Bertin’s Reorderable Matrix

I recently had the opportunity to attend a workshop at ESAD Valence. To my surprise, in their collection, they have original parts from one of Bertin’s reorderable matrix!


I had the opportunity to use the rebuilt matrix at VisWeek in Paris 2014. I’ve simulated the matrix using Excel macros and Excel conditional formats. Essentially the reorderable matrix is a physical visualization that takes a table of structured data and enables resorting of rows and columns based on data values to reveal clusters. Each block shows data on the top surface which represents a numeric value varying from the lowest value (full white) to the highest value (full black) and various textures inbetween. The user can then shuffle (i.e. reorder) full rows or full columns to regroup the data based on values so that clusters visually appear (Bertin called the process diagonalization, see the video). It’s a human-powered physical clustering algorithm.

This particular version is made with tiny plastic blocks, about the size of Lego 1×1 bricks and sound the same as Lego when they jostle in the big bag of bricks (Bertin called them dominoes). I arranged a few on a desk into a matrix (the connecting rods weren’t available). You can see how patterns of all black, textured, and partially textured surfaces are highly visible:


One really interesting aspect that I noticed is the colored edge stripe on some of the bricks, seen in the picture below (and quite noticeable in the bag where you can see some blocks have bright stripes in green, blue, yellow, orange, etc). I asked, but it was uncertain what their purpose was. The stripes are always on the sides where the rods go in; never the top. I’m guessing that it is some kind of recording system. Perhaps the user would draw a stripe across a row of bricks, maybe as a way to record the state. Since these colors were on the sides of the blocks, they wouldn’t be visible from above and therefore not interfere with patterns and clusters being created.

Another interesting aspect is that both the tops and bottoms of the blocks have the black-to-white texture patterns. We speculated that the blocks were reused from analysis to analysis, and it was easy to code both sides of the blocks. But, maybe there’s more. It would be feasible to re-order a matrix, take some kind of intervention, collect more data, then color the new state on the bottom of the blocks. Then a user could flip over the entire matrix, to see if the pattern had changed in some way. Again, speculation on my part.

The Lego-like aspect also suggests to me that a reorderable matrix could potentially be constructed out of standard Lego-blocks today: a 1×1 with holes on both sides, rods, and tiles in assorted shades of grey. And then concepts about data clustering could be taught in grade school.



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Visualizations with perceptual free-rides

We create visualizations to aid viewers in making visual inferences. Different visualizations are suited to different inferences. Some visualizations offer more additional perceptual inferences over comparable visualizations. That is, the specific configuration enables additional inferences to be observed directly, without additional cognitive load. (e.g. see Gem Stapleton et al, Effective Representation of Information: Generalizing Free Rides 2016).

Here’s an example from 1940, a bar chart where both bar length and width indicate data:


The length of the bar (horizontally) is the percent increase in income in each industry.  Manufacturing has the biggest increase in income (18%), Contract Construction is second at 13%.

The width of the bar (vertically) is the relative size of that industry: Manufacturing is wide – it’s the biggest industry – it accounts for about 23% of all industry. Contract Construction is narrow, perhaps the third smallest industry, perhaps around 3-4%.

What’s really interesting is that area represented by each bar is highly meaningful: the percent increase x size of industry = total income gained in that industry. For example, the area of Transportation and Contract Construction are perceptually quite similar. This can be validated mathematically, Transportation at 7% increase x 7% industry size, is a similar total income gain as Contract Construction at 13% increase x 3.5% industry size. Or Mining at 9% increase x 3% industry size, is about the same total income gain as Agriculture 3.5% increase x 8% industry size.

This meaningful area is the free-ride. Perceptually, one can directly observe and compare relative areas. Total income gain hasn’t been explicitly encoded, it’s a result of the choice on encoding length and width. If the viewer is potentially interested in total income gain in addition to percent increase and relative size, this is a useful encoding. Total income gain might be very important in government policy, for example, as the total income gain is directly proportional to the taxes generated.

