# 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

## 2 Answers

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.

Edit: explanations following the comments.

To my understanding, each variable is displayed on its axis if the radar chart. If each variable is set to its max value, the chart covers the largest surface (for instance a perfect pentagon when there are 5 variables). On the contrary when each variable is set to its min value, the chart is reduced to a point.

If the area of the radar chart is filled, the percentage is visually represented by that area. This lets you visually compare two radar charts. Unless you meant to put all your sets of data on the same chart.

• I want to visualize different combinations of variables and the achieved accuracy (in this case the 68%). Therefore, I think Radar Charts will not be that good. It should be one diagram showing all combinations. A Parallel Coordinates Plot would be okay, however, there are better ideas. – david May 12 '19 at 18:22
• I believe you when you say a radar chart will not be that good, but you’re not explaining. We need your reasons and thought process to be able to help you. – Mart May 12 '19 at 21:40
• a radar chart would be nice (also like a parallel coordinate plot). However, I want to focus on two different aspects: 1) the parameter combinations and 2) the acieved accuracy with a certain combination. If I use the radar chart, the accuracy will be visualized as another variable, am I right? So, the visualization would be nice, but the information of the accuracy will be lost. The focus should focus on both aspects (one numerical value and a list of parameters). Any suggestions? – david May 16 '19 at 13:16
• A radar chart seems to be good to visualize one combination at all. However, I want to have one chart that visualizes all possible combinations with the achieved accuracy value, you see? – david May 16 '19 at 13:23
• Imagine you have two parameters and an accuracy value. Then, I could use a scatternplot and the size of the dot represents the accuracy (the bigger the higher the value). However, I have, let us say 10 variables that will be combined in many different combinations. I am not able to visualize a 10th dimensional vector space. Therefore, I need another idea how to visualize the data... – david May 16 '19 at 13:31