last updated July 25, 1999
 
 
 

 

 

The dynamic parallel coordinate plot 

Introduction 
The dynamic parallel coordinate plot is one of the primary interface and display tools in the exploratory visualization environment being constructed within the Apoala project.  The parallel coordinate technique was originally proposed and implemented by Inselberg (1985) and task-specific variations of the device have been put forth by other statisticians (Wegman, 1990; Miller and Wegman, 1991; Jang and Yang, 1996).  Its primary advantage over other types of statistical graphics is its ability to display multi-dimensional data in one representation, breaking the traditional bounds of two- or three-dimensional multivariate representations such as scatter plots. 

Each observation in a data set is represented as an unbroken series of line segments which intersect vertical axes, each scaled to a different variable.  The value of the variable for each observation is plotted along each axis relative to the minimum and maximum values of the variable for all observations; the points are then connected using line segments.  The result is a "signature" across n dimensions for each observation. 

Observations with similar data values across all variables will share similar signatures.  Clusters of like observations can thus be discerned.  Associations among variables can also be visualized; two variables inversely proportional to each other will be connected by line segments (observations) which all cross in the region between the axes, while two directly proportional variables will be connected by parallel line segments.  In fact, the number of crossings of line segments is directly related to the correlation coefficient r (Wegman, 1990). 

The Apoala PCP: a user's guide 
The dynamic parallel coordinate plot developed here facilitates the exploration of these relationships. 

  • The user is able to explore relationships among any set of variables by manipulating the variable displayed on each axis.
  • The user can strum the lines of the plot, highlighting the trace of an individual observation across all variables.
  • Clusters of lines may be brushed, to discover whether the correlations exhibited among observations between two variables are consistent among all (or some) other variables.
  • The observations are classified (with different colors) according to one of the variables:
  • Observations which share a range of one variable may be focused upon, allowing visual exploration of a subset of queried observations.
  • The plot may be used as an interface to other exploratory analysis tools; though not implemented in this web version of the tool, the buttons along the top of the plot would be used to dictate the variables plotted on a two- or three-dimensional scatter plot which would complement the parallel coordinate display.
An Application 
Though the dynamic PCP is a valuable tool for many statistical and information visualization applications, it was designed for use in a geographic visualization context.  It will serve as an interface tool in the Apoala space-time GIS environment being developed in the Geography department at Penn State.  The first application was the visualization on the results of the data mining of a set of climate data in and around Texas and northern Mexico.  This application is described in full in a paper in the International Journal of Geographic Information Science (IJGIS).  There is a link to a condensed version of the printed paper at the web site for the GeoVISTA center

What you need to view the plot 
The parallel coordinate plot is a "tclet" (pronounced "TICK-let"), scripted in the Tcl/Tk interface developers' language.  You'll need the Tcl plug-in, available from Scriptics.  If you have the Tcl plug-in already installed, there should be a green dot in this spot ---> <-. If it's blank, or not green, you need to download the most recent version. 

Contact us 
We are very interested in you reactions to these tools.  Please e-mail Apoala with comments, suggestions, and questions. 

Further Reading 
Inselberg, A. (1985), "The Plane with Parallel Coordinates," The Visual Computer, 1, 69-91. 
Jang, D.H., and Yang, S-J. (1996) "The Dynamic Parallel Coordinate Plot and its Applications," Journal of the Korean Statistical Society, 9:1, 45-52. 
Miller, J.J., and Wegman, E.J. (1991), "Construction of Line Densities for Parallel Coordinate Plots," in Computing and Graphics in Statistics, ed. by Buja, A., and Tukey, P. (New york: Springer-Verlag), pp. 107-123. 
Wegman, E.J. (1990), "Hyperdimensional Data Analysis Using Parallel Coordinates," Journal of the American Statistical Association, 85:411, 664-675. 

text and graphics by Rob Edsall, web design by Mark Harrower
©1999 The Pennsylvania State University