A few small bugs in the implementation of our algorithm have been fixed thanks to feedback from Ahmet Karahan who is working on a Java version. I have also added a number of other labeling algorithms that have been proposed or used in the past, including those by Sparks, Thayer, and Nelder (from about 40 years ago), and adaptations of the matplotlib, gnuplot, and R’s pretty labeling functions.

Hop visual interface

The graphical elements were produced using Protovis since I needed an excuse to play around with it. We ran into minor performance problems using Protovis for so many plots in a single page. In a production system it would be wiser to generate and cache the plots on the server side.

Update: The screenshot shows a task scheduling imbalance bug that we found in HOP using the visual interface.

The abstract:

The non-data components of a visualization, such as axes and legends, can often be just as important as the data itself. They provide contextual information essential to interpreting the data. In this paper, we describe an automated system for choosing positions and labels for axis tick marks. Our system extends Wilkinson’s optimization-based labeling approach to create a more robust, full-featured axis labeler. We define an expanded space of axis labelings by automatically generating additional nice numbers as needed and by permitting the extreme labels to occur inside the data range. These changes provide flexibility in problematic cases, without degrading quality elsewhere. We also propose an additional optimization criterion, legibility, which allows us to simultaneously optimize over label formatting, font size, and orientation. To solve this revised optimization problem, we describe the optimization function and an efficient search algorithm. Finally, we compare our method to previous work using both quantitative and qualitative metrics. This paper is a good example of how ideas from automated graphic design can be applied to information visualization.

Update: We’ve released a preliminary R package implementing the three labeling algorithms we compared in the paper. Feedback is appreciated. The final version should be released by InfoVis (in October).

Half Dome under a cloud. The weather was changing quite dramatically over the week and I got pictures under a number of different atmospheric conditions.

This is Royal Arch Fall. I hiked to this fall in the morning before my family got up. Royal Arch runs down over a long curving rock. From far away it’s quite beautiful. From the base, you can’t see much of the falls since it curves away out of sight.

On our way out of the park on the 120 we saw our third bear of the trip and I finally got a picture (click to make it large enough to see). The surroundings here were much more picturesque than either of the other bears.

This is cheating somewhat; we passed this field outside of the park, but I loved the combed look of the rows of hay. (I really like the dramatic aspect ratio of the picture. I cropped it this way to get rid of an ugly fence on the bottom and power lines on the top, but the result is quite pleasing I think.)

Fortunately, the components of the Well-Being Index are reported as well. Two components, Life Evaluation and Emotional Health, measure self-reported happiness. If Will’s hypothesis were correct, we would expect these components to account for a disproportionate share of Utah’s overall index. In the scatterplots to the right, the three Utah congressional districts are highlighted in orange. Contrary to Will, Utah is above average only in the Work Quality component. On all the others, including Life Evaluation and Emotional Health, Utah is average or below average.

Wellness data in Excel, since I couldn’t figure out how to get it from the Gallup-Healthways site. The visualization was done in Tableau.

That said, I think it lets you find some rather interesting patterns in how people use their time. Most noticeable is the extra hour or so that people sleep in on the weekends.

He criticizes boxplots, which caused a discussion in the comments to Andrew’s post. I read Tukey’s EDA recently and was surprised to see how much of Tukey’s work was focused on visualization by hand. The boxplot is a sensible visualization when you had to compute and plot manually. Using only 5 numbers it portrayed much of what was important about the data. However, now that plotting is cheap, it makes a lot more sense to just plot all the data.

In general, summaries, visual or otherwise, which assume a single mode, or worse normality, should be treated with a great deal of caution.