Parallel coordinates

Parallel Coordinates plots are a common method of visualizing high-dimensional datasets to analyze multivariate data having multiple variables, or attributes.

The concept of Parallel Coordinates is often said to originate in 1885 by a French mathematician Philbert Maurice d'Ocagne.

[1] d'Ocagne sought a way to provide graphical calculation of mathematical functions using alignment diagrams called nomograms which used parallel axes with different scales.

The use of Parallel Coordinates as a visualization technique to show data is also often said to have originated earlier with Henry Gannett in work preceding the Statistical Atlas of the United States for the 1890 Census, for example his "General Summary, Showing the Rank of States, by Ratios, 1880", [2] that shows the rank of 10 measures (population, occupations, wealth, manufacturing, agriculture, and so forth) on parallel axes connected by lines for each state.

The value of parallel coordinates is that certain geometrical properties in high dimensions transform into easily seen 2D patterns.

For n = 2 this yields a point-line duality pointing out why the mathematical foundations of parallel coordinates are developed in the projective rather than euclidean space.

Hence by using curves in parallel coordinates instead of lines, the point line duality is lost together with all the other properties of projective geometry, and the known nice higher-dimensional patterns corresponding to (hyper)planes, curves, several smooth (hyper)surfaces, proximities, convexity and recently non-orientability.

When used for statistical data visualisation there are three important considerations: the order, the rotation, and the scaling of the axes.

[8] Scaling is necessary because the plot is based on interpolation (linear combination) of consecutive pairs of variables.

However, when the axes do not have a unique order, finding a good axis arrangement requires the use of experimentation and feature engineering.