Parallel Coordinates

The Parallel coordinates is a technique pioneered in the 1970s which has been applied to a diverse set of multidimensional problems (Inselberg et al. 1987). In the parallel coordinates plot, each dimension (variable) 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.

A Parallel Coordinate Representation of One Case: This graph shows a data point that is CROWD=0, DENSITY=-0.9, LLTI=-0.6, SC1=0.2, SPF=-1, UNEMP=-0.2

Parallel Coordinates Plot: To view an entire dimensional data set, one simply plots all observations on the same graph. For large data sets, the appearance of such a plot appears confusing, but can be used to highlight outliers.

Blushing of Parallel Coordinates Plot (Example - Lowest Decile of LLTI is Highlighted): However, the real strength of this technique can be seen when subsets of the data are selected, usually on the basis of one particular variable. In this example, the subset of the data in the lowest decile of the variable LLTI is shown in black, and the remainder of the dataset in grey. However, looking at the locations of the black lines on the other axes shows whether the low values of this variable tend to be accompanied by any notable distributional patterns in the other variables. From the plot, it may be seen that often there are also low values of DENSITY and UNEMP.

High Linear Correlation in Parallel Coordinates – Example (the fish data with 9 variables): The parallel coordinates plot shows that the three fish length variables (L1, L2, L3) are very highly correlated. This finding implies that L2 and L3 contribute very little additional information from L1.

Parallel Coordinates & Scatter Plot Matrix: This example shows that Var1-Var2 has no correlation; Var2-Var3 has very strong positive correlation; Var3-Var4 has very strong negative (inverse) correlation.

Reference:

Inselberg, A., Tuval, C. and Reif, M. Convexity algorithms in parallel coodinates. Journal of the ACM 34: 765-801, 1987.

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