GENERALIZED JACCARD COEFFICIENT
GENERALIZED JACCARD DISTANCE

GENERALIZED JACCARD COEFFICIENT (LET)
GENERALIZED JACCARD DISTANCE (LET)

Let Subcommand

Compute the generalized Jaccard coefficient or the generalized Jaccard distance between two variables.

The generalized Jaccard coefficient between two variabes X and Y is
\( J(X,Y) = \frac{\sum_{i=1}^{n}{\min(X_{i},Y_{i})}} {\sum_{i=1}^{n}{\max(X_{i},Y_{i})}} \)

The Jaccard distance is then defined as 1 - J(X,Y).

LET <par> = GENERALIZED JACCARD COEFFICIENT <y1> <y2>
                        <SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
            <y2> is the second response variable;
            <par> is a parameter where the computed generalized Jaccard coefficient is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET <par> = GENERALIZED JACCARD DISTANCE <y1> <y2>
                        <SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
            <y2> is the second response variable;
            <par> is a parameter where the computed generalized Jaccard distance is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = GENERALIZED JACCARD COEFFICIENT Y1 Y2
LET A = GENERALIZED JACCARD DISTANCE Y1 Y2
LET A = GENERALIZED JACCARD COEFFICIENT Y1 Y2 ...
                        SUBSET Y1 >= 0 SUBSET Y2 >= 0

Dataplot statistics can be used in a number of commands. For details, enter
HELP STATISTICS

None

None

BINARY JACCARD DISSIMILARITY	=	Compute the Jaccard dissimilarity coeficient for two binary variables.
COSINE DISTANCE	=	Compute the cosine distance.
MANHATTAN DISTANCE	=	Compute the Euclidean distance.
EUCLIDEAN DISTANCE	=	Compute the Euclidean distance.
MATRIX DISTANCE	=	Compute various distance metrics for a matrix.
GENERATE MATRIX <stat>	=	Compute a matrix of pairwise statistic values.

Multivariate Analysis

2017/08

 
SKIP 25
READ IRIS.DAT Y1 TO Y4 X
.
LET DIST  = GENERALIZED JACCARD DISTANCE Y1 Y2
SET WRITE DECIMALS 4
TABULATE GENERALIZED JACCARD DISTANCE Y1 Y2 X
     
            Cross Tabulate GENERALIZED JACCARD DISTANCE
 
(Response Variables: Y1       Y2      )
---------------------------------------------
       X          |   GENERALIZED JAC
---------------------------------------------
         1.0000   |            0.3152
         2.0000   |            0.5334
         3.0000   |            0.5486
     
.
XTIC OFFSET 0.2 0.2
X1LABEL GROUP ID
LET NDIST = UNIQUE X
XLIMITS 1 NDIST
MAJOR X1TIC MARK NUMBER NDIST
MINOR X1TIC MARK NUMBER 0
CHAR X
LINE BLANK
LABEL CASE ASIS
CASE ASIS
TITLE CASE ASIS
TITLE OFFSET 2
.
TITLE Generalized Jaccard Distance (IRIS.DAT)
Y1LABEL Generalized Jaccard Distance
GENERALIZED JACCARD DISTANCE PLOT Y1 Y2 X
    

 
set write decimals 3
dimension 100 columns
.
skip 25
read iris.dat y1 y2 y3 y4
skip 0
.
let z = generate matrix generalized jaccard coefficient y1 y2 y3 y4
print z
    

The following output is generated

 
        MATRIX Z       --            4 ROWS
                       --            4 COLUMNS

 VARIABLES--Z1             Z2             Z3             Z4      

          1.000          0.523          0.586          0.148
          0.523          1.000          0.469          0.283
          0.586          0.469          1.000          0.252
          0.148          0.283          0.252          1.000