2a:null 2b:["$","title",null,{"children":"How we made Waves of Interest | João Ricardo Mendes | Observable"}] 30:T72d,md`## Data Our design process began with a general exploration of the data space: what happened in the US between 2004 and 2020, and how would this be reflected in the ‘search interest’ trends measured by Google News. We started a list of about a hundred topics — a mixture of top searched political terms on Google, terms from Pew's survey on most important political topics as well as a few manually added terms to account for current events. In the end, we boiled them down to the following list of 69 topics, comprising the currently most searched political concepts in the United States and topics from Pew Research Center's election surveys, as well as a few manual additions to account for emerging 2020 issues:

${await FileAttachment("topics.png").image()} Each news search topic has an id (such as \`/m/01hy1q\`) that can be used to query the [Google Trends](https://trends.google.com/trends/explore?date=all_2008&geo=US&gprop=news&q=%2Fm%2F02l3h,%2Fm%2F07__7) website. The values returned represent a measure of the relative search interest of the topic across time (monthly and yearly over the 2004—2020 period) and geography (in this case, the granularity was the individual state, or the US as a whole). In order top start prototyping quickly, we used a [Jupyter](https://jupyter.org/) notebook to call the API repeatedly for each date and state. The result was a dataset of 200 dates × 100 topics × 52 locations, with a value for each data point. That's roughly a million data points, so explored the data in various ways to see if we could find interesting perspectives. We made some maps in python with [UMAP](https://umap-learn.readthedocs.io/), and exported the dataset to a static file. Further explorations took place in [Observable notebooks](https://observablehq.com/). `31:T847,md`

### Box: Analysis pitfall On Google Trends, the values are all **normalized between 0 and 100**, and returned as integers. If you query two topics separately, each response contains values that span the range [0, 100]. But if you query them together, you can compare them:

${await FileAttachment("comparison.png").image()} In this case, though, the numbers for ‘Vaccine’ would be dwarfed by the values for ‘Election’, and never be anything else than 0, 1 or 2—or up to 5 in 2020, as the interest in the topic of vaccines was suddenly renewed. As a consequence, a value=20 returned by one query could not be compared with a value=20 returned by another query. Now, unfortunately, because we aggregated monthly data to yearly data early in the pipeline, we did not **even see the normalization anymore**, and kept experimenting with the data to find patterns and stories to to tell. For instance, one machine learning analysis of the data sets by geographic region (i.e. individual states) returned a very interesting pattern: the states in the central region presented a clear difference from coastal states. We felt great: we were making sense of the data! Then after a while we plotted two choropleth maps: one colored with the overall search interest pattern we had identified:

${await FileAttachment("clustered-map.png").image()}

Clusters obtained with UMAP

… and the other with the states’ population:

${await FileAttachment("population-map.png").image()}

Population of each state

Oh my… [The business implications were clear](https://xkcd.com/1138/). Apparently, the scaling to the maximum caused lower total values for smaller states (due to regression to the mean, or related effects...) So, we stepped right into the trap of **re-aggregating already normalized data** (which one should never do), and should have just waited for a proper un-aggregated dataset before exploring freely. Lesson learned :D `32:T569,md`

${await FileAttachment("crazy-map-year.png").image()}

UMAP 1—each point is a state’s vector for a given year (colored by date)

So there was definitely a structure in our data: although the UMAP algorithm had not been informed of the date of each dot, it had correctly grouped together the vectors from each year. The years 2004 to 2007 were difficult to separate, but after that, each year was quite clearly identifiable,. Great take-away: although each state’s numbers are very different, looking at the vector of 69 topics interest is enough to say ‘this was in 2012’. We could also see that the terms of the debate progressed in some sort of a continuous way, with a sharper jump between ’12 and ’13. 2020 was quite literally off the chart: a completely different world, for the obvious reasons (the COVID epidemy, the resulting spike in unemployment, etc). Then, by coloring the states with a color representing the way they had voted in the nearest presidential election, we were able to see that UMAP had also picked this secondary signal: blue states were on one side, and red states on the other side of each of the blobs.

