MINKOWSKI DISTANCE

MINKOWSKI DISTANCE (LET)

Let Subcommand

Compute the Minkowski distance between two variables.

The Minkowski distance between two variabes X and Y is defined as
\[ (\sum_{i=1}^{n}{|X_{i} - Y_{i}|^{p}})^{1/p} \]

The case where p = 1 is equivalent to the Manhattan distance and the case where p = 2 is equivalent to the Euclidean distance.

Although p can be any real value, it is typically set to a value between 1 and 2. For values of p less than 1, the formula above does not define a valid distance metric since the triange inequality is not satisfied.

The value of p is specified by entering the command

LET P = <value>

before entering the MINKOWSKI DISTANCE command. If p is not specified, a default value of p = 1 will be used.

LET <par> = MINKOWSKI 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 Minkowski distance is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET P = 1
LET A = MINKOWSKI DISTANCE Y1 Y2
LET A = MINKOWSKI DISTANCE 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

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.

Mathematics

2017/08

 
SKIP 25
READ IRIS.DAT Y1 TO Y4 X
LET P = 1.5
.
LET DIST  = MINKOWSKI DISTANCE Y1 Y2
SET WRITE DECIMALS 4
TABULATE MINKOWSKI DISTANCE Y1 Y2 X
    
            Cross Tabulate MINKOWSKI DISTANCE
 
(Response Variables: Y1       Y2      )
---------------------------------------------
       X          |   MINKOWSKI DISTA
---------------------------------------------
         1.0000   |           21.5631
         2.0000   |           43.1725
         3.0000   |           49.3414
     
.
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 Minkowski Distance with P = 1.5 (IRIS.DAT)
Y1LABEL Minkowski Distance
MINKOWSKI DISTANCE PLOT Y1 Y2 X
    

    
    

 
set write decimals 3
dimension 100 columns
.
skip 25
read iris.dat y1 y2 y3 y4
skip 0
.
let p = 1.5
let z = generate matrix minkowski distance y1 y2 y3 y4
print z
    

The following output is generated

 
        MATRIX Z       --            4 ROWS
                       --            4 COLUMNS

 VARIABLES--Z1             Z2             Z3             Z4      

          0.000          5.100          5.600          6.600
          5.100          0.000          4.300          4.000
          5.600          4.300          0.000          4.700
          6.600          4.000          4.700          0.000