One of my learning goals this year was to really understand d3.js, and become more proficient in creating interactive data visualizations. In turn, this lead me to attempting to learn and analyse Chord diagrams. Chord diagrams visualize relationships either unilaterally or bilaterally. For example, they have been used to show capital flows inbound and outbound in financial visualization.
Learning how Chord diagrams are constructed in d3.js
Firstly, I wanted a solid primer on how Chord diagrams are constructed in d3.js. Steven Hall’s excellent blog post for Delimited provided the best overview, and clearly articulated elements of a Chord diagram such as the Matrix, the map of flows, arcs and paths. Using this approach, I decided to construct my own scenario and see if I could visualize it. The scenario had to have:
- Bi-directional data flows which may be asymmetric (x has a relationship with y, but y may have a different relationship with x)
- A small enough dataset that I could manually construct it (without having to do a lot of CSV or json processing – this exercise was about learning Chords, not about grokking data loading in d3.js)
- A dataset that could be easily understood by a layperson
I settled on the concept of Valentine’s Day crushes, because they satisfy the above criteria. Next, I constructed a number of statements that were to be visualized. They assumed that one person expressed a crush on one other person, and that this may or may not be mutual. After doing an initial list, I had to call myself out – I’d assumed hetero-normative relationships (male attracted to female and vice-versa), but of course that’s simply not diverse or inclusive thinking.
- Bob (male, hetero) likes Emily (female, hetero)
- Giovanni (male, hetero) likes Emily (female, hetero)
- Kevin (male, hetero) likes Poh (female, hetero)
- Art (male, hetero) likes Viva (female, hetero)
- Pyotr (male, hetero) likes Viva (female, hetero)
- Rohan (male, hetero) likes Rachel (female, hetero)
- Sasha (male, same-sex attracted) likes Pyotr
- Emily likes Bob
- Rachel likes Rohan
- Poh (female, hetero) likes Sasha
- Viva likes Pyotr
- Lee (female, same-sex attracted) likes Poh
The next step was to convert these statements into a matrix.
The matrix
Matrices are usually built from spreadsheet or other tabular datasets. Therefore, it was helpful for me to represent the above relationships in a table.
| Valentine’s Day preferences | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Name | Bob | Giovanni | Steve | Kevin | Art | Pyotr | Rohan | Sasha | Emily | Rachel | Poh | Viva | Lee |
| Bob | – | No | No | No | No | No | No | No | Yes | No | No | No | No |
| Giovanni | No | – | No | No | No | No | No | No | Yes | No | No | No | No |
| Steve | No | No | – | No | No | No | No | No | No | Yes | No | No | No |
| Kevin | No | No | No | – | No | No | No | No | No | No | Yes | No | No |
| Art | No | No | No | No | – | No | No | No | No | No | No | Yes | No |
| Pyotr | No | No | No | No | No | – | No | No | No | No | No | Yes | No |
| Rohan | No | No | No | No | No | No | – | No | No | Yes | No | No | No |
| Sasha | No | No | No | No | No | Yes | No | – | No | No | No | No | No |
| Emily | Yes | No | No | No | No | No | No | No | – | No | No | No | No |
| Rachel | No | No | No | No | No | No | Yes | No | No | – | No | No | No |
| Poh | No | No | No | No | No | No | No | Yes | No | No | – | No | No |
| Viva | No | No | No | No | No | Yes | No | No | No | No | No | – | No |
| Lee | No | No | No | No | No | No | No | No | No | No | Yes | No | – |
The matrix is an inherent part of Chord diagrams. Chord diagrams are based on a symmetric matrix – that is, there are as many rows in the matrix as there are columns. One of the first mistakes I made in this exercise was not to have the columns and rows in the same order – I ordered the names of people in the columns differently to the rows. When this was implemented as a Chord layout in d3.js, it was an incorrect representation.
Trap: Ensure that in your data matrix, that the data in rows and columns is in the same order. If you don’t have your data in the same order, the Chord diagram will assume that your row data is in the same order as your column data.
From this table, I was then able to declare a matrix variable:
var matrix = [ [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], // Bob [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], // Giovanni [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], // Steve [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], // Kevin [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], // Art [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], // Pyotr [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], // Rohan [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], // Rachel [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], // Sasha [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], // Emily [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], // Lee [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], // Viva [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0] // Poh ]
Chords and ribbons
The next step in this process is to calculate the flows in the matrix in both directions. In this example, it means calculating the relationship between each of the people, and that relationship may not be equal or symmetric. For instance, Rachel likes Rohan, and Rohan likes Rachel this is a symmetric relationship. However, Kevin likes Poh, but Poh likes Sasha. The relationship is asymmetric. This is reasonably simple to do (and Steven Hall provides an excellent pseudocode example in his blog post). d3.js being the knock-your-socks-off piece of awesome that is provides an inbuilt function for this:
chords(matrix)
This function calculates several values needed to calculate the chords in a Chord diagram, including the starting and ending angle of the chords, as well as the values (inbound and outbound) of the chords. See the d3.js manual entry for more information.
