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Dataplot Vol 2 Vol 1

PEARSON DISSIMILARITY

Name:
    PEARSON DISSIMILARITY (LET)
Type:
    Let Subcommand
Purpose:
    Compute the Pearson correlation coefficient transformed to a dissimilarity measure between two variables.
Description:
    The correlation coefficient is a measure of the linear relationship between two variables. It is computed as:

      \( S_{xx} = \sum_{i=1}^{N}{(X_{i} - \bar{X})^{2}} \)

      \( S_{yy} = \sum_{i=1}^{N}{(Y_{i} - \bar{Y})^{2}} \)

      \( S_{xy} = \sum_{i=1}^{N}{(Y_{i} - \bar{Y})(X_{i} - \bar{X})} \)

      \( r = \frac{S_{xy}}{\sqrt{S_{xx} S_{yy}}} \)

    A perfect linear relationship yields a correlation coefficient of +1 (or -1 for a negative relationship) and no linear relationship yields a correlation coefficient of 0.

    In some applications, such as clustering, it can be useful to transform the correlation coefficient to a dissimilarity measure. The transformation used here is

      \( d = \frac{1 - r}{2} \)

    This converts the correlation coefficient with values between -1 and 1 to a score between 0 and 1. High positive correlation (i.e., very similar) results in a dissimilarity near 0 and high negative correlation (i.e., very dissimilar) results in a dissimilarity near 1.

    If a similarity score is preferred, you can use

      \( s = 1 - d \)

    where d is defined as above.

Syntax:
    LET <par> = PEARSON DISSIMILARITY <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 Pearson dissimilarity is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = PEARSON DISSIMILARITY Y1 Y2
    LET A = PEARSON DISSIMILARITY Y1 Y2 SUBSET TAG > 2
Note:
    The two variables must have the same number of elements.
Default:
    None
Synonyms:
    None
Related Commands: Reference:
    Kaufman and Rousseeuw (1990), "Finding Groups in Data: An Introduction To Cluster Analysis", Wiley.
Applications:
    Clustering
Implementation Date:
    2017/08:
Program 1:
     
    SKIP 25
    READ BERGER1.DAT Y X
    LET CORR = CORRELATION Y X
    LET D    = PEARSON DISSIMILARITY Y X
    PRINT CORR D
        
    The following output is generated
     PARAMETERS AND CONSTANTS--
    
        CORR    --          0.946
        D       --          0.027
        
Program 2:
     
    SKIP 25
    READ IRIS.DAT Y1 Y2 Y3 Y4
    SET WRITE DECIMALS 3
    .
    LET M = GENERATE MATRIX PEARSON DISSIMILARITY Y1 Y2 Y3 Y4
    PRINT M
        
    The following output is generated
     
            MATRIX M       --            4 ROWS
                           --            4 COLUMNS
    
     VARIABLES--M1             M2             M3             M4      
    
             -0.000          0.559          0.075          0.155
              0.559          0.000          0.736          0.534
              0.075          0.736          0.000          0.144
              0.155          0.534          0.144          0.000
        
Program 3:
     
    SKIP 25
    READ IRIS.DAT Y1 Y2 Y3 Y4 TAG
    .
    TITLE CASE ASIS
    TITLE OFFSET 2
    LABEL CASE ASIS
    TIC MARK OFFSET UNITS DATA
    Y1LABEL Pearson Dissimilarity Coefficient
    YLIMITS 0 1
    MAJOR YTIC MARK NUMBER 6
    MINOR YTIC MARK NUMBER 1
    Y1TIC MARK LABEL DECIMAL 1
    Y1LABEL DISPLACEMENT 20
    X1LABEL Species
    XLIMITS 1 3
    MAJOR XTIC MARK NUMBER 3
    MINOR XTIC MARK NUMBER 0
    XTIC MARK OFFSET 0.3 0.3
    X1LABEL DISPLACEMENT 14
    CHARACTER X BLANK
    LINES BLANK SOLID
    .
    MULTIPLOT CORNER COORDINATES 5 5 95 95
    MULTIPLOT SCALE FACTOR 2
    MULTIPLOT 2 3
    .
    TITLE Sepal Length vs Sepal Width
    CORRELATION PLOT Y1 Y2 TAG
    .
    TITLE Sepal Length vs Petal Length
    CORRELATION PLOT Y1 Y3 TAG
    .
    TITLE Sepal Length vs Petal Width
    CORRELATION PLOT Y1 Y4 TAG
    .
    TITLE Sepal Width vs Petal Length
    CORRELATION PLOT Y2 Y3 TAG
    .
    TITLE Sepal Width vs Petal Width
    CORRELATION PLOT Y2 Y4 TAG
    .
    TITLE Petal Length vs Petal Width
    CORRELATION PLOT Y3 Y4 TAG
    .
    END OF MULTIPLOT
        

    plot generated by sample program

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Date created: 09/05/2017
Last updated: 09/05/2017

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