${await FileAttachment("crazy-map-vote.png").image()}

UMAP 2—each point is a state’s vector for a given year (colored by election result)

`33:T495,md`What surprised us the most, is that when we plugged in the _monthly_ data (which is obviously much more noisy), the crazy map held up pretty well.

${await FileAttachment("crazy-map-monthly.png").image()}

The crazy map with monthly data points

There's a lot to parse in a map like this. For example, some Junes seem strangely related (2012, 2013 and 2016), for reasons we did not elucidate. We can further see that the chaos of 2020 began to show in the Google news search interest in April. By zooming in and looking more in details we saw other interesting patterns, outliers (such as Virginia, California, and especially Washington, DC), and so on. At this point we were happy about what this crazy map was telling us: that the data had a superb structure and could be trusted. But, however we turned it, we also kept realizing that it could definitely not be used to convey a story to regular, non-data sciency audiences. The concept of similarity maps is already hard to convey, and then with 50 states moving through time… It was just too much. So, sadly, we had to decide to not include it into the final product. `34:T7ea,md`## Line charts

${await FileAttachment("humble-line-charts.png").image()}

There is a lot to see in humble line charts

Shying away from the complexities of machine learning, we were also exploring humble line charts. By highlighting presidential election years over non-election years, we could definitely show that, for some topics, the search interest is really spiking just before the elections. Whereas some topics are linked to the deep econonomic or international trends (War, Recession), others (like Abortion) are tied to the rapid and almost artificial electoral news cycle. (Of course, terms such as Election, President, are naturally linked to the electoral calendar.) Yet others have been the subject of debates for years, and have since vanished, the debate having been solved (Same-sex marriage).

${await FileAttachment("ssm.png").image()} The base for these charts is standard [D3](https://d3js.org), rendered with [svelte](http://sveltejs.org), which made adding animations and UI really easy. We create the charts as SVG, each line being drawn as a path with d3.line. The technique for tooltips is worth noting: when pointing the mouse on the paths, we are using the famous Voronoi search technique pioneered [by Nadieh Bremer](https://www.visualcinnamon.com/2015/07/voronoi.html). The code however is completely different, as we’re using d3-delaunay’s search method on the Delaunay triangulation of the data points. For performance, the triangulation is computed lazily, _i.e._ only the first time (and if) the pointer flies over the chart; furthermore, we don’t create the actual Voronoi shapes as svg paths, and use [delaunay.find](https://observablehq.com/@d3/delaunay-find) instead, so the chart does not require more memory. We've also extended the technique to take into account the whole curved paths, not just the control points. See [this specific notebook for details](https://observablehq.com/@fil/paths-delaunay-hover).`35:T77e,md`## Hero line chart

${await FileAttachment("woi-header-quick-twitter@1.gif").image()}

the hero in action

Hero, in the web design parlance, means “large image in the header”, but there was something heroic also in the code for this chart. The initial design for _animated_ and _blurred_ lines was beautiful, but the implementation was just not cutting it. First, it was slow. SVG’s [gaussian blur filter effect](https://developer.mozilla.org/fr/docs/Web/SVG/Element/feGaussianBlur) works by rasterizing the path to a canvas, then blurring the canvas pixel by pixel (maybe sending it to the GPU), then merging the blurred canvas to its final destination. Doing this for 17 paths (one for each year) on a large screen would take much much more than the ~16ms budget we had (ideally), resulting in a very jumpy animation. Second, cross-browser issues. Try as we may, Safari would not accept these filters. The text labels were also looking wrong, because the minimum blur radius for Safari is 1, and our design had blur radius values of 0.5, 0.1, etc. So we had to write our own blurring code for the line chart’s wavy paths. We switched to canvas, and with a few tricks managed to write a reasonably fast and cross-browser blur function that was visually acceptable (though admittedly not as good as gaussian blur). Indeed we wrote two methods, one optimized for the paths, and one optimized for text! (See [this notebook for details](https://observablehq.com/@fil/canvas-path-blur).) Note: we also tried switching to the CSS blur filter, but then Safari uses the wrong color space (see the image below)!

