The MODECLUS Procedure

Example 79.2 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 79.2.1 through Output 79.2.3.

The following statements produce Output 79.2.1:

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 79.2.1: Clustering with K-Nearest-Neighbor Density Estimates

Modeclus Analysis of 10 American Cities
Based on Flying Mileages

The MODECLUS Procedure

Nearest Neighbor List
CityNeighborDistance
AtlantaWashington D.C.543.0000000
 Chicago587.0000000
ChicagoAtlanta587.0000000
 Washington D.C.597.0000000
DenverLos Angeles831.0000000
 Houston879.0000000
HoustonAtlanta701.0000000
 Denver879.0000000
Los AngelesSan Francisco347.0000000
 Denver831.0000000
MiamiAtlanta604.0000000
 Washington D.C.923.0000000
New YorkWashington D.C.205.0000000
 Chicago713.0000000
San FranciscoLos Angeles347.0000000
 Seattle678.0000000
SeattleSan Francisco678.0000000
 Los Angeles959.0000000
Washington D.C.New York205.0000000
 Atlanta543.0000000

Modeclus Analysis of 10 American Cities
Based on Flying Mileages

The MODECLUS Procedure
K=3 METHOD=1

Sums of Density Estimates Within Neighborhood
ClusterCityEstimated
Density
Same
Cluster
Other
Clusters
TotalCluster
Proportion
Same/Total
1Atlanta0.000255540.000527500.00052751.000
 Chicago0.000251260.0005317800.000531781.000
 Houston0.000170650.000255540.000170650.000426190.600
 Miami0.000162510.0005317800.000531781.000
 New York0.000210380.000527500.00052751.000
 Washington D.C.0.000276240.0004659200.000465921.000
2Denver0.000170650.000180510.000170650.000351150.514
 Los Angeles0.000180510.0003918900.000391891.000
 San Francisco0.000221240.0003369200.000336921.000
 Seattle0.000156410.0004017400.000401741.000

Boundary Objects -Cluster Proportions-
CityDensityCluster12
Denver0.000170648520.4860.514
Houston0.000170648510.6000.400

Cluster Statistics
ClusterFrequencyMaximum
Estimated
Density
Boundary
Frequency
Estimated
Saddle
Density
160.0002762410.00017065
240.0002212410.00017065

Modeclus Analysis of 10 American Cities
Based on Flying Mileages

The MODECLUS Procedure

Cluster Summary
KNumber of
Clusters
Frequency of
Unclassified
Objects
320


The following statements produce Output 79.2.2:

*------Clustering with Uniform-Kernel Density Estimates--------;
proc modeclus data=mileages all m=1 r=600 800;
   id CITY;
run;

Output 79.2.2: Clustering with Uniform-Kernel Density Estimates

Modeclus Analysis of 10 American Cities
Based on Flying Mileages

The MODECLUS Procedure

Nearest Neighbor List
CityNeighborDistance
AtlantaWashington D.C.543.0000000
 Chicago587.0000000
 Miami604.0000000
 Houston701.0000000
 New York748.0000000
ChicagoAtlanta587.0000000
 Washington D.C.597.0000000
 New York713.0000000
HoustonAtlanta701.0000000
Los AngelesSan Francisco347.0000000
MiamiAtlanta604.0000000
New YorkWashington D.C.205.0000000
 Chicago713.0000000
 Atlanta748.0000000
San FranciscoLos Angeles347.0000000
 Seattle678.0000000
SeattleSan Francisco678.0000000
Washington D.C.New York205.0000000
 Atlanta543.0000000
 Chicago597.0000000

Modeclus Analysis of 10 American Cities
Based on Flying Mileages

The MODECLUS Procedure
R=600 METHOD=1

Sums of Density Estimates Within Neighborhood
ClusterCityEstimated
Density
Same
Cluster
Other
Clusters
TotalCluster
Proportion
Same/Total
1Atlanta0.000250.0005833300.000583331.000
 Chicago0.000250.0005833300.000583331.000
 New York0.000166670.0003333300.000333331.000
 Washington D.C.0.000333330.0006666700.000666671.000
2Los Angeles0.000166670.0001666700.000166671.000
 San Francisco0.000166670.0001666700.000166671.000
3Denver0.00008333000.
4Houston0.00008333000.
5Miami0.00008333000.
6Seattle0.00008333000.


