MANHATTAN DISTANCE

MANHATTAN DISTANCE (LET)

Let Subcommand

Compute the Manhattan distance between two variables.

The Manhattan distance between two variabes X and Y is defined as
\( d = \sum_{i=1}^{n}{|X_{i} - Y_{i}|} \)

The Manhattan distance is also referred to as the city block distance or the taxi-cab distance. It is equivalent to a Minkowsky distance with P = 1.

The Manhattan distance is the distance measured along axes at right angles.

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

LET A = MANHATTAN DISTANCE Y1 Y2
LET A = MANHATTAN 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.
EUCLIDEAN DISTANCE	=	Compute the Euclidean distance.
MATRIX DISTANCE	=	Compute various distance metrics for a matrix.

Mathematics

2017/03

 
SKIP 25
READ IRIS.DAT Y1 TO Y4 X
.
LET DIST  = MANHATTAN DISTANCE Y1 Y2
SET WRITE DECIMALS 4
TABULATE MANHATTAN DISTANCE Y1 Y2 X
.
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 Manhattan Distance (IRIS.DAT)
Y1LABEL Manhattan Distance
MANHATTAN DISTANCE PLOT Y1 Y2 X
    

The following output is generated

            Cross Tabulate MANHATTAN DISTANCE
 
(Response Variables: Y1       Y2      )
---------------------------------------------
       X          |   MANHATTAN DISTA
---------------------------------------------
         1.0000   |           78.9000
         2.0000   |          158.3000
         3.0000   |          180.7000
    

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