# Visualization of variable combinations

What is the best way to visualize variables each of them with a certain range:

Following example:

possible values for ...

1. variable 1: [1,2,3,4]
2. variable 2: [40,50,60]
3. variable 3: [100k, 150k, 200k]

and now, for each combinations I get a certain value, for example the combination [V1: 2, V2:50, V3: 200k] leads to a percentage of 68%.

How do I visualize all of the possible combinations in a comprehensive way? Until now, I was only thinking about a Parallel Coordinate Plot, but does anybody have other idea?

Thanks a lot.

• Are the values discrete? Your comments sound like this is for something like hyperparameter tuning. In that case, marginal line plots work well (one variable on the x axis, one for line color, one for point shape and accuracy on the y axis) – AlexR Jun 23 '19 at 8:43

You have 4 dimensions: V1, V2, V3 and percentage. In our 3-dimensional world it is hard to visualize a 4-dimensional object.

A) If you have a tool that can represent 3D objects, can rotate then, can zoom in, zoom out: Then use V1, V2 and V3 as 3D coordinates and place at corresponding point a ball or a cube that represents percentage; the size of this ball or cube should represent percentage value. To be able to analyze such representation, e.g. to see min and max values, to see any dependencies, users will have to rotate this scene and to zoom in/zoom out. I believe only users with strong technical background will be able to understand such representation.

B) Use normal 3D-chart. Select 2 variables for axes, e.g. V1 and V2. Use columns to represent percentage. Create a separate 3D-chart for each value of the variable V3. So you will have 3 3D-charts.

C) Use normal 3D-chart. Select 2 variables for axes, e.g. V1 and V2. Use columns to represent percentage. For each value of V3 use different color. So for each combination of V1 and V2 you will have 3 columns of different colors (representing values of V3) and of difference height (representing percentage).

None of these approaches is perfect. But representing 4D objects in our 3D world is really hard.

What is the most relevant piece of information in your example, 68%?

You could use a Radar Chart with the percentage displayed in the middle.