Arcs
A Chord diagram often has labels around the outside of the diagram, and these are produced in d3.js by passing the subgroups (from the matrix() function) to the
d3.arc()
generator. See the d3.js manual entry for more information.
Problems encountered
One of the key issues I encountered in getting this far with the data visualization was the syntax changes between version 3 of d3.js and version 4. There are a number of changes to method names, and the way that they are called under version 4. Many of the examples I used as a jumping off point were done prior to mid-2016 (when version 4 was released), using the older syntax. My example used version 4, and this resulted in a number of syntax errors if I was ‘copying and pasting’ code.
The way I handled this was to have a good read through the ChangeLog for version 4, noting in particular the changes to Chord and Ribbon methods.
Another issue that occupied some brain cycles was the different way that the matrices were calculated. Many earlier examples and tutorials included a ‘mapper’ function where series data was mapped to a matrix. In my example, the matrix() function did mapping as well.
As someone who’s familiar with OO-style programming, I’m still getting used to the way that d3.js modifies the document object model, first by selecting, entering and then modifying one or more DOM elements. This is something I’m just going to have to “get used to” as I use d3.js more.
Trap: Ensure you’re using the correct method calls for the version of d3.js you’re using
Visual design aspects
Data is only one part of the data visualization lifecycle. In order to be useful, it has to be visualized in a meaningful way.
Colours
The first major choice was how to represent the different people in the visualisation. It made sense to use different colours for men and women, and following (traditional, socialised, boring, gender-normative – I get it) what people are expecting, I chose blue for men and pink for women (from the Pantone Colours of Spring 2016 palette. Because Pantone). This provided a pleasant looking graphic, but data visualization is about telling a story.
I decided to add in two more colours to represent the same-sex attracted people in the data series (Sasha and Poh). This added visual interest, and made it easier to interpret some of the interesting details about the whole that were not apparent from the initial statements.
Using gradients in the ribbons
As you can see from the above, the solid colours (well, solid colours with a transparency applied) don’t really narrate the story of this visualisation very well. The pink colour dominates, and nuances (such as the unrequited love triangle between Poh, Sasha and Lee) in the data are less obvious.
Visually, I wanted the ribbons in the diagram to have gradients. At first glance this looked incredibly complex, and I was about to give up, when I found an excellent article by Nadieh Bremer, one of the gurus of d3.js, on this exact topic. Nadieh’s article provides the mathematical basis for visually appealing gradients in ribbons, including how the direction of the gradient is calculated, based on the position and direction of the ribbon. It’s very well articulated, and you don’t even need basic trigonometry skills to get it – it’s visually explained.
In a nutshell, Nadieh’s code calculates the gradient start and stop points for each ribbon, and the angular direction in which the gradient should be applied.
Using Nadieh’s code, I then applied gradients to the ribbons, for a much more informative and meaningful visualization.
Arc labels
The next tricky piece visually was adding the name of each person to the arc. For this, I relied on code from this Chord example from AndrewRP. This included applying CSS styles to the svg text, which I hadn’t done before. Because you’re styling text within an svg element, you need to prefix the selector with the svg element:
svg .titles {
font-size: 180%;
font-family: "Abel", sans-serif;
font-weight: bold
}
This wasn’t something I’d done before, so it was a great learning experience.
I’m still not entirely happy with the labels in the arcs – I would much prefer them to be larger, bolder and centred within the arc segments themselves. A good extension activity for another day.
Telling the story
Of course a key point with a data visualization is for the data to tell a story.
Visualizing the Valentine’s day sentiments that we started off with allows us to derive a lot more meaning from the data overall:
- We can see a tragic unrequited love triangle. Lee is attracted to Poh, who is attracted to Sasha, who is attracted to Pyotr, but Pyotr and Viva are mutually attracted
- No-one is attracted to Lee, Giovanni, Kevin or Art
- We can see that Rohan and Rachel, Bob and Emily and Viva and Pyotr have mutual attraction.
- Rachel and Viva are both liked by two men and thus are the most popular women
Next steps
There were some additional elements I would have liked to have added to this visualization, but ran out of time to implement – but I’m noting them here as extension activities if I come back to this in the future.
- As mentioned, I’d like to clean up the arc titles and visually enhance them
- Being able to click on a ribbon and learn more information about a particular relationship would be useful and visually pleasing. Nadieh Bremer again has a worked example of how to achieve this, however the code is quite complex and requires a large code base for the ToolTip functionality.
- It would also be ideal to isolate a particular ribbon – especially given that so many ribbons are overlapping in the centre, making it harder to follow visually who is attracted to who. This would use some form of opacity change to ‘fade’ the ribbons not selected.
- A number of the variables are statically declared in the code, as arrays. While this is totally fine as a learning example, for reusability I’d much prefer to put them into CSV or JSON files, then use Javascript to read them in.
Get the code
See the final visualization at:
http://blog.kathyreid.id.au/valentines/
And get the source code on GitHub at:
https://github.com/KathyReid/valentines-dataviz