Parallel coordinates

Everybody knows how to plot a point in two or three dimensional space. Now, when it comes to more than three dimensions, it requires different techniques. A common way of visualizing high-dimensional data is parallel coordinates. Parallel coordinates have been proposed, first, by Inselberg (1985). To show a set of points in a n-dimensional space, n parallel lines are drawn, typically vertical and equally spaced. A point in n-dimensional space is represented as a polyline with vertices on the parallel axes; the position of the vertex on the i-th axis corresponds to the i-th coordinate of the point. Figure 1 shows a linear function represented in a two-dimensional graph and in a parallel coordinates graph.

In parallel coordinates, the order of the axes is critical for finding features and for a better data analysis. Some authors have suggested some ordering heuristics that improve data visualization. This improvement is illustrated through a simple example on figure 2.