A scale for visualizing ambiguity

7 min read

I summarize here a short talk I gave in Dagstuhl the 2023-09-21. It offers a scale of how ambiguity is taken into account in a visualization. Here is the scale.

Ambiguity…

  1. …as noise (absent)
  2. …as an accident (present)
  3. …as context (+ significant)
  4. …as a problem (+ in focus)
  5. …as a feature (+ articulated)

That scale is intended as a way to push back against the idea that any form of empirical account is a measurement (why not call that measurism, by the way). Not every description can be reduced to a number, in particular when the phenomenon visualized is inherently ambiguous. I do not mean here that ambiguity cannot be measured if you want, but that visualizing an ambiguous phenomenon can be about accounting for ambiguity as a feature.

The scale is intended as an itching powder to apply on the skin of measurism. It begs:
Where is the feature of ambiguity? Who discarded it and why? It aims at reminding that reductionism is a choice, to expose its commitments, and to reopen the doors to other empiricisms.

Explanation

I use a toy dataset to illustrate my point. I curated a list of 243 articles about actresses in the French version of Wikipedia, and I harvested the hyperlinks between them. I made a network where the articles are the nodes and the hyperlinks the edges. Then I computed groups of pages through community detection using the Louvain method (modularity maximization). I did it five times. Since it is not deterministic, I obtained different results. I had 3 groups every time, but they were not exactly the same. The visualizations that follow have different ways of accounting for these discrepancies.

Setup of the experiment

What is ambiguous?

The categories of actresses are ambiguous by nature. The three groups I found can be labeled as such:

  1. Contemporary Hollywood (ex: Julia Roberts, Meryl Streep, Susan Sarandon)
  2. Golden Age Hollywood (ex: Marylin Monroe, Katharine Hepburn, Greta Garbo)
  3. French Actresses (ex: Catherine Deneuve, Juliette Binoche, Jeanne Moreau)

This partition can be explained by the fact that the data is from the French Wikipedia. Hollywood is very influent in France, but the national cinema too. But of course, some French actresses have been acting in Hollywood, both now and in the past. It’s not that those categories don’t exist, it’s that not everyone fits nicely into one and only one. The groups exist, but they are not well demarcated. This is where, in this particular instance, ambiguity lies.

Ambiguity is not uncertainty. You can reduce uncertainty by obtaining more knowledge. Ambiguity works the other way around. The more you know about something ambiguous, the more ambiguous it becomes. The more you know about Marion Cotillard, the more it becomes clear that she’s both French and a Hollywood actress. In that sense, ambiguity is an empirical feature to account for.

I will show one visualization per stage of the scale. Those are not complicated, I did not even try to do my best. I went for the simplest. It was done in Tableau, except the last one in Gephi.

1. Ambiguity as noise: not visualized

Here I just picked the first of the 5 renderings of community detection. I just ignored the discrepancies.

If you do not even account for the existence of ambiguity. I proactively assumed that each actress could be mapped to exactly one category. I eliminated ambiguity as if it were noise, nuisance.

2. Ambiguity as an accident: visual anecdote

Here I affected each actress to a given category if they were matched to it at least 3 times out of 5. Of all the actresses, only Naomi Watts could not be mapped to a group (she had a 2/2/1 split).

Here ambiguity is apparent, but it is just a detail. It is set up to help you ignore it. Functionally, the result is not much different from ambiguity as noise, but at least, if you pay attention, you have a chance to become aware that something is going on under the hood.

3. Ambiguity as context: visualized as an afterthought

Here I mapped each actress to a group like previously, but I visualized the “definiteness” of that mapping with a glyph. The dot representing each actress is only full if she was strongly mapped to the group (5/5 times). Else, the glyph is smaller. I used a Herfindahl-Hirschmann index, which works in many other settings.

Here ambiguity is framed as context. The premise of that visualization is that (1) you still get one group per data point, but (2) you are made aware that for some data points, the mapping to that group is less solid. The visualization is build primarily as if ambiguity did not exist and secondarily, ambiguity is painted on it; which is why I characterize it as an afterthought. It does not fundamentally challenge the existence of demarcations, but at least you can now focus on the ambiguous cases.

4. Ambiguity as a problem: it gets in the visual way

Here I used a small multiple to display the group split of each actress (the picture below is just a part of it). We can now see the split of Naomi Watts, and other actresses. We can read the full information. But as a result, we lose the sense of the repartition of actresses into approximately three groups.

Ambiguity is entirely visualized, but it takes all the room. We cannot see anything else, which is a problem. Ambiguity coexists with other things. In this particular case, the groups do exist even though their cannot be firmly demarcated.

5. Ambiguity as a feature: purpose of the visualization

Here I visualized the network of relations from which the groups were computed. I did not draw the edges, but they are represented within node positions, through the effect of the layout. This allowed me to map the groups, but I did it intentionally loosely, using these big circles, refraining from drawing precise demarcations.

In this setting the eye can navigate and tell you how strongly each actress is associated to its group. In the middle, we find quite a few actresses that do not seem firmly attached to either group. We find Marion Cotillard between France and Hollywood, and so on. The eye can grasp both the existence of the groups and the continuum between them.

Beyond the case

Forget about the case. It was to give you an example. I don’t pretend here that network maps are the best solution to visualize ambiguity. I fully acknowledge by bias here, and I don’t have to apologize. I became aware of the importance of ambiguity by realizing that it was the reason why network maps were so good, in practice, for exploration. My intuition is that extensionist (non-reductionist) visualizations are good at that in general. But even there might be even more different visualizations that I don’t think of that can represent ambiguity as a feature. It’s not about my particular example.

It’s about the scale. If you try applying it, you will see that the scale makes it clear that some otherwise great types of charts are doomed, by design, to fail at representing ambiguity as a feature. I hope it helps people figure out what part of our visualization apparatus can be rethought to meet non-measurist goals, as we find in the humanities. And there is more to that than ambiguity, but that is for another post.



Cite this blog post
Mathieu Jacomy (2023, October 4). A scale for visualizing ambiguity. Reticular. Retrieved April 24, 2024, from https://reticular.hypotheses.org/7979

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