Re: DM: Parallel coordinates

[Alfred Inselberg]

Hi again dear Warren,

Re my previous discussion instead of "side" (of the hypercube) read
"diagonal". Thanks


Alfred Inselberg

***********************************************************************

On Thu, 8 Jan 1998, Warren Sarle wrote:

> 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
> saswss@unx.sas.com    SAS Campus Drive     are mine and not 
>necessarily
> (919) 677-8000        Cary, NC 27513, USA  those of SAS Institute.
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>