Re: Parallel coordinate plot type?

[Ethan M. <merritt@u.washington.edu>]

On Monday 12 June 2006 02:11 am, Niklas Elmqvist wrote:
> I am looking to create a parallel coordinate plot for a paper I am
> working on. 

I was not familiar with this plot type, so I did some Googling.
Is this an adequate description of what you want?

  http://www.agocg.ac.uk/reports/visual/casestud/brunsdon/parallel.htm

> I've started looking at using gnuplot for this purpose, but there
> appears to be no PC plot type

Correct, there is no such plot type in gnuplot.
It does look quite interesting, however, so I encourage you to submit
it as a "Feature Request" on gnuplot's SourceForge site.

> Any ideas on how to achieve this? Using gnuplot or some other (freely
> available) tool?

I think it would not be very hard to tweak your input data file so
that gnuplot can produce a reasonable approximation of what you want.
If if understand correctly (which I may not) then your data consists
of a set of observations, each of which contains 5-10 associated values:

# Obs	#Val_1	#Val_2	#Val_3	...	#Val_10
###############################################
1	val1	-	val3		val10
2	val1	val2	val3		val10
3	val1	val2	val3		-
4	-	val2	val3		val10
...

I have marked missing values with a '-' character.
You want to plot this so that there is a line on the graph for each
observation, and that line passes through val1 at x=1, val2 at x=2,
and so on.  I hope I got that correctly.

The first issue is that gnuplot normally uses the x-axis to separate
the *row* entries rather than the  *column* entries.
So you probably will have to transpose the rows and columns of
your input data file, so that now it looks like this:

Dim	Obs1	Obs2	Obs3	...	Obs100
##############################################
Val_1	val1	val1	val1		val1
Val_2	-	val2	val2		val2
Val_3	val3	val3	val3		val3

At this point it is relatively simple to plot in gnuplot.
I will use auto-labelling commands from version 4.1, but
you could get the same plot in earlier versions by placing
the labels manually.
 
Your plot commands would be something like

set datafile missing '-'
set key autotitle columnheader
set key outside left

set xrange [0.5:10.5]       # Span the 10 dimensions
set auto y                  # y will scale itself

set style data line         # plot with lines, no points
                            # (lt -1) is thin black line

plot "datafile" using xticlabel(1):2 lt -1, \
     "" using 3 lt -1, \
     "" using 4 lt -1, \
     "" using 5 lt -1, \
...
     "" using 100 lt -1


The vertical bars can be added manually:

set arrow 1 from 1, graph 0 to 1, graph 1 nohead
set arrow 2 from 2, graph 0 to 2, graph 2 nohead
...
set arrow 10 from 10, graph 0 to 10, graph 10 nohead

If you have a scaling function for a particular dimension,
it can be defined and added as follows:

# Normalization function for dimension 2
f_2(g) =  (g - GMIN) / (GMAX-GMIN)
input_2(g) = ($0 == 3) ? f_2(g) : g        

plot "datafile" using xticlabel(1):(input_2($2)), \
     "" using (input_2($3)), \
     ...

> (Sorry if this is an obvious question, but I have cast around a bit
> and I did not find an obvious answer.)

Not so obvious, but quite possible.

I am intrigued by the plot mode, and will seriously consider
adding it as a supported plot type. It is similar in many ways
to the stacked histogram plot modes, so a model already exists
for its implementation in gnuplot.


-- 
Ethan A Merritt
Biomolecular Structure Center
University of Washington, Seattle WA