Parallel coordinate graphics
using MATLAB

Introduction

Multivariate or high-dimensional (HiD) systems are hard to visualize because we are wired for a 3D world. Many different systems have been suggested to help visualize HiD data. Most of them use some system of subspace selection to reduce the dimensionality to 2 or 3 (e.g. 1-4) or use some procedure to identify important axes (e.g. principal component analysis or projection pursuit).

The parallel coordinate (PC) scheme due to Inselberg and others (5-13) attempts to plot HiD systems in a different manner. Since plotting more than 3 orthogonal axis is impossible, parallel coordinate schemes plot all the axes parallel to each other in a plane. Amazingly enough, squashing the space in this manner does not destroy too much of the geometric structure. The geometric structure is however projected in such a fashion that most geometric intuition has to be relearned.

The plan here is to build up intuition for HiD representations in parallel coordinates:

Examples

References

(1) Calibrate you eyes to recognize high-dimensional objects from their projections. Diane Cook and Peter Sutherland. http://www.public.iastate.edu/~dicook/JSS/paper/paper.html

(2) Visualisation of High Dimensional Data. Dr. Carolina Cruz-Neira and Laura Arns

http://www.vrac.iastate.edu/research/visualization/multivariate/

(3) Polytope visualization. Gordon Kindelmann.
http://www.graphics.cornell.edu/~gordon/peek/

(4) N-Land: a Graphical Tool for Exploring N-Dimensional Data. Matthew O. Ward Jeffrey T. LeBlanc and Rajeev Tipnis.
http://davis.wpi.edu/~matt/courses/nland/cgi93.html

(5) Don't panic ... just do it in parallel! Al Inselberg, COMPUTATION STAT 14: (1) 53-77 1999

(6) Visual data mining with parallel coordinates Al Inselberg, COMPUTATION STAT 13: (1) 47-63 1998

(7) MULTIDIMENSIONAL LINES .1. REPRESENTATION. INSELBERG A, DIMSDALE B, SIAM J APPL MATH 54: (2) 559-577 APR 1994

(8) MULTIDIMENSIONAL LINES .2. PROXIMITY AND APPLICATIONS. INSELBERG A, DIMSDALE B, SIAM J APPL MATH 54: (2) 578-596 APR 1994

(9) HYPERDIMENSIONAL DATA-ANALYSIS USING PARALLEL COORDINATES. WEGMAN EJ. J AM STAT ASSOC 85 (411): 664-675 SEP 1990

(10) THE ANALYSIS OF T48 LOW PRESSURE TURBINE INLET TEMPERATURES USING PARALLEL COORDINATES. Frank S. Budny.
http://www.che.ufl.edu/visualize/THESIS/thesis.html

(11) Visualizing the Behavior of Higher Dimensional Dynamical Systems. R. Wegenkittl, H. Löffelmann, and E. Gröller.
http://www.cg.tuwien.ac.at/research/vis/dynsys/ndim/

(12) Hierarchical Parallel Coordinates. Ying-Huey Fua.
http://davis.wpi.edu/~yingfua/cs563_1/hiervis.html

(13) High Dimensional Clustering Using Parallel Coordinates and the Grand Tour. Edward J. Wegman and Qiang Luo.
http://www.galaxy.gmu.edu/papers/inter96.html


Copyright Cornell University, 2001