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A relation between two sets can be visualized with a grid-like table in which the rows are labelled along the left with the elements of one set and the columns are labelled along the top with the elements of the other, and in which each cell of the table is occupied by a symbol (usually a dot) if & only if the elements for that row & column are related. What is this kind of diagram called?

An example:


(I made this image myself, but I'm positive I've seen these charts elsewhere before.)

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up vote 5 down vote accepted

I would use the term binary heat map - although I'm not sure if there is a unified term. (There are probably other names used in various fields of application.) Heat maps more often display continuous attributes in cells via a color ramp, but there are plenty of matrix like representations of binary data. For instance Bertin in Semiologie talks about reordering the matrix to make certain patterns clearer.

For Bertin's examples (and older ones) see:

  • Wilkinson, L. and Friendly, M. (2009). The history of the cluster heat map. The American Statistician, 63(2):179-184. Online PDF Pre-print

Here is an example figure taken from Wilkinson & Friendly (2009) but is originally from the work of Bertin:

enter image description here

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Also note sometimes the graph is named after what it is showing rather than the form it takes. For instance Wilkinson & Friendly show examples for displaying a Guttman Scalogram that is equivalent. I have seen binary adjacency matrices (used in network and spatial analysis) displayed in the same way. The charts are the same though as displayed above. – Andy W Apr 28 '14 at 18:57
I considered adjacency matrices too, but they seem to have the same variables defining both rows and columns (such that the diagonal is the relationship of one level of a variable with itself). – Nick Stauner Apr 28 '14 at 19:25
Interestingly, the caption to your illustration calls these "matrix displays." – whuber Apr 28 '14 at 21:08
@NickStauner if you consider the nodes to be columns or rows in this example this may be considered an adjacency matrix for a bipartite graph. – Andy W Apr 30 '14 at 22:19

I think this is somewhat harder to answer than it would otherwise be because it's a very simple and commonly used style of chart. My answer may not be universally applicable, and other terms are likely to exist for the exact same layout, but I'm finding a lot of similar results in a Google image search for "comparison chart" without further references for support (haven't been able to find any yet), I'd recommend calling it a comparison chart. For comparison, another result from my image search:

This one is a little more complex, in that it has three kinds of dots (see the legend in the top left corner) and numeric entries on the bottom row. The University of Toronto titles this as a comparison chart.

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Pretty much all charts make comparisons, so I don't think I'd advocate that name - although in fairness there are certainly other chart names I'm sure you can trawl up that are unwarranted. – Andy W Apr 28 '14 at 18:53
Yeah, I wouldn't have chosen this name if I were making it up from scratch, but in fairness, plenty of charts have bars besides bar charts ;) – Nick Stauner Apr 28 '14 at 19:26

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