Computing a Distance Matrix
/****************************************************************/
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: CLUSDIST */
/* TITLE: Computing a Distance Matrix */
/* PRODUCT: SAS */
/* SYSTEM: ALL */
/* KEYS: CLUSTER DISTANCE */
/* PROCS: CLUSTER TREE PRINT SORT */
/* DATA: */
/* */
/* SUPPORT: WSS UPDATE: January 2010 */
/* REF: */
/* MISC: */
/* */
/****************************************************************/
Title 'Computing a Distance Matrix';
/***
NOTE: Most commonly-used distance measures can be computed by
PROC DISTANCE. But if you need to use a distance measure that
is not in PROC DISTANCE, you can compute it using a DATA step.
This example shows how to loop over the rows and columns of a
coordinate data set to compute a distance matrix. You can adapt
this DATA step code to compute many other types matrices.
***
A wide variety of distance and similarity measures are used in
cluster analysis (Anderberg 1973, Sneath and Sokal 1973).
If your data are in coordinate form and you want to use a non-Euclidean
distance for clustering, you can compute a distance matrix using a
DATA step or the IML procedure.
Similarity measures must be converted to dissimilarities before
being used in CLUSTER. Such conversion can be done in a variety
of ways, such as taking reciprocals or subtracting from a large
value. The choice of conversion method depends on the application
and the similarity measure.
In the following example, the observations are states. Binary-valued
variables correspond to various grounds for divorce and indicate
whether the grounds for divorce apply in each of the states.
A DATA step is used to compute the Jaccard coefficient (Anderberg
1973, 89, 115, and 117) between each pair of states. The Jaccard
coefficient is defined as the number of variables that are coded
as 1 for both states divided by the number of variables that are
coded as 1 for either or both states. The Jaccard coefficient is
converted to a distance measure by subtracting it from 1.
***/
options ls=120 ps=60;
data divorce;
title2 'Grounds for Divorce';
input State $15.
(Incompatibility Cruelty Desertion Non_Support Alcohol
Felony Impotence Insanity Separation) (1.) @@;
if mod(_n_,2) then input +4 @@; else input;
datalines;
Alabama 111111111 Alaska 111011110
Arizona 100000000 Arkansas 011111111
California 100000010 Colorado 100000000
Connecticut 111111011 Delaware 100000001
Florida 100000010 Georgia 111011110
Hawaii 100000001 Idaho 111111011
Illinois 011011100 Indiana 100001110
Iowa 100000000 Kansas 111011110
Kentucky 100000000 Louisiana 000001001
Maine 111110110 Maryland 011001111
Massachusetts 111111101 Michigan 100000000
Minnesota 100000000 Mississippi 111011110
Missouri 100000000 Montana 100000000
Nebraska 100000000 Nevada 100000011
New Hampshire 111111100 New Jersey 011011011
New Mexico 111000000 New York 011001001
North Carolina 000000111 North Dakota 111111110
Ohio 111011101 Oklahoma 111111110
Oregon 100000000 Pennsylvania 011001110
Rhode Island 111111101 South Carolina 011010001
South Dakota 011111000 Tennessee 111111100
Texas 111001011 Utah 011111110
Vermont 011101011 Virginia 010001001
Washington 100000001 West Virginia 111011011
Wisconsin 100000001 Wyoming 100000011
;
/* compute distance matrix containing (1.0 - Jaccard coefficient) */
data distjacc(type=distance);
array dj(*) dj1-dj50; /* variables to contain 1-Jaccard */
retain dj1-dj50 .; /* initialize to missing values */
do row=1 to 50; /* loop over rows of distance matrix */
set divorce point=row; /* read row state */
array grounds(*) incompatibility--separation; /* declare arrays*/
array save(*) save1-save9; /* after the SET statement */
do g=1 to 9; /* save data for row state */
save(g)=grounds(g);
end;
do col=1 to row; /* loop over columns of distance matrix */
set divorce(drop=state) point=col; /* read column state */
num=0; /* number of grounds that apply to both states */
den=0; /* number of grounds that apply to either state */
do g=1 to 9; /* loop over grounds for divorce */
num=num+(grounds(g) & save(g));
den=den+(grounds(g) | save(g));
end;
if den then dj(col)=1-num/den; /* convert to distance */
else dj(col)=1;
end;
output; /* output a row of the distance matrix */
end;
stop; /* stop statement is needed because SET statement
uses POINT= option */
keep state dj1-dj50; /* keep only the state and distance matrix */
run;
proc print data=distjacc(obs=10);
title2 'First 10 States';
id state;
var dj1-dj10;
run;
title2;
proc cluster data=distjacc method=centroid pseudo outtree=tree;
id state;
var dj1-dj50;
run;
proc tree data=tree noprint n=9 out=out;
id state;
run;
proc sort;
by state;
run;
data clus;
merge divorce out;
by state;
run;
proc sort;
by cluster;
run;
proc print;
id state;
var incompatibility--separation;
by cluster;
run;