Imagine a point cloud with multiple dimensions. To plot this and provide an interactive way to "play around", there are the following common ways:
- parallel axis, star axis
- 2D scatter plot
- 3D scatter plot
- scatter plots + colors + shapes + ...
- reductions (non-interactive)
So of course you can add even more dimensions by varying different aspects of the plotted points. But it never feels like a real dimensions to the user. Let us call these dimensions secondary while the dimensions that alter the position of a point are primary. The primary dimensions can be scaled, moved and rotated and a user get an intuition how the work together. A rotation between a primary and secondary is mostly forbidden.
Now you can add more primary dimensions by using a good projection to the 2D/3D space (depends if you have a 3D screen). But most projections are very hard to understand. I also feel that the typical 4D hypercube where you get a big and a small cube gives you a very wrong intuition about the dimensions.
So I started an experimental 4D scatter plot. It's a 3D plot where the fourth primary dimension gets mapped to color+transparency. The mapping is with a predefined real value X:
- -X: blue + full transparent
- ...: interpolated transparent and light blue
- 0: white + full visible
- ...: interpolated transparent and light red
- +X: red + full transparent
The intuition is that you also cannot see objects that are far in the first 3 dimensions. The color is just to differ between the two cases of "far away". Rotation/scaling/moving is possible.
Now my questions are: Does this really help (especially in contrast to a normal color mapping of the 4th dimension)? Is it possible to get a better understanding of 4 dimensions?
Disclaimer: I'm the creator of the mentioned scatter plot. It's open source and non-commercial. I don't collect any user data apart from the standard GitHub data.