Parallel Coordinates – How it
My interest in visualization was
sparked while learning Euclidean geometry. Later, while being a Ph.D. student
in Mathematics at the University of Illinois (Champaign-Urbana), and studying
multi-dimensional geometry I became frustrated by the absence of visualization. Basically, we were doing
Algebra which was being interpreted as Geometry but without the fun and
benefit of pictures. I kept
wondering about ways to make accurate “multi-dimensional
pictures” and derive insights about what may or may not be true in the
multi-dimensional worlds. Since parallelism is the fundamental concept
in geometry, and not orthogonality which uses the
plane very fast, I experimented with putting the coordinate axes parallel to
In 1959 Prof. S.S.Cairns,
during a lecture in his Topology course, lamented our inability to visualize
“high-dimensions” and prompted us for suggestions. I shared with the class
the idea of parallel
coordinates (abbr. ||-coords). In turn Prof.
Cairns mentioned it to another topologist Prof. D. Bourgin and they both encouraged me to pursue the idea.
Other than deriving the basics like the point ↔ line duality, it took
me many years to take their advice seriously. It was in 1977 while giving a
Linear Algebra course that I was challenged by my students to “show” them
some multi-dimensional spaces. This was the catalyst leading to the
of the methodology : How do multi-dimensional lines, planes,
curves, surfaces etc look in ||-coords ? Later I had the good fortune to
collaborate with Bernard Dimsdale (an associate of
John von Neuman) , at the IBM Los Angeles Science Center, who made many important
In 1987 IBM and another competitor were
left at the last stage of the contract competition for the new Air Traffic
Control (ATC). One of the contract specifications was for an
“Automatic Collision Detection and Avoidance ” Algorithm. Together with
Bernie Dimsdale, Mike Boz
(a superb student at UCLA and part-time at IBM) using ||-coords
we came up with a solution (USA patents # 4,823,272
, # 5,058,024 , # 5,173,861). In retrospect, it was the ATC
application (T.R.Willemain , J. Hu et. al ,
Chiang et al. and others ) which brought
serious and broader interest to ||-coords.
As of 2004 the most
common applications are on Visual and Automatic (Classification) Data Mining
(USA patent # 5,546,516), Optimization (C.V.
Jones, D. Joos, A. Goel and others), GIS ( J.A.
Dykes, N. &
R. Edsall and others) , Process Control, Decision
Support, Approximations (USA patent # 5,631, 982) and elsewhere.