DM: CSI DVW Preservation of "Nearness"

[Warren Sarle]

Monte Hancock <mhancock@csihq.com> writes:
> Because the DVW regression is continuous and regular, points which
> are proximate in Rn remain proximate on the display, and in a way
> which preserves intuitive visual elements of the local geometry.

In any linear 2D projection, points which are proximate in Rn remain
proximate on the display. What's special about what CSI Visualizer
does?
 
> The DVW regression preserves many of the same intuitive aspects of
> proximity which, for example, make a flat photograph of a
> 3-dimensional scene useful.  Objects are recognizable and
> interpretable.  High-dimensional theoretical geometric effects can
> be visually observed (e.g., in 4-space, 3-spheres appear
> ellipsoidal/flat from certain perspectives, while 4-spheres are
> "round" from all perspectives).

These examples are not challenging. What happens with nontrivial
examples such as those in Furnas & Buja (1994), "Prosection views:
dimensional inference through sections and projections, J. of 
Computational and Graphical Statistics, 3, 323-385?

Since the original announcement was posted to
datamine-l@nautilus-sys.com, it would be nice to have an explanation
posted to that list of what the marketese really means.

-- 

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