Representing a higher-dimensional chart I'm hitting an unusual roadblock in my quest to represent a set of data for the layman, and thought I'd ask for advice on how best to accomplish this task.

My data points are represented by a 4-float tuple (a, b, c, d), the sum of which is constant. These represent test conditions, to which an outcome z is assigned. This outcome is also a float, but that's largely irrelevant.

The fact that there are four effective x-axes really is throwing me off regarding the choice of visualization, and that's where I'd really like some help. If you were in my shoes, what would you render this as?

Just for completeness sake, here is a (small) extract of one of the sets:

0,3000,2500,750,101788
250,3000,2500,500,100458
500,3000,2500,250,99439
750,3000,2500,0,98573
0,3000,2750,500,101993
250,3000,2750,250,100834
500,3000,2750,0,99813
0,3000,3000,250,102370
250,3000,3000,0,101150
I think there is 2 ways to do it.



Dimensionality reduction

Using technique such as PCA, you can represent your data in lower number of dimensions.

This is a good approach if you want to represent all your data in one graph.



Dimension removal

Another way to visualize is simply to visualize only a few dimensions at a time. For example you can visualize a/b, c/d, a/c in 3 different 2D graphs.

While much simpler, this approach does not allow you to have a single graph visualization.