
PEARSON DISSIMILARITYName:
\( S_{yy} = \sum_{i=1}^{N}{(Y_{i}  \bar{Y})^{2}} \) \( S_{xy} = \sum_{i=1}^{N}{(Y_{i}  \bar{Y})(X_{i}  \bar{X})} \) \( r = \frac{S_{xy}}{\sqrt{S_{xx} S_{yy}}} \) 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
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
where d is defined as above.
<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.
LET A = PEARSON DISSIMILARITY Y1 Y2 SUBSET TAG > 2
SKIP 25 READ BERGER1.DAT Y X LET CORR = CORRELATION Y X LET D = PEARSON DISSIMILARITY Y X PRINT CORR DThe following output is generated PARAMETERS AND CONSTANTS CORR  0.946 D  0.027Program 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 MThe following output is generated MATRIX M  4 ROWS  4 COLUMNS VARIABLESM1 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 0.000Program 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  
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Date created: 09/05/2017 