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Dataplot Vol 2 Vol 1

GENERALIZED JACCARD COEFFICIENT
GENERALIZED JACCARD DISTANCE

Name:
    GENERALIZED JACCARD COEFFICIENT (LET)
    GENERALIZED JACCARD DISTANCE (LET)
Type:
    Let Subcommand
Purpose:
    Compute the generalized Jaccard coefficient or the generalized Jaccard distance between two variables.
Description:
    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).

Syntax 1:
    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.
Syntax 2:
    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.
Examples:
    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
Note:
    Dataplot statistics can be used in a number of commands. For details, enter

Default:
    None
Synonyms:
    None
Related Commands: Applications:
    Multivariate Analysis
Implementation Date:
    2017/08
Program 1:
     
    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
        
    plot generated by sample program
Program 2:
     
    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
        

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Date created: 08/31/2017
Last updated: 08/31/2017

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