# Infographics: show relationships between two sets and within them

I have two sets of objects, called "positive" and "negative". Objects are of the same type and can be compared, comparison results in real number from 0.0 to 1.0 (similarity).

What puzzles me right now is the choice of chart type to show the following hypothesis to the user: objects within one set are more similar to each other than to objects from other set. Two sets must be distinguishable just by looking on this chart, probably by the size of bubbles, or by area or whatever(as you can see, i have no idea, how to show this on one chart).

Which kind of chart can I use to represent this kind of information?

• Is a "Venn diagram" what you are looking for? en.wikipedia.org/wiki/Venn_diagram – Jørn E. Angeltveit Apr 27 '12 at 9:24
• Didn't quite get if you are comparing the sets with each other, or if you are comparing the objects within each set and then visualize the "similarity level" of each set. – Jørn E. Angeltveit Apr 27 '12 at 9:29
• The latter. For example, i compare "positive" objects to other "positive" objects(first case) and to "negative" objects(second case) and want to show that in first case results are very close to 1, and in second they are close to 0. I came up with double-colored bubbles of different size, depending on similarity, so red-blue bubbles will be smaller that blue or red ones. Was wondering if theres a better way. – Anton Apr 27 '12 at 9:34

Without attempting to second guess your actual data, here's the process I'd recommend:

• Frame the problem to be solved: The way of displaying the information helps ROLE make sense of OBJECT in order to answer QUESTION
• Identify nodes of information
• Explore ways to put that together - patterns, metaphors, shapes, etc. This may identify more nodes of information.
• Clean, test, iterate

In more detail:

Your problem is reasonably framed apart from the role - that may help you present the information in a way that makes sense to your specific user type.

Your obvious nodes of information on one object are:

• Set to which object belongs (S)

• Similarity to other objects in the same set (S1)

• Similarity to other objects in the other set (S2)

• Similarity to any other object (S0)

But you can also create/calculate less direct nodes of information Eg:

• The mean of the similarities between an object and all other objects in the same set (M1)

• The mean of the similarities between an object and all other objects in the other set (M2)

• The mean of the similarities between an object and all other objects (M0)

• The difference between M0 and M1 (M01)

Then explore ways of bringing those together in a way that uses 2 or 3 of the meaningful nodes of information for the axes/dimensions - using position, colour, size, shape, etc.

For example plot M01 against M1 for each object with positive or negative x depending on set - whatever - just explore it.

So maybe you go through this process like this:

Then see if that exploration turns something else up, For example the angle of the best line through the points or the tightness of the clumps and number of outliers.

From this generate new nodes of information, then clean up, iterate.

This process is good for trying to visualise any type of data

You can try displaying two scatterplots, where the position of the objects is determined by the parameters of the comparison (if there's more than two, some derivative can be used). In this way, the distance between the objects reflects their similarity, and you can immediately see both the within-set similarity and the between-sets similarity.

In your comments you're referencing size. Size is a relatively weak attribute for visual comparison. So I'd favor doing position in a scatter plot and consider differentiating between Positive & Negative by using shapes. It might come out something like the following:

Note you didn't specify another quantitative value, so I just plugged in a sequential "ID" on the horizontal axis to differentiate the objects within each positive/negative set.