A more common design choice these days might be to use a treemap to show one variable (relative industry size) and color to show the second variable (color to indicate percent increase); like this:


In the treemap, size and color are explicit, but there’s no free-ride. The combination of color and area isn’t a perceivable combination: the similarity in total income between Transport and Construction is not obvious; nor the similarity between Mining and Agriculture. In the treemap, the area encodes relative size, but the length and the width of the boxes are not meaningful. The color encodes percent change, but color isn’t effective for comparing relative quantities. If total income gain is a desirable insight, then the treemap fails.

Edward Tufte (1983) discusses multi-functioning graphic elements, which doesn’t quite  align with the idea of a free-ride. Johanna Drucker (2014) discusses this notion as generative: a representation that produces knowledge as opposed to a representation that simply displays data. But I like the definition of a free-ride, which succinctly explains the perceptual benefit created by the choice of representation. See Gem’s paper for an example applied to Euler diagrams.

Visualization designers need to consider the free-rides and other perceptual inferences different visualization alternatives provide, and choose among visualizations on how those inferences suit the viewers’ task.

Percent Increase in National Income by Industry is from page 178 in the book How to Chart: Facts from Figures with Graphs, by Walter Weld, 1960. Walter didn’t particularly like this chart, partially because there is no legend nor axis for the widths. Personally, I have seen this type of bar chart used effectively in financial services.

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Metabolic Pathways and Visualization Pathways

Metabolic pathway diagrams show series of linked chemical reactions occurring within cells (Wikipedia). These diagrams started more than a half-century ago, such as this example from 1967 in the Smithsonian:


These diagrams have been continuously expanded over decades as new research identifies new reactions and new connections. A 2017 version at Roche is a massive interactive poster documenting thousands of compounds and reactions:


These are extremely interesting visualizations that document the knowledge of a research community showing the connection and flows of chemical reactions.

Could the equivalent exist in data visualization and analytics? The field is growing rapidly and there are many techniques. Like biology, as the visual analytics field grows, it becomes more difficult to keep track of all the evolving techniques. Surely, a similar diagram of data and the many ways it can flow through analytics into visualizations (and other perceptualizations) and interactions – should be feasible and useful for the community. Here’s an attempt to sketch out a bit of it related to data that expresses structures such as hierarchies, graphs or sequences; and corresponding visualization approaches:


It’s bit trickier than biochemical processes as there are many-to-many relationships potentially making it overloaded with too many connections, so there’s some editorial or process to determine which pathways to show. And, it’s missing so much, e.g. no interactions, many data analytic techniques, and no visual attributes (color, size, icons, etc). And it’s not obvious how to group visualization layouts, e.g. by mark type, by coordinate system, or maybe by the primary structure that they represent?

Perhaps someone else has already created something going down this path already? If not, is something like this valuable? Let me know.

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Legacies of Isotype

ISOTYPE was a dramatic reconceptualization of statistical graphics in the 1930’s by Otto and Marie Neurath and their collaborators. Contemporary charts, such as seen in Brinton, were mostly black, simple dots or lines, tiny captions and full of dense grid lines, axes, ticks and labels. Isotype instead was bold; almost always devoid of grid lines, axes and tick marks; minimal bold sans serif text; and usually relied on repetition of expressive icons to convey quantities. Compare the two images below. Isotype evolved at the same time as Modernism, where these same ideas — broadly, “less is more” — was applied to many areas of design including architecture, art, dance, industrial design, etc.

