Parallel Coordinates

Figure 2.5: Parallel coordinates used to visualize a four-dimensional iris dataset with 150 data items. The image was generated with XmdvTool [32,24,36].

A representation of data in parallel coordinates consists of a number of parallel axes and line segments between the axes [11,12,15,5]. The axes are assigned one variable of a dataset each. There are as many lines as observations in the dataset. The lines intersect the axes at a point that corresponds to the value the observation has in that variable. The axes are usually vertical, but they can also be horizontal. Figure 2.5 shows such a graph in parallel coordinates.

The relationship of two dimensions can easily be read from parallel coordinates if these two dimensions are assigned to neighboring axes. The locations and angles of the lines are important. The relationship between more than two dimensions is harder to see, because it is difficult to follow the lines across several axes. To solve this problem one can use brushing if the tool supports it. This means selecting certain lines that are of interest. These lines are then marked in some way and one can follow them easier across several axes.

Parallel coordinates are good for displaying about a dozen dimensions in one graph. The number of lines and therefore the number of observations that can be displayed is limited to a few dozen to a few hundred, depending on the amount of screen space and the implementation used.

Parallel Coordinates are used in several visualization tools [29,7,32,6]. The inventor of parallel coordinates explains how parallel coordinates can be used to solve real world problems [13,14]. He tells about the properties of parallel coordinates, the advantages of the concept, and gives guidelines how to effectively use the technique.

Figure 2.6: Hierarchical parallel coordinates [6], showing the same dataset as in Figure 2.5. Although cluttering is not severe in Figure 2.5, hierarchical parallel coordinates make it easier to identify clusters and correlations. The advantage is even clearer with bigger datasets.

A variation of parallel coordinates are hierarchical parallel coordinates [6]. This concept reduces the amount of overplotting that parallel coordinates suffer from when large datasets (more than a few hundred observations) are visualized. Data aggregation techniques are used to collapse data into clusters. The population and extends of these clusters are shown in parallel coordinates with bands of varying translucency (Figure 2.6). The opacity of the bands is highest in the center of the clusters, and the bands fade out towards their edges. The clusters are assigned different colors to make it easier to tell them apart.