Using Space Effectively: 2D

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Lecture on Sep 26, 2007



[edit] Readings

  • Multi-Scale Banking to 45 Degrees. Heer & Agrawala. (pdf)
  • Hyperdimensional data analysis using parallel coordinates, Wegman (jstor)
  • Pad++: A zooming graphical interface for exploring alternate interface physics, Bederson & Hollan (acm)
  • Chapter 11: The Cartogram: Value-by-Area Mapping. In Cartography: Thematic Map Design. Dent (pdf)

Optional Readings

[edit] Willettw - Sep 25, 2007 11:55:08 pm

Having spent a bit of time looking into cartogram generation methods and tracking down examples over the summer, I thought I'd add a couple of interesting side-notes. It's interesting that even though a number of different algorithmic approaches have been proposed over the past thirty years, the vast majority of cartograms seen in print are still generated by hand, by a designer. Obviously it's very difficult to automatically generate continuous cartograms that strike the right balance between preserving shapes, preserving adjacencies, and obtaining a correct value to area mapping. Even Daniel Dorling, the researcher behind some of the more interesting algorithmic approaches to cartogram generation has returned to using manually constructed cartograms in his more recent publications.

A few interesting approaches have surfaced recently, including a diffusion-based method published in 2004 which garnered a reasonable amount of press. A nice example is seen below (and more here).


US counties by population, colored by 2004 Democrat/Republican votes(from

Hybrid rectilinear cartograms composed of small squares are probably the most commonly seen variety (example below). They are also arguably the most successful, since they preserve shape better than standard rectangular cartograms and their areas are easier to judge than cartograms with irregular angles and side lengths (the squares can also be counted, providing even more accurate assessment of area). However, there don't appear to be any published algorithms for generating this specific cartogram type. This could be an interesting class project if someone cares to take it up.


US states by number of electoral votes. (New York Times, 2004)

[edit] Hazel Onsrud - Sep 29, 2007 06:21:31 pm

Although I have worked and studied in the field of Geodesy and Geomatics Engineering and have seen some of the transitions from drawing maps by hand to printing them off on a plotter, and it fascinates me that there is still a lack of automation and real need for artistic feel even in the cartography of today which is well equipped with geographic information systems, global positioning systems, google earth and a plethora of digitized maps. Despite these fantastic resources (transformations embedded into complex software packages, and complex algorithms reduced to a few buttons etc.) anyone who has used a GIS or has been surveying in the field is well aware of the subjective "give and takes" not yet automated...and I though thought the chapter by Dent nicely illuminated some of these issues. I wonder to what degree we will eventually be able to program our aesthetics...and what exactly it is that we won't be able to capture in our software algorithms.

Check out the 2007 Visualization winners from Science:

[edit] Ken-ichi - Sep 30, 2007 03:01:54 pm

One reason I think parallel coordinates are initially hard to read is that they always throw away one spatial dimension (upon which the axes lie), but it isn't immediately obvious that this dimension is meaningless. I find this especially true when the axes are arrayed horizontally. I always have to remind myself that I'm not looking at some kind of time series data, and that the lines connecting measurements of the same objects are measuring different attributes, not the same attributes again and again.

I'm glad willettw brought up the NYTimes 2004 election map cartograms (and also sad that he beat me to the punch). Those are the only cartograms I've ever found truly revelatory, and do more to explain the power of population and the electoral college than any textual description. The interactivity adds even more, providing an animated morph between a geogrpahic and value-by-area projections that really hammers in the differences between space and population.

[edit] Andrew McDiarmid - Sep 30, 2007 06:57:05 pm

As I read Wes's post, I was reminded of a blog post posted to the iSchool fun list a while back ( Ultimately it leads back to the same sources mentioned in his comment, but I did notice that the code for generating the cartograms is available here.

In thinking about banking to 45 degrees and application of low-pass filters and trying to make sense of how it all works, I came up with the following qualitative explanation to help me understand. If data such as the CO2 levels is periodic then adjusting aspect ratio to in a sense make the average slope equal to 1 averages roughly the same slope over and over, minimizing any slower trends low-frequency periodicity. Applying a low-pass filter smooths these cycles (thank you, whoever said "Think smoothing" in class) thus allowing the banking procedure to apply to the larger trends, bringing their average slope closer to one.