How did Isotype’s visual language become diffused across charts, visualization and interfaces over the next few decades? Here’s three:

Pictographic Icons

Perhaps the best known feature of Isotype is the use of pictographic icons. Use of pictographic icons to indicate things became increasingly important with post-war globalization. Pictographic icons are recognizable across language and use less space than long labels. Standardized icons became popular across many areas of society such as highway traffic signs, Olympic symbols, airport signage, warning symbols and so on. And then Mac and Windows used icons as core interaction elements in graphic user interfaces (How many icons are visible in your screen right now? I have more than 125). Here’s a mid-1970’s set of standardized symbols for the US Dept. of Transport:


Standardized icons from mid 1970’s, US Dept. of Transport.

No Grids

The diffusion of Isotype benefited in part from technical changes to printing, moving from metal-based printing (which could handle fine detail) to offset printing (which was based on photographic compositing techniques and this reduced the ability to use fine details such as thin lines and crisp serifs). As such, thin grid lines and small text are more difficult to use than chunky icons, large patches of color and bold, heavy-weight labels. This lines up well with design ideology of Isotype. If we look at some charts from the mid-1970’s, we can see the remains of Isotype — few or no grid lines, minimal text, and expressive pictographs:


Charts from 1975: low on grids, low on text and some icons (Graphis Diagrams, 1976)

Labeled Values

Isotype worked hard to reduce text, but showing the numeric values seems to be important when we look at charts after Isotype. In the prior image, there are explicitly labelled numeric values in all six charts. Presumably viewers want an estimate of numerical quantities corresponding to the visual marks, and they don’t want the cognitive load of counting icons or guessing the area associated with a circles, folded corners or the relative width of smoke. Or, perhaps icons are difficult to express fractions. Regardless, the addition of numerical values either as labels on marks or labels on axes come back. This was probably one of the first aspects of Isotype that may have slipped — here’s a US Dept Agriculture bar chart from 1950, highly influenced by Isotype:


Chart from 1950, highly influenced by Isotype (compare to first pair of images).

It has the icons (although moved to the axis and explicitly labelled), and minimal grids (although an outer frame has been added to the plot area). And it labels the bars. In this chart, like the 1970’s charts, the values are explicitly labelled.

The take-away is that removing value labels completely may have been a bit too far on Isotype’s part. Even Haroz et al‘s study on “Isotype” charts always included quantities along the y-axis in all test conditions. Either a numeric axis or labelled bars or some numeric guidance on the values seems to be broadly desired. We see these labelled values in many charts, such as many Excel charts that label both the numeric axis and number value per bar (3 of the 11 quick styles provide both) such as this one:


or the USA Today Snapshots (which use many cues from Isotype, including pictographs, minimal text and no grids):
Or in the very first bar chart in the very first tutorial of D3js (“Let’s make a bar chart):





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Which scatterplot is preferred?

Next week, we’ll be presenting a machine learning (ML) and visualization paper at the IV2019 conference in Paris. The core idea is to tag and display relevant news headlines in a real-time ambient visualization system.

From an ML perspective, the challenge is to use an open source news dataset (e.g. GDELT) where thousands of headlines are available and updated frequently (e.g. every 15 minutes) but the tags provided don’t match the needs. In general, classifying news stories is an ongoing challenge, as new topics and words emerge (e.g. Brexit, tariffs), and topics may change over time (e.g. Clinton, environment, etc.) We provide a classification module where expert users start with a simple text search against the headlines. Then we automatically suggest additional relevant keywords, which the user may explore, add, or remove. Additionally, the user may inspect sample headlines associated with any of the keywords, grouped by similarity. Then the the user can explicitly select target headlines and keywords that match their intended search topic (or not). Finally, we can run a classifier to tag all the headlines with respect to this topic defined by sample keywords and headlines. The user can iterate, modify, reclassify, and so on. Lots more detail on the technical approach is in the paper.

From the visualization perspective, the challenge is how to display a subset of these headlines. We were working with an existing animated ambient visualization which provided either a scatterplot or map upon which we could display headlines and would automatically select headlines at random to popup. Note that a map with point data is essentially the same as a scatterplot: the x and y location of the data points is based on latitude and longitude; plus an underlying image is used to show geographic features, such as land/sea.

