PARALLEL COORDINATES PLOT

PARALLEL COORDINATES PLOT

Graphics Command

Generate a parallel coordinates plot.

A parallel coordinates plot is a graphical data analysis technique for plotting multivariate data.

In the parallel coordinates plot, a set of parallel axes are drawn for each variable. Then a given row of data is represented by drawing a line that connects the value of that row on each corresponding axis. For example, given the row of data (0, 1, 0) for variables X1, X2, and X3:

      X3  +----------------------

      X2  ----------------------+

      X1  +----------------------

          0                     1
    

The "+" positions identify plot coordinates (these would be drawn as connected lines on a graphics device).

Paralled coordinate plots were first recoginized as a data analysis tool by Ed Wegman (see the Reference section below).

There have been a number of variants of the parallel coordinate plots recommended in the literature. These are not implemented in the current Dataplot parallel coordinates plot, but may be added at a later date.

PARALLEL COORDINATES PLOT <y1> <y2> ... <yk>
                        <SUBSET/EXCEPT/FOR qualification>
where <y1> through <yk> are the response variables;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

GROUP PARALLEL COORDINATES PLOT <y1> <y2> ... <yk> <tag>
                        <SUBSET/EXCEPT/FOR qualification>
where <y1> through <yk> are the response variables;
            <tag> is a group-id variable;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

With this syntax, the last variable listed is interpreted as a group-id variable. All rows of the response variable with the same group-id are plotted with the same line and character attributes. See the Note section below for additional clarification.

PARALLEL COORDINATES PLOT Y1 Y2 Y3 Y4 Y5
PARALLEL COORDINATES PLOT Y1 TO Y5
PARALLEL COORDINATES PLOT Y1 Y2 Y3 Y4 Y5 SUBSET TAG > 2

The data are typically scaled for a parallel coordinates plot. In Dataplot, you can use the following command:
SET PARALLEL COORDINATES PLOT STANDARDIZE <NONE/USCORE/ZSCORE>

where

NONE	-	means no scaling is applied
USCORE	-	scales the data between 0 and 1 (specifically xscale = (x - xmin)/(xmax - xmin)
ZSCORE	-	scales the data by subtracting the mean and dividing by the standard deviation

The default is USCORE. The NONE option is useful if you want to apply your own scaling. For example, you may want to scale the data based on the full data set, but only generate the parallel coordinates plot for a subset of the data.

For the GROUP PARALLEL COORDINATES PLOT case, you can use whatever numerical grouping scheme you find convenient. For example, you can use a categorical response variable that already provides grouping or you can define your own groups based on whatever criterion you find relevant.

However you define the original grouping, Dataplot automatically recodes the group id's as the integers from 1 to NG where NG is the number of groups. The coding is from smallest value of the original group id's to the largest value of the original group id's.

When the parallel coordinates plot is generated, observations with a group value of 1 use the first settings of the line and character settings, observations with a group value of 2 use the second settings of the line and character settings, and so on.

By default, Dataplot draws the parallel axes on the vertical axis and the data scale on the horizontal axis. To reverse this, enter the command
HORIZONTAL SWITCH ON

The order of the variables on the plot can affect the appearance of the parallel coordinates plot. At the current time, Dataplot simply draws the axes in the order they are given on PARALLEL COORDINATES PLOT command.

Dataplot currently allows up to 30 variables to be plotted.

The TO syntax is allowed on this command. For example
PARALLEL COORDINATES PLOT Y1 TO Y10

None

None

LINES	= Sets the types for plot lines.
PLOT	= Generates a data or function plot.
ANDREWS PLOT	= generate an Andrews plot.
STAR PLOT	= Generate a star plot.
PROFILE PLOT	= Generate a profile plot.

"Hyperdimensional Data Analysis Using Parallel Coordinates", Edward Wegman, Journal of the American Statistical Association, 85, 664-675.

Multivariate Analysis

2003/3
2003/5: Added GROUP PARALLEL COORDINATE PLOT case and fixed a bug where the pre-sort was not automatically turned off for this command.

ROW LIMITS 26 50
COLUMN LIMITS 20 132
READ AUTO79.DAT Y1 TO Y9
.
YLIMITS 0 8
MAJOR YTIC MARK NUMBER 9
MINOR YTIC MARK NUMBER 0
Y1TIC MARK LABEL FORMAT ALPHA
Y1TIC MARK LABEL CONTENT PRICE MPG 1978SP()REPAIR 1977SP()REPAIR ...
HEADSP()ROOM REARSP()SEATCR()ROOM TRUNKSP()SPACE WEIGHT LENGTH
YGRID ON
TIC OFFSET UNITS SCREEN
TIC OFFSET 3 3
.
PRE-SORT OFF
FRAME CORNER COORDINATES 20 20 90 90
PARALLEL COORDINATES PLOT Y1 TO Y9