1.000 | |
| New York | 0.00016667 | 0.00033333 | 0 | 0.00033333 | 1.000 | |
| Washington D.C. | 0.00033333 | 0.00066667 | 0 | 0.00066667 | 1.000 | |
| 2 | Denver | 0.00008333 | 0.00016667 | 0 | 0.00016667 | 1.000 |
| Los Angeles | 0.00016667 | 0.00016667 | 0 | 0.00016667 | 1.000 | |
| San Francisco | 0.00016667 | 0.00016667 | 0 | 0.00016667 | 1.000 | |
| Seattle | 0.00008333 | 0.00016667 | 0 | 0.00016667 | 1.000 | |
| Cluster Statistics | ||||
|---|---|---|---|---|
| Cluster | Frequency | Maximum Estimated Density | Boundary Frequency | Estimated Saddle Density |
| 1 | 6 | 0.00033333 | 0 | . |
| 2 | 4 | 0.00016667 | 0 | . |
| Modeclus Analysis of 10 American Cities |
| Based on Flying Mileages |
| Sums of Density Estimates Within Neighborhood | ||||||
|---|---|---|---|---|---|---|
| Cluster | City | Estimated Density | Same Cluster | Other Clusters | Total | Cluster Proportion Same/Total |
| 1 | Atlanta | 0.000375 | 0.001 | 0 | 0.001 | 1.000 |
| Chicago | 0.00025 | 0.000875 | 0 | 0.000875 | 1.000 | |
| Houston | 0.000125 | 0.000375 | 0 | 0.000375 | 1.000 | |
| Miami | 0.000125 | 0.000375 | 0 | 0.000375 | 1.000 | |
| New York | 0.00025 | 0.000875 | 0 | 0.000875 | 1.000 | |
| Washington D.C. | 0.00025 | 0.000875 | 0 | 0.000875 | 1.000 | |
| 2 | Denver | 0.0000625 | 0.000125 | 0 | 0.000125 | 1.000 |
| Los Angeles | 0.000125 | 0.0001875 | 0 | 0.0001875 | 1.000 | |
| San Francisco | 0.0001875 | 0.00025 | 0 | 0.00025 | 1.000 | |
| Seattle | 0.000125 | 0.0001875 | 0 | 0.0001875 | 1.000 | |
| Cluster Statistics | ||||
|---|---|---|---|---|
| Cluster | Frequency | Maximum Estimated Density | Boundary Frequency | Estimated Saddle Density |
| 1 | 6 | 0.000375 | 0 | . |
| 2 | 4 | 0.0001875 | 0 | . |
| Modeclus Analysis of 10 American Cities |
| Based on Flying Mileages |
| Cluster Summary | |||
|---|---|---|---|
| R | CK | Number of Clusters | Frequency of Unclassified Objects |
| 600 | 2 | 2 | 0 |
| 800 | 2 | 2 | 0 |