[comp.graphics.visualization] Multivariate realtions

andyrose@batcomputer.tn.cornell.edu (Andy Rose) (11/16/90)

For a truly novel approach to visualizing data of n-dimensions see:

The Visual Computer (1985) 1:69-91  (C) Springer Verlag

The plane with parallel coordinates
Alfred Inselberg

IBM Scientific Center
11601 Wilshire Boulevard
Los Angeles, CA 90025-1738  USA

Department of Computer Science
University of California Los Angeles, CA 90024 USA


Abstract:
By means of _Parallel Coordinates_ planar "graphs" of multivariate
relations are obtained.  Certain properties of the relationship 
correspond to _the geometrical properties_ of its graph.  On the
plane a point <- -> line duality with several interesting properties
in induced.  A new duality between _bounded and unbounded convex sets
and hstars (a generalization of hyperbolas)_ and between Convex Unions
and Intersections is found.  This motivates some efficient Convexity
algorithms and other results in _Computational Geometry_.  There is
also a surprising "cusp" <- -> "inflection point" duality.  The
narrative ends with a preview of the corresponding results in R^n.

Key words: Convexity, Duality, Parallel Coordinates, Intelligent control


Inselberg spoke at Cornell Theory Center a few weeks ago and he is 
on to something.  If you have data for, say, the eating habits of
Europeans and you wish to see correlations in the data try this.  
Set up some lines like so

  |   |   |   |  |  ... |
  |   |   |   |  |      |
  P   R   S   C  B      T
  o   i   u   l  e      o
  r   c   g   a  a      f
  k   e   a   m  n      u
          r   s  s  

And plot a "line" for each country in a different color.  I say "line" 
because it obviously won't be straight.  You have now represented 
n-dimensional data on a two-D plot.  Inselberg's paper is very deep
so I won't try to guess...



-- 
Andrew Newkirk Rose '91 Department of Visualization CNSF/Theory Center
632 E & T Building, Hoy Road Ithaca, NY 14583  
607 254 8686  andy@cornellf.tn.cornell.edu