Is this accurate and/or helpful? I welcome correction!

[edit] Robin Held - Oct 01, 2007 12:10:23 am

Wegman mentions an interesting method for indicating "overplotting." Overplotting occurs when one has multiple data points overlapping at one location. Wegman chose to indicate overplotting by using scintillation. He assigned 16 colors to the data, and then for an overplotted point, sequentially switched between the colors of overlapping data. I would be like to see how this works in action. It seems like the animated points would be hard to interpret. Ideally, with modern graphics one could assign transparency to the various data points, which would make it easier to see where the different patterns overlap. This would relieve the user from needing to keep track of scintillating colors, and the absence of animated features would be less distracting.

[edit] James O'Shea - Oct 1, 2007 6:59:36 am

The Bederson and Hollan paper (Pad++) discussed how using metaphors to organize GUIs can ultimately limit the development of novel systems for interactively exploring large data sets. Specifically, they focused on the adoption of file, menu, folder, metaphors (among others) for organizing a directory structure. I think it is true that the use of these metaphors may constrain our thinking when developing new visualization tools for directory structures, for example. I also believe this paper highlights a significant hurdle with any visualization technique. Often, new visualizations are only useful if people can make sense of them, and this is often difficult if they do not build upon some familiar framework or metaphor. I think the original windowing systems for computers were easier for people to adopt because they were based on these familiar ideas. The Cartogram paper points out a similar problem: if the distorted maps depart from the familiar shapes too much, people will have difficulty recognizing it. Sometimes I wonder if effective advances in visualization need to be made incrementally, each one building upon the other, such that there is a progression from the familiar visualizations to the more novel ones. I recall one of the criticisms of Tufte's new graphs (like the reformated box-plot) was that nobody would know what is was since people are only familiar with a specific type of box plot.

[edit] Ariel Rokem - Oct 01, 2007 10:03:06 am

Concerning banking to 45 degrees. Perceptually, most people are actually worse at making perceptual discriminations around 45 degrees than they are in performing perceptual discriminations around the cardinal orientations (12 o'clock, 3 o'clock, 6 o'clock and 9 o'clock). So 0 and 3 degrees are more readily distinguished than 45 and 48 degrees. This is known as the "oblique effect". This effect may be counteracted by supplying strong contextual cues, such as axis orientations and corners. This implies that if you want your readers to make fine distinctions between the angle of slopes in different parts of a time-series, you might not want to follow Tufte's suggestions on removing a lot of the non-data ink. The contextual cues provided by the non-data ink may render your graphic more easy top interpert .

[edit] Kenrick Kin - Oct 02, 2007 01:42:33 am

I thought the banking to 45 degrees method was a very effective way to present global and local trends. However, it limits itself because the y-scale tends to be reduced, to achieve a good aspect ratio (or the x axis would have to be increased by a lot), making it harder to read the y values of the data points. If you do care about the data values, I wonder if it's worth compromising and choosing one of the multi-scale banking aspect ratios, or if it's better to have a more y-axis readable graph that contains a small sparkline sized version of the graph as an insert to illustrate the trend.

[edit] James Andrews - Oct 02, 2007 07:32:26 pm

Ariel -- does the 'oblique effect' contradict the observations from this slide [1] -- that two line segments are maximally discriminable when their average absolute angle is 45 degrees? I tried to find references about it, but most seem to be talking about it in the context of recognizing patterns: eg, recognizing a vertical or horizontal pattern (like |||| or _ _ _) is easier than recognizing an oblique pattern (like ////). Which isn't really about line discriminability, but extrapolating from it I'd say it actually supports the slide: if we're more likely to recognize 'sameness' in two horizontal lines, then I'd think we'd be more able to discern difference in two oblique lines. Could you point to a good reference that comments more directly on the oblique effect in the context of line/angle discriminability?