We created four scatterplot variations: 1) a scatterplot map (with underlying land/sea image); 2) a scatterplot with explicit axes (recency vs. # stories); 3) a scatterplot based on a multi-dimensional projection (e.g. PCA or t-SNE); and 4) scatterplot based on random layout (i.e. like a wordcloud) – which is visually similar to the multi-dimensional projection:


These visualizations were then reviewed with a small target group of users, in a meeting environment. This is where things get really interesting:

  1. Map: Everyone likes the map. It is immediately understandable.
  2. Scatterplot with explicit axes: Everyone logically understands the representation, but otherwise largely unenthusiastic. A few people are very interested, but given the broad audience for an ambient visualization, there is not enough support to push this into production.
  3. Scatterplot projection: The experts are not expert in multidimensional data projection. Multidimensional data projection is difficult to explain and difficult for people to comprehend. They can’t use what they don’t understand.  Unfortunately, dead on arrival.
  4. Scatterplot random layout (aka cloud): Surprisingly, some people really like word clouds, but this community of experts is not interested. It’s art, not information.

So, the map wins: there is a strong preference for the map over all other scatterplot variants. Why should the map have such a strong preference? Unfortunately, the project didn’t have scope to consider this, and there are various confounding effects going on too: titles are smaller on the map, the scatterplot also uses color-coding of text, the map had leader lines to association headlines with locations, etc.

Here are some hypotheses why there was such a strong preference for maps:

a. Maps are easy to decode. The specific map we used is always global. A global map is easy to decode because people are very familiar with them. A global map has very low cognitive load. Low cognitive load may be very important in an ambient visualization as people don’t want to have to think too hard about what they are seeing. Scatterplots, however, have higher cognitive load. You have to be actively engaged to decode it: you have to reference back and forth between data points and an axis, or you need to understand what a projection means. And a cloud doesn’t have anything to decode positionally, so there’s no information there. From an information standpoint, the map provides more information than a random cloud.

b. Maps automatically engage prior knowledge. A news headline situated in Iowa means that we can bring all of our knowledge about Iowa immediately as context to interpret the visual representation. If the news headline is about corn, that probably matches prior knowledge that Iowa is farmland and may have a lot of corn crops.

c. Maps are visceral. In Norman’s Design of Everyday Things, some objects elicit a visceral response. A visceral responses are immediate and emotive. The map is immediately accessible and engaging. In a ranking of maps vs. scatterplot with axes vs. multidimensional projection scatterplot, my hunch is that the map is most viscerally engaging.

Thoughts? Comments?



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SparkWords are words in running text, such as narrative prose or lists, where the words have additional data embedded in them as visual attributes, such as color, bold or italic. The simplest use is differentiation, such as italic to indicate the name of a ship, such as Titanic, however SparkWords can go much further. Attributes can be combined, for example, one could indicate political candidates using color to represent their political party, italic to indicate gender and underline to represent an incumbent: Mazie Hirono, John McCain or Bernie Sanders.

SparkWords can go a lot further. Here’s a paragraph with some text about departments in France using SparkWords:


Word weight and proportion of red, green, blue are based on data. Four different quantitative data values are conveyed by visual attributes applied to the words. There is no need for a separate legend, it’s embedded in the explanation. There’s no need for spark lines or spark bars: it bars were used instead, you would still need some kind of interaction to identify the individual bars. With SparkWords, the words uniquely encode the identity of each item. That is, in addition to weight, color, etc, the word itself is encoding one more dimension of data.

Note that SparkWords do NOT adjust size of words, because, in running text the size of text stays consistent.

Here’s another example, an entire paragraph of SparkWords showing all the 2018 baseball games of the NY Yankees:

Each three letter sequence is an opposing team (e.g. TOR for Toronto, TBR for Tampa Bay). Each character is a game, red for a loss, green for a win (grey if no game). The background bar is the score differential: The initial game, represented by the first T in the paragraph was a win for the Yankees with five runs over the Toronto Blue Jays. The second game was won with a smaller run differential (2), the third game was lost by a couple runs.

