This is just an experiment: I want to embed higher dimensional graphs into
lower dimension. E.g. layout graph with 4D algorithm, use first three dimensions
to render graph in (X, Y, Z) space, and use fourth dimension to set color of
a node.
The graph layout is computed in four-dimensional and five-dimensional spaces. Then I render them in 3D, using fourth dimension as a node color. The smaller the numerical value of the fourth coordinate - the darker is the node.
In the 5-dimensional case, only four coordinates are used. Click on images to see interactive version.
| Graph | 4-D Layout | 5-D Layout |
|---|---|---|
HB/bcsstk26 |
 |
 |
TOKAMAK/utm300 |
 |
 |
Once the graph is rendered in 5d, we can switch between two available extra dimensions,
without affecting node placement. Here is what I found for HB/bcsstk26:
As you can see, the switch affects different parts of a graph, which means that nodes that are closer to us in the fourth dimension are farther from us in the fifth, and vice versa.
The graphs are taken from the UFL dataset.
Consider using PCA for projecting multidimensional layouts to 3d
MIT