Parallel Coordinates

Figure 3

Parallel coordinates is a technique pioneered in the 1970's which has been applied to a diverse set of multidimensional problems [INS:90]. In this method, each dimension corresponds to an axis, and the N axes are organized as uniformly spaced vertical lines.  A data element in N-dimensional space manifests itself as a connected set of points, one on each axis.  Points lying on a common line or plane create readily perceived structures in the image.

In generating the display of parallel coordinates in XmdvTool, the view area is divided into N vertical slices of equal width.  At the center of each slice an axis is drawn, along with a label at the top end.  Data points are generated as polylines across the N axes.

Figure 3 shows an example of the Parallel Coordinates technique using the same data set as in Figure 1.  Clustering is evident among some of the lines, indicating a degree of correlation.  For example, the X-shaped structure between the axes for cleared cases and homicides indicates an inverse correlation, and the nearly parallel lines betwen the axes for manufacturing workers and handgun licenses suggests a relatively constant increase in the rate of handgun ownership as manufacturing jobs increase (some exceptions exist, however).

The major limitation of the Parallel Coordinates technique is that large data sets can cause difficulty in interpretation; as each point generates a line, lots of points can lead to rapid clutter.  Also, relationships between adjacent dimensions are easier to perceive than between non-adjacent dimensions. The number of dimensions which can be visualized is fairly large, limited by the horizontal resolution of the screen, although as the axes get closer to each other it becomes more difficult to perceive structure or clusters.

We have extended flat Parallel Coordinates to hierarchical Parallel Coordinates. In hierarchical Parallel Coordinates, we represent clusters instead of data points. The information of a cluster is visually encoded by a variable-width opacity bands. The mean stretches across the band and is encoded with the deepest opacity. The extend of the band indicates the extend of the cluster.  Movie 3 is a multiresolutional cluster display of hierarchical Parallel Coordinates.

References

[INS:90]:  Inselberg, A., Dimsdale, B..  Parallel coordinates: a tool for visualizing multidimensional geometry.  Proceedings of Visualization '90, pp. 361 - 378, 1990.

[ward:94]:  M. Ward.  Xmdvtool: Integrating multiple methods for visualizing multivariate data.  Proc. of Visualization '94, p. 326-33, 1994.