 Dataplot Vol 2 Vol 1

# MANHATTAN DISTANCE

Name:
MANHATTAN DISTANCE (LET)
Type:
Let Subcommand
Purpose:
Compute the Manhattan distance between two variables.
Description:
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.

Syntax:
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.
Examples:
LET A = MANHATTAN DISTANCE Y1 Y2
LET A = MANHATTAN DISTANCE 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:
 COSINE DISTANCE = Compute the cosine distance. EUCLIDEAN DISTANCE = Compute the Euclidean distance. MATRIX DISTANCE = Compute various distance metrics for a matrix.
Applications:
Mathematics
Implementation Date:
2017/03
Program:

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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Date created: 07/20/2017
Last updated: 07/20/2017