Re: DM: CSI Visualizer Workstation Announcement

[P.G.Hamer]

Georges Grinstein <ggg@spacetec.com> writes:

> Rhonda Delmater <rdelmater@csihq.com> writes:
>> CSI's Visualizer Workstation Provides Important New Data Mining 
>Insights 
>>                Data can be viewed in multi-dimensional space. 
>> ... The Visualizer Workstation allows
>> users to view, manipulate and analyze sets of discrete data points
>> in up to 10-dimensions simultaneously.  Nearness, occlusion, and
>> perspective are preserved. 
>and Warren Sarle <saswss@unx.sas.com> comments:

>> 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.

>Nope. Any projection (in the classic sense) that projects down to 2D 
>is
>continuous. That is if 2 points are close in 10D space then they are
close in the projected 2D space (the converse is not true).

Surely this simply repeats the point that Warren was making. That you 
cannot (in the general case)  map points in a 10D space to points in 
a 
2D space while preserving distance relationships. To argue that you 
can 
preserve near-ness but not far-ness seems sophistry.

>I want to
>add also that there are  transformations of 10D to 2D which do 
>present
>all 10D data (with no loss of data) and for which closeness in 2D
>implies closeness in 10D (a parallel coordinate representation of 
>that
>10D data for example).

This is an important point, which involves the mapping of points in 
10D
to lines in 2D. Unfortunately its hard to follow individual lines when
using techniques such as Andrews curves and parallel coordinates for
even moderate numbers of points. Which greatly limits their utility.  

Peter