DM: Parallel coordinates

[Warren Sarle]

I wrote:
> It is mathematically impossible except in degenerate cases to 
>display
> 10-dimensional data in such a way that nearness of points in the 10D
> space is visually preserved.

Alfred Inselberg <aiisreal@math.tau.ac.il> replied:
> There is no problem doing this in Parallel Coordinates and for a 
>lot more
> dimensions.

This raises some interesting questions. It is certainly true that a
trained analyst can, with sufficient effort, assess distances in a
parallel coordinates plot. But I don't think that the visual 
impressions
of distance provided by a parallel coordinates plot are a monotone
function of actual Euclidean distance. Consider four cases in a 2D
Euclidean space:

      X Y
   A  0 0
   B  1 1
   C  0 1
   D  1 0

The distance between A and B equals the distance between C and D.
But a parallel coordinates plot of A and B looks like this:

      X  Y
   0  ----


   1  ----

while a parallel coordinates plot of C and D looks like this:

      X  Y
   0  \  /
       \/
       /\
   1  /  \

I think that C and D _appear_ closer than A and B. Whether this
psychological impression is shared by other people is, of course,
an empirical question. Does anyone know of experiments that have
been done on the perception of distance in parallel coordinates plots?

-- 

Warren S. Sarle       SAS Institute Inc.   The opinions expressed here
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