So What?

Perhaps most interesting is that SparkWords represent a different way to think about visualizations. Instead of a separate visualization and a separate paragraph explaining the visualization, with SparkWords the visualization moves directly into the words of the narrative text and there is no need for an additional visualization.  The notion of a separate plot area or even a micro-sized plot such as a spark line, is not required. And the SparkWords do provide more information context than just text: in the example above, there’s a lot of similarity between Gers, Creuse and Lozere — same green, same light weight. But Paris, Seine and Nord are different: Paris is more blue (services) while Nord is more industrial (red). Or in the case of the Yankees, there’s alot of green overall, but some bad sequences of losses (TBR and BOS swept 3 games series in the middle of the season).

Instead of putting text into a visualization, SparkWords puts the visualization into the text.

So why should we want to use SparkWords? There is an increasing need to explain data: data journalism, explainable AI, automated insights, data-driven natural language generation. Visualization, by itself, does not direct attention — there are many possible patterns and it’s not obvious what to look at and what the specific insights are. Data narratives do explicitly talk about specific data points and trends — but do not provide context to help inform critical understanding. Techniques which offer tighter integration between explanation and visualization can be much more informative. SparkWords, like data comics, automated annotations, and in-line visualizations (e.g. spark lines) all bring visualization and narrative closer together. SparkWords are the only option that is pure text, so maybe there are some use cases where SparkWords are uniquely well suited for explanations.

I’ll be talking more about SparkWords at EuroVis on Thursday next week (June 6) at the 11-1 session on Text Visualization.

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Data Comics (with NFL play example)

Data comics are a great extension to infographics. Data comics are essentially a narrative explanation of a visualization set out in a comic-like format. The overall sequence explains the story. (e.g. see this paper for some examples comparing infographics to data comics).

I wanted to get a better sense of data comics, so I made one. For a starting point, I took an example of NFL data from my previous book Graph Analysis and Visualization (Brath and Jonker, 2015). Here’s the resulting data comic of two NFL teams and the sequence of plays that they did during 2011:


Hopefully the story is self-explanatory in the comic. The purpose of making this comic though was to learn more about data comics – what works and what doesn’t? Essentially this is research-through-design, wherein insights are gained by making something rather than studying theory:

“The term ‘experiment’ is narrowly understood (in ‘the scientific method’) as a piece of controlled research, in which variables are isolated and controlled, and a hypothesis is validated or rejected. But the term has another use – in a much broader sense of ‘trying something out to see if it works’ as either part of an inquiry or program (Redström 2011) or as part of an action-oriented intervention (Halse et al. 2010)” – Stappers and Giaccardi.

Steps include having some problem or hypothesis, design iteration to create prototypes, and an end result of knowledge gain.

Why a data comic?

So first question is: why a data comic? There are many different ways to combine narrative explanations with visualization, ranging from infographic posters, to interactives with steppers, to long narratives alternating between paragraphs and charts, to long scrolling narratives where the scroll triggers an interaction such as a filter or zoom, to visualizations with sequential tutorials in a side panel (step 1 do this, step 2 now do this), and so on.

So why data comics? Like most infographics, most of the data and the story is made explicit. The story isn’t buried under tooltips or required interaction. I’ve always been an advocate of not hiding too much data under interactions. However, unlike some infographics, the narrative story telling sequence is much more explicit in a data comic. If you have an explicit narrative, a comic offers a strong sequential structure and follows a recognized conventions.

