Commentary

This is certainly not an exhaustive review of the topic. There are many kinds of visualizations I won’t be able to explore in a blog post. The common thread here is simply “things I’ve found while researching another project I’m working on for my information visualization class.”

Nightengale’s Coxcomb

One of the earliest examples is Nightengale’s Coxcomb. This graph was created by Florence Nightengale during the Crimean War to advocate for better sanitation. It shows that the number of deaths due to preventable causes (blue wedges) exceeds the number of deaths due to wounds (red) and other causes (gray). It also shows the success of sanitation efforts – the decrease in preventable deaths in April 1855 corresponds to sanitation cleanup efforts in Turkey.

Figure 1: Nightengale’s Coxcomb

The major advantage of the circular layout of the coxcomb is the way months have a consistent placement around the axis. This makes it easier to do year-on-year comparisons. (This will be a recurring theme.)

Nightengale was careful to map data values to the area of wedges, not the radius. This solved one problem, but introduced another. Nightengale was avoiding the problem where area increases as the square of radius. Had she mapped her data values to the radius, this would have exaggerated the values, since a doubling of the radius would show a quadrupling of the area (Rehmeyr, 2009). But by avoiding that lie factor, Nightengale made it somewhat harder to compare months. You can somewhat easily tell that the radius for January 1855 is about twice as long as the radius of November 1854. But what of the area? People aren’t that good at estimating area, especially of odd shapes like wedges (or even rectangles with differing aspect ratios).

Teoria Generale Della Statistica

Figure 2 avoids the area/radius confusion of Nightengale’s coxcomb, by plotting the data as spokes on a wheel. It is also much less visually striking than the coxcomb. It’s okay, sometimes, to sacrifice some utility (but not honesty) to increase impact.

Figure 2: An early circular plot (Gabaglio, 1888)

The graph comes from Teoria Generale Della Statistica, an 1888 statistics book by Antonio Gabaglio. Although the book is cited often by visualization papers, I haven’t found out much about it. And since it’s in Italian, I can’t even tell you what this is a chart of.

One final note about this chart: It doesn’t scale to showing large numbers of years in one plot. You could represent a few years by having several colored lines along each spoke, but you’d quickly run out of colors.

Spirals

By plotting data on a spiral, we can show several years worth of data. Figure 3 shows quantities of a certain food eaten by chimpanzees in the Gombe preserve in Tanzania between 1980 and 1988. Each revolution of the spiral represents a year, and the months are aligned on the spokes. This supports both month-to-month and year-to-year comparisons. And notice that there are no breaks in the data: other, non-spiral, layouts would have breaks, such as between December and January. With the spiral, every data point is adjacent to the the previous and next month, and the previous and next year (Carlis & Konstan, 1998). The downside, compared to a table, is that it becomes more difficult to compare months of the same year that are located on opposite sides of the spiral.

Figure 3: A spiral plot (Carlis & Konstan, 1998)

To compare two or more data sets, Carlis and Konstan placed bars onto the spiral. Figure 4 compares chimpanzee consumption of two food types. The visualization seems fundamentally sound, although it could certainly be improved. At first, I was concerned about perspective effects. Since the spiral is shown in perspective, would the brain perceive bars in the back as larger objects whose sizes have diminished in the distance? The answer seems to be no. I checked, and bars in the front and back that appear to have the same height actually do. (Comparing heights is something the brain is pretty good at.) The display of the graph could certainly be improved to have less occlusion of the blue bars.

Figure 4: Comparing multiple values on a spiral plot (Carlis & Konstan, 1998)

An Aside About Scales and Legends

You probably noticed that there aren’t any labels on the spiral plots I’ve shown. That practice will continue. I don’t have a good explanation as to why that is, but I do have a guess. The visualizations are generally created by interactive programs where the user can specify lots of parameters. I’m assuming the scales and legends (months, years, etc.) are shown in those controls.

However, the nature of the spiral doesn’t leave a lot of room for annotations. The spokes can easily be labeled, but the revolutions of the spiral are harder to annotate, especially if the spiral is tightly wound. Weber et. al. (authors of a paper on the subject, from 2001) suggest making an interactive visualization, where the user gets gets information about the data underneath the mouse pointer.

This is also a good time to mention that Gabaglio, the Italian statistician, did an early spiral chart. I think it’s hard to read (you have to compare sizes of rotated rectangles), but it at least manages to label both axises. You can see this reproduced in The Visual Display of Quantitative Information (Tufte, pg. 72).