[edit] Amanda Alvarez - Oct 02, 2007 09:06:59 pm

re: OBLIQUE EFFECT: some papers [2], [3], [4] esp. figure 1 in this last paper.

the poor discriminability concerns lines that are all oriented (roughly) the same way, eg. a grating. so you can't tell a 3 degree difference between lines pointing out at about 45 deg, but you can tell the difference when they are pointing at 0 or 90 deg. this seems to be a different scenario from that presented in the slides. clearly by enlarging the angle between two lines we are going well above threshold, no matter what orientation the lines themselves have. if we try to orient all the lines in the graph to 45 with respect to the axes (or something else) and not to each other, then we will have a problem, which i think is what ariel is getting at.

re: cartograms. space is an important visual variable, but it seems like in manipulating or re-representing the space in a cartogram, the end goal is more sensationalism than prudent use of space to convey information. i'm not denying that cartograms can convey information well, but probably only after one has gotten over the initial shock of distorted space (if one ever gets over it, because sometimes it might just be too confusing). when space is altered, one is required to hold a number of other attributes fairly constant: shape, orientation, contiguity. space is an effective visual variable, but what is the trade-off when altering space hinders shape or data recognition? if the user often has to mentally restructure the image, is that effective communication?

[edit] Karen Hsu - Oct 02, 2007 09:13:47 pm

Re: Oblique Effect

On p. 146 of Universal Principles of Design, Lidwell et al. describe the oblique effect as "the ability to more accurately percieve and judge line orientations that are close to vertical and horizontal, than line orientations that are oblique." The book goes on to explain that our neural predilection biases our judgments toward the nearest axis; in other words, lines oriented close to horizontal or veritcal tend to be recalled as truly horizontal or vertical.

So, in addition to the heightened discernibility of small angles when one line segment resides on an axis, I think the oblique effect is also applicable when either segment is near an axis. More specifically, if either of two line segments nears an axis, then the perceived angle between them might be greater or less, depending on the orientation of the two line segments. But, as Amanda just pointed out, if we have a large enough angle this becomes inconsequential.

[edit] David Jacobs - Oct 02, 2007 09:15:21 pm

I think all this discussion about the "oblique effect" is interesting, but I'm having a hard time figuring out how to apply it to visualizations. If it's perceptually easier to discriminate between nearly horizontal or vertical lines, then we should try to massage the slopes of the lines in that direction, right? The problem is, in order to bank towards 0º or 90º, we'd have to distort the aspect ratio so much that the entire graph would be unreadable (10 miles tall and two inches wide, for example). I think it's not too hard to claim that 45º is the next easiest angle to discern after the cardinal directions. Maybe we can do something like banking to 0º by rotating the entire visualization (axes included) rather than messing with aspect ratio. Sounds terrible, I know, but it might be able to work.

[edit] Mark Howison - Oct 08, 2007 01:45:37 pm

I think that Wegman's parallel coordinate graphs offer a "high threshold, high ceiling" solution for visualizing multivariate data. While they can capture correlations among multiple variables fairly succinctly, they also require some degree of knowledge as to how they work. That is, a person who hadn't read this paper who had just picked up one of the graphs would probably not be able to make much sense of it initially. That said, there does seem to be a fairly easy heuristic for interpreting correlations between adjacent axes: more perpendicular lines corresponds to a positive correlation, and more crossing lines to a negative one. However, since the number of possible permutations of axis adjacencies increases with the number of variables, it doesn't seem like this type of visualization would be feasible for data sets larger than say 5 variables. Maybe introducing interactive manipulation of the axis adjacencies could alleviate this problem.

[edit] N8agrin - Oct 22, 2007 09:25:28 am

The initial feeling I was left with after reading the Pan++ article several weeks ago was that zooming is an unlikely method of navigating what is generally perceived to be a 2 dimensional space. My reasoning was simply that the act of zooming in a two dimensional space is cumbersome, it generally requires awkward or unintuitive gestures to preform, and it's not the way people tend to expect to interact with their interfaces.

My feelings about this have somewhat changed after finding this interesting visualization:

Essentially this is a browser of first-order tag relationships in flickr. I believe it successfully accomplishes several things at once. First it shows you not just the tags that are related to the tag that you're searching for, but the images associated with that tag. It makes the thumbnails of those images small enough that they are recognizable, but encourage further inspection. This takes place through a simple mouse-over, instead of an awkward gesture. This sort of defined zoom space doesn't seem annoying or cumbersome. The interactions are cleanly separated into almost completely different interfaces within themselves. I really think this is a great use of a zooming interface, and that the designer is managing the tag space well. It would be nice to see the effect of adding second-order tag queries into the visualization to see if it could hold up.

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