But wait a minute. There are other ways to provide a strong narrative structure. Long scrolling visual stories on websites are pretty much data comics too – aren’t they? (e.g. there’s 15 long scrolling visual stories in Archie Tse’s post about scrolling story telling at the NY Times). While a comic is page orientated with a left-to-right structure (left image), the scrolling layout is essentially a set of panels oriented vertically (center image):


And I’ve created other strongly narrative visualizations that are somewhere between a data comic and an infographic, as shown by the third example. We’ve implemented the third example in some fully automated data-driven charts. This third example was informed by a process we’ve often used for documenting visualization wireframes: Rather than many pages of wireframes, we create a single wireframe with sequential annotations around it (some old examples here referred to as paper landscapes). Cues such as sequential numbers and leader lines are used in addition to a general left-to-right top-to-bottom flow to enhance the sequential narrative.

Knowledge gained

Strong narrative sequence is inherent in a data comic. It follows well-known comic conventions, likely familiar world-wide, and therefore requires little training. This narrative sequence does not need additional supporting narrative cues, such as a numbers to sequence chunks of text.


Text and visualization don’t need to be constrained to panels. Just like in a movie where the character is still talking even after the scene cuts to the next scene, the annotation or the visualization can extend across multiple panels. I initially attempted to make the above data comic work by repeating the visualization tree in each panel:


This is an arbitrary constraint inherited from the comic convention. Yes, it’s a small multiple that can be compared and contrasted – but in the NFL example above nothing is changing to compare and contrast! It’s a waste of ink. Instead, the visualization can extend across the panels. This reduces the pain of repetition of the same visualization scene to scene: plus it creates more space to enrich the visualization – in this NFL example it allows the addition of useful labels:


And, spanning text or visuals is a technique used in comics for many decades – here’s an example from 1953 from the Digital Comic Museum: (Aehaya!)



Incremental legend. Because the panels are smallish and the text is brief, the visualization can’t be explained up front: the layout, the colors, the scales can’t all be covered in the first panel. So the notion of the legend gets split up into pieces in different panels and revealed throughout the story. But they don’t always occur in the panel where they are discussed. For example, the horizontal scales at the bottom of the second row are also applicable to the corresponding panels  on the upper row – but that might not be obvious.

Similarly the column labels (team, 1st down, 2nd down, etc) float strangely between the narrative text and the visualization. Ideally, they are associated with the viz (same color and same font as the viz).  But there is the potential for confusion. The integration of visualization legend and labels – and explanation of the visualization technique in relation to the narrative story – could likely have been done in a better way.

Narrative. The top row of panels tends to be descriptive observations regarding the data. The narrative in the lower panel is more comparative of the difference between the two rows. Unfortunately, the narrative in this NFL example is hand-written, and it’s not easy to write a story to fit the limited space available. And the hand-written story was created only for these two teams, so the stories are no longer useful when looking at other teams.

An even better solution would be machine generation of the story such that when the viewer changes the team, the narrative would update appropriately (see previous post on insight generation). Obviously there is some interesting research opportunities for interactive-data-comics + natural-language-generation.

Callouts. Speech bubbles from comics can be easily used to call out some data or insights. They can act like tooltips to let the data speak. In this NFL example, the individual plays and players are lost when the data is aggregated to create the tree visualization. So some info from the top players behind the plays are made visible using call outs.

SparkWords. One challenge in any visual explanation is linking the narrative text to the visual representation. In a comic, the text and the characters can be tightly linked using a variety of cues. For example, the pointy bit on the speech bubble links it to a character. The placement of a sound-effect is proximate to the thing making the sound. Or the font used matches the character and their emotional state (e.g. shaky scary letters for a ghost).

SparkWords encode data using the same color-coding as the visualization. In this NFL example, the words run, pass, and other in the narrative use the same color-coding as the corresponding bar in the visualization. Given that there are many bars, the color-coded words presumably can be more easily associated with the corresponding colored bar. However, the color-coding of the words occurs before the explanation of the color-coding, so there is the potential that these colors could confuse the reader. SparkWords will be the subject of a future post.




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