Spirals and Periodic Data

The spiral layout can make periodic trends in the data easily apparent, as long as the correct period is chosen. Figure 5 shows the importance of choosing the correct period. The chart on the left has a 27-day cycle (that is, 27 days per revolution), the correct period, 28 days, is shown on the right. There are some data analysis techniques that the computer could use to suggest a time scale to the user (Müller & Schumann, 2008).

Figure 5: The importance of having the correct period for your spiral chart (Müller & Schumann, 2008)

Glass Patterns, Pattern Recognition, and the Kaliedomap

Another interesting feature of circular data layouts is that it can make it easier to recognize patterns. To understand why, we’ll begin by discussing Glass patterns.

If a field of random dots is copied, rotated slightly, and superimposed on the original, people will notice a circular pattern in the dots (Glass, 1969). Simply shifting the dot pattern along one axis (not rotating it) produces a dot field in which it is much harder to notice a pattern (Wilson & Wilkinson, 1998). This leads to the observation that perhaps it will be easier to notice trends in data if they’re arranged circularly instead of rectangularly.

Figure 6: A Glass pattern (Glass, 1969)

Kim Bale tried this in a design she and her colleagues called a kalliedomap (so named because the result resembles a kaleidoscope). Each segment of the kaleidomap plots one value, with time increasing by hours as the angle increases, and time increasing by days as the radius increases (see fig. 7). Bale et. al. compared this with a more traditional cascade plot, where time increases by hours on the x axis and days on the y axis.

Figure 7: Reading a kaleidomap

Figures 8 and 9 show air quality data from London in 2002 and 2004. Traffic calming measures were introduced in 2003, and the graphs are investigating changes that may have resulted. There are some stripes in the data, which are particularly evident in NO as NO2 segment. The stripes are weekends, where there is less traffic and hence less pollution.

Figure 8: “Two Kaleidomaps showing the air quality data from around Westminster during March 2002 (left) and March 2004 (right).” (Bale, 2007)

Figure 9: “Air quality data from around Westminster during March 2002 (top) and March 2004 (bottom) displayed as a series of 2D cascade plots.” (Bale, 2007)

Bale et. al. contend that the striping effects are easier to see in the kaleidomaps than in the cascade plots (and they did some research to support that claim). In my experience, the striping is more striking in the kaleidomap than in the cascade plot. However, the kaleidomap has the drawback that it’s difficult to find the same point in time in different segments – you have to mentally flip a segment upside down to compare it to a segment across the circle.

There’s Much More

There are many more possibilities that I don’t have time to cover here. The papers I’ve cited go into more detail about the solutions they propose. If you’re interested in this subject, they make good reading. And there are many uses of circular visualizations I haven’t covered – clustering and identifying relationships is one such topic.

Evan Dickinson is a former Portlander currently pursuing an MA in interaction design at Simon Fraser University in Vancouver, BC. He blogs about his studies for CHIFOO. Write him at evan_dickinson at sfu dot ca.

References

Bale, Kim et al. “Kaleidomaps: a new technique for the visualization of multivariate time-series data.” Information Visualization 6.2 (2007): 155-167.  

Carlis, John V., and Joseph A. Konstan. “Interactive visualization of serial periodic data.” Proceedings of the 11th annual ACM symposium on User interface software and technology. San Francisco, California, United States: ACM, 1998. 29-38. 3 Nov 2009 .

Gabaglio, A. Teoria generale della statistica. U. Hoepli, 1888.  

Glass, Leon. “Moiré Effect from Random Dots.” Nature 223 (1969). 7 Oct 2009 .  

Glass, L., and R. Pérez. “Perception of random dot interference patterns.” Nature 246.5432 (1973): 360–362.  

Muller, W., and H. Schumann. “Visualization methods for time-dependent data - an overview.” Simulation Conference, 2003. Proceedings of the 2003 Winter. 2003. 737-745 Vol.1.

Tufte, Edward. The Visual Display of Quantitative Information. 2nd ed. Cheshire, Conneticut: Graphics Press, 2002.  

Rehmeyer, Julie. “Florence Nightingale: The Passionate Statistician.” Science News 26 Oct 2008. 8 Nov 2009 .

Weber, M., M. Alexa, and W. Muller. “Visualizing time-series on spirals.” Information Visualization, 2001. INFOVIS 2001. IEEE Symposium on. 2001. 7-13.