Visualizing Higher-Dimensional Data
I’ve wondered for quite a while about how one could view data in more than 3 dimensions. Even 3 dimensions is difficult to view sometimes, since we really only see 2 dimensional images that have a depth component, not an entire 3D volume. With that in mind, it’s not reasonable to try to view and understand all of the structure of a higher-dimensional object all together.
I found on Wikipedia this representation of a 10-cube, which got me thinking of how to view all vertices of such a hypercube. I also noticed that the logarithm of n choose n/2 increases only linearly with n (in fact it appears that n choose n/2 can be approximated with for some a and b such that the relative error approaches zero as n increases), but it’s a bit harder to see the relevance of this. I then decided to make a similar visualization of the coloured vertices of an n-dimensional hypercube for my Computational Geometry (COMP 5008) project.
Here’s that project. I wrote up a document on it too, so I won’t dwell on it more. Ben, a good friend of mine, is making a version that shouldn’t eat up nearly so much CPU time by rendering the visualization with OpenGL.