VC: Parallel Coordinates

Parallel Coordinates

Parallel coordinates can be used to visualize multi-dimensional data. Each parallel axes correspond to attributes. The axes are scaled to the [min, max]. Every data item corresponds to a polygonal line which intersects of the axes at the point which corresponds to the value for the attribute.

Point-line duality for parallel coordinates

A straight line (y = m*x + b)in Cartesian coordinates results in a single intersection point in parallel coordinates.

Intersection Point

Example

The intersection point is generated depend on the cartesian line of slope:

1. Negative Slope: Between the X1 and X2
2. Slope > 1: Left of X1
3. 0 > slope > 1: Right of X2
4. Slope = 1: Parallel lines.

Now you can interpret this parallel coordinates, Color for tracking individual points.

We can plot the nominal data:

hospital lab dataset

Axis order is matters:

Axis order is matters

There are some techniques to interact:

Brushing and Linking

Brushing: highlighting part of the data by selecting it with the mouse.

Linking: also highlighting the same data in another view.

Overdraw

Overdraw is a problem.

Same data with semi-transparent

We can solve this problem with semi-transparent and subsampling.

Hierarchical Parallel Coordinates

After clustering, it plots clusters instead of individual data points

Plotting clusters instead of individual data points is another way to reduce overdraw.

Variation: Star Glyphs & Sun Ray Plots

Star Glyphs [Fienberg 1979]

Equally spaced radii with a common origin. The length of each spike is proportional to the value of the respective attribute.

Sun Ray Plots

Almost the same as a star glyph, except that we draw full axes.

This post is published on 9/2/2020