We frame the aspect ratio selection problem as one of minimizing the length of the data curve while keeping the area of the plot constant. This leads to a method that is substantially more robust than previous approaches. We’re also able to demonstrate empirically that the resulting aspect ratios are a compromise between those suggested by previous methods. As shown below, the arc length method can also effectively bank both standard line charts (in this case a loess regression line) as wells as contour charts.

Perhaps the most surprising result is that good aspect ratios can be selected without explicit reference to the slopes or orientations of the line segments within the plot.

Let me know if you run into any problems with it or have any suggestions for improvement.

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).

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.

Here are a few pointers:
Parallel coordinates for exploratory modelling analysis (Antony Unwin)
Exploratory modelling analysis: visualizing the value of variables (Antony Unwin)
Meifly: Models explored interactively (Hadley Wickham)

I tried installing meifly, but it appears to depend on ggplot which is no longer available since ggplot2 has been released.

[2004] Exploratory data analysis for complex models (with discussion) (Andrew Gelman)
Discussion of this paper by Andreas Buja (Andreas Buja)
Rejoinder to discussion (Andrew Gelman)

This discussion is quite inspiring. The idea that visualizations can be thought of a statistical tests was quite eye opening. I think that this suggests quite a few directions for research in InfoVis. However, there hasn’t been much work in this area in the 4 years since the paper came out. Why? Perhaps the artificial division between InfoVis and statistical visualization has kept it from being noticed. Perhaps it’s just very hard