No Boundary Objects

Cluster Statistics
ClusterFrequencyMaximum
Estimated
Density
Boundary
Frequency
Estimated
Saddle
Density
140.000333330.
220.000166670.
310.000083330.
410.000083330.
510.000083330.
610.000083330.

Modeclus Analysis of 10 American Cities
Based on Flying Mileages

The MODECLUS Procedure
R=800 METHOD=1

Sums of Density Estimates Within Neighborhood
ClusterCityEstimated
Density
Same
Cluster
Other
Clusters
TotalCluster
Proportion
Same/Total
1Atlanta0.0003750.00100.0011.000
 Chicago0.000250.00087500.0008751.000
 Houston0.0001250.00037500.0003751.000
 Miami0.0001250.00037500.0003751.000
 New York0.000250.00087500.0008751.000
 Washington D.C.0.000250.00087500.0008751.000
2Los Angeles0.0001250.000187500.00018751.000
 San Francisco0.00018750.0002500.000251.000
 Seattle0.0001250.000187500.00018751.000
3Denver0.0000625000.


No Boundary Objects

Cluster Statistics
ClusterFrequencyMaximum
Estimated
Density
Boundary
Frequency
Estimated
Saddle
Density
160.0003750.
230.00018750.
310.00006250.

Modeclus Analysis of 10 American Cities
Based on Flying Mileages

The MODECLUS Procedure

Cluster Summary
RNumber of
Clusters
Frequency of
Unclassified
Objects
60060
80030


The following statements produce Output 79.2.3:

*------Clustering Neighborhoods Extended to Nearest Neighbor--------;
proc modeclus data=mileages list m=1 ck=2 r=600 800;
   id CITY;
run;

Output 79.2.3: Uniform-Kernel Density Estimates, Clustering Neighborhoods Extended to Nearest Neighbor

Modeclus Analysis of 10 American Cities
Based on Flying Mileages

The MODECLUS Procedure
CK=2 R=600 METHOD=1

Sums of Density Estimates Within Neighborhood
ClusterCityEstimated
Density
Same
Cluster
Other
Clusters
TotalCluster
Proportion
Same/Total
1Atlanta0.000250.0005833300.000583331.000
 Chicago0.000250.0005833300.000583331.000
 Houston0.000083330.0002500.000251.000
 Miami0.000083330.0002500.000251.000
 New York0.000166670.0003333300.000333331.000
 Washington D.C.0.000333330.0006666700.000666671.000
2Denver0.000083330.0001666700.000166671.000
 Los Angeles0.000166670.0001666700.000166671.000
 San Francisco0.000166670.0001666700.000166671.000
 Seattle0.000083330.0001666700.000166671.000

Cluster Statistics
ClusterFrequencyMaximum
Estimated
Density
Boundary
Frequency
Estimated
Saddle
Density
160.000333330.
240.000166670.

Modeclus Analysis of 10 American Cities
Based on Flying Mileages

The MODECLUS Procedure
CK=2 R=800 METHOD=1

Sums of Density Estimates Within Neighborhood
ClusterCityEstimated
Density
Same
Cluster
Other
Clusters
TotalCluster
Proportion
Same/Total
1Atlanta0.0003750.00100.0011.000
 Chicago0.000250.00087500.0008751.000
 Houston0.0001250.00037500.0003751.000
 Miami0.0001250.00037500.0003751.000
 New York0.000250.00087500.0008751.000
 Washington D.C.0.000250.00087500.0008751.000
2Denver0.00006250.00012500.0001251.000
 Los Angeles0.0001250.000187500.00018751.000
 San Francisco0.00018750.0002500.000251.000
 Seattle0.0001250.000187500.00018751.000

Cluster Statistics
ClusterFrequencyMaximum
Estimated
Density
Boundary
Frequency
Estimated
Saddle
Density
160.0003750.
240.00018750.

Modeclus Analysis of 10 American Cities
Based on Flying Mileages

The MODECLUS Procedure

Cluster Summary
RCKNumber of
Clusters
Frequency of
Unclassified
Objects
600220
800220