${await FileAttachment("safari css blur.png").image()}

Safari CSS blur—emetic

(Note: we haven't reached the goal of 16ms per frame, but the movement is continuous enough to pass.) `36:T1046,md`## Contour map After some (soul) searching, we decided that a map of the U.S. with states represented in a usual geographic layout would be more comfortable to read than a ‘crazy map’ positioned in a virtual (and arbitrary) multidimensional topic space. But we still wanted it to be a ‘topic map’ and not a geographic map. The design idea was to use a contour layout, creating “blobs” in high-interest regions. The reader would be able to parse this map, see how it evolves in time, and compare it by switching the topic.

${await FileAttachment("hexmap.png").image()}

States organized on an hexagonal grid

The first implementation used [density contours](https://observablehq.com/@d3/density-contours). We put each state in a certain position on the map (on an hexagonal grid), and gave it a weight equal to the value (for the given date and topic).

${await FileAttachment("density-contours.png").image()}

Density contours

Visually this made overall sense, but the mathematician was not happy: density contours are for… densities, and we were using them for spatial interpolation. A consequence was that States that had a low value, but were surrounded by states with a high value, had a high “density” and showed with a high value. Conversely, states that were isolated geographically, such as Alaska or Hawaii, or which were alone with a high value and surrounded by low-value states, did not emerge much—they needed to have a much higher value to register visually. We tried to tweak the weights based on the number of neighbours of each data point—it was looking a bit better but it was still “too wrong”. And once we showed the actual numbers on the map, the discrepancy between the value and its representation was unbearable. So, while the graphics were nice, they were not accurately representing our values. A review of the available spatial interpolation algorithms was underwhelming: most of them tend to result in (very subjectively) ‘ugly’ shapes, and are quite slow. We ended up creating a new layout for D3, dedicated to contours of spatially interpolated data. The concept, in a few words, uses the voronoi diagram of the data points: each pixel is associated to the closest data point, and painted with a level of gray that corresponds to its value. By blurring the resulting image with a blur radius that corresponds to our data’s granularity, the level of gray is interpolated (averaged) naturally between neighboring points—we can finally compute the contours, which result in natural-looking blobs, like density contours, but with the correct values on the control points.

Voronoi to contours

${await FileAttachment("greyscale.png").image()}

Underlying greyscale field of blurred values

This approach doesn’t have a definite name yet, and there are a few settings to adjust, but we’re happy to share an early release and explain it [in this specific notebook](/@fil/spatial-interpolation-voronoi-blur). Looking at the maps in the final product, we are really happy we went the extra mile here!

${await FileAttachment("minimum-wage.png").image()}

Minimum Wage islands

As a final addition, in order to animate with the timeline, we turned the values for each state and topic (a vector of values for 2004, 2005… 2020) into a continuous interpolator (with [d3.piecewise](https://observablehq.com/@d3/d3-piecewise)). So querying a map for “year 2004 + 0.3” (somewhere between 2004 and 2005) would work, and give an interpolation of the maps for respectively 2004 and 2005. Interpolating the values also means we can avoid doing slow and awkward path interpolation.

Voronoi to contours

`37:T541,md`## Conclusion ‘Crazy’ (or far-fetched) representations involving advanced data processing are very powerful to dive into the data. They show structure, enable to pinpoint outliers, and help understand what information is there. But none of the UMAP maps that we prepared passed the litmus test of basic readability. They helped us find stories and structure, but they were not in themselves supporting the stories, and they make intimidating charts. These algorithms are useful for domain specialists who will take the time to learn how to read their outputs, but they are too full of arbitrary choices (and indeed random) to be instantly recogniseable, and to be able to convince a skeptic reader. We needed these images in the exploratory phase to drive our understanding, but by using more classical views—line charts to show an evolution in time, superimposed charts to show variance or coordination between states, and a somehow geographic map to display the topic—we can make sure everyone in a general public can get a sense of what’s happening, and relate to the main story. Another take-away is that all the charts, even the modest line chart, can be enhanced by advanced techniques. 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This project illuminates the interests and concerns of Americans in recent election years, as seen through the lens of Google Search Interest in the United States from 2004—2020.\n\n