Statistical Considerations
When used for statistical data visualisation there are three important considerations: the order, the rotation, and the scaling of the axes.
The order of the axes is critical for finding features, and in typical data analysis many reorderings will need to be tried. Some authors have come up with ordering heuristics which may create illuminating orderings.
The rotation of the axes is a translation in the parallel coordinates and if the lines intersected outside the parallel axes it can be translated between them by rotations. The simplest example of this is rotating the axis by 180 degrees.
The necessity of scaling stems from the fact that the plot is based on interpolation (linear combination) of consecutive pairs of variables. Therefore, the variables must be in common scale, and there are many scaling methods to be considered as part of data preparation process that can reveal more informative views.
A smooth parallel coordinate plot is achieved with splines. In the smooth plot, every observation is mapped into a parametric line (or curve), which is smooth, continuous on the axes, and orthogonal to each parallel axis. This design emphasizes the quantization level for each data attribute. If one uses the Fourier interpolation of degree equals to the data dimensionality, then an Andrews plot is achieved.
Read more about this topic: Parallel Coordinates