Using Space Effectively: 2D

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Lecture on Sep 29, 2008




  • Multi-Scale Banking to 45 Degrees. Heer & Agrawala. (pdf)
  • 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

  • Generalized fisheye views, Furnas. (acm)
  • Hyperdimensional data analysis using parallel coordinates, Wegman (jstor)
  • A framework for unifying presentation space, Carpendale & Montagnese. (acm)
  • Nomography
  • Cartogram central

Kuang - Sep 29, 2008 12:33:26 pm

The banking to 45 degrees work led me to think about about sufficient statistics for doing this kind of stuff. By pre-computing a small subset of aggregate values, like count and sum, one could ship far less than the whole dataset to, say, a mobile client, and still do this type of visualization optimization.

Ketrina Yim - Sep 29, 2008 10:34:50 pm

I have mixed feelings about the concept of cartograms. On one hand, they are good for displaying geographical distributions and are capable of offering spatial information along with statistics. Plus they are a welcome change from bar graphs and tables. On the other hand, cartograms appear disturbingly distorted to the uninitiated and run up against the issue of representing one-dimensional data with area. They also tend to have difficulty representing extreme values, as seen in the Elvis concert attendance cartogram (figure 11.2 in Dent). In that particular cartogram, states with 0 attendance are not visible, while Nevada's attendance is so large that it would not fit in the cartogram.

As much as I like the visual style of the cartogram, I would err on the side of caution and use more familiar forms of visualization for geographically-based statistics.

Razvan Carbunescu - Sep 30, 2008 04:44:15 pm

I actually found that the 3rd reading was from the main book we used for a Computer Cartography class I took in my undergrad at LSU. I remember from it that one of the main problems with cartograms is that they require a deep knowledge of the data being viewed; if for example there's a cartogram of Africa and all countries are shown with some equal value it may be hard to realise which one is significant since not many of us know the size of all countries in Africa. I agree with Ketrina that they should be used sparingly and with great caution but they can be used to great effect like the cartogram showing the states of the US modified in size with respect to the cost of flying across from one town/state to another.

Scott Murray - Sep 30, 2008 07:36:47 pm

I've always thought that line charts were supposed to look something like EKG plots, with sharp spikes and deep valleys. But after the reading and lecture, banking to 45 degrees makes a lot of sense. Even without formally calculating the "ideal" aspect ratio, I think just eyeballing for 45-degree slopes helps present ones data most clearly.

Dmason - Oct 01, 2008 12:27:07 pm

After reading the above comments, I am left with the following impressions:

  1. Regarding the power-spectrum analysis for aspect ratios, I absolutely love the presentation in the PDF which describes the process, and my mind immediately went to some generalizations of this presentation style to my own research. For instance, I am working with random variations in physical devices, and these can be described in one-dimensional power spectra. It's occurred to me that certain properties can be ascribed to each point in the power spectrum, and one could imagine a weighted average of these quantities to predict the properties of these devices. How would this translate back to aspect? We know that we have these different properties of the graph we can highlight, but we can't highlight them all at the same time. Small multiples is one solution, but I offer one more: choose an aspect ratio as a weighted average of aspect-ratio-per-frequency-decomposition. I think similar suggestions are made throughout the reading, and this seems like a tantalizing possibility.
  2. I love cartograms, and I always have, because they are so visually intuitive. Sorry, Ketrina, I have to disagree with you there. It really gives you the impression of regions "bursting at the seams" and others "whithering away" and this impression can be used to convey a fair amount of emotional meaning to otherwise dry data.

Michael So - Oct 03, 2008 03:07:53 pm

I found the cartogram to be an interesting read. I find them interesting because of the difficulty in understanding them. The readers need either prior geographical knowledge, or (if a map of the actual geographic space is shown) to put in some effort in understanding what it is trying to communicate. It is not like those visualizations that sort of make the message initially apparent. I myself found the Elvis Concerts cartogram to be confusing. States were missing and things felt disorienting. However, I think if one gives time and effort to interpreting the distortions, the cartogram might feel more effective at communicating some message (like distributions, or relations) than a thematic map where the message can be obscured by the actual sizes of the "enumeration units". I also think that cartograms might show more about distributions than bar charts because you get a better feel of the spatial context and you get an overview of how the data is distributed over the "enumeration units".

Seth Horrigan - Oct 04, 2008 09:10:06 pm

First, I would like to state that it was enjoyable to read a publication from the University System of Georgia (since I am not in the social sciences, I do not have much exposure to anything published from GSU or UGA).

I found cartograms very interesting. There are many advantages and many drawbacks to the concept. I found the Dorling cartogram of county populations (shown in the slides) to be fairly well done and informative; however, in the case of contiguous cartograms, the odd distortions of boundaries seems to be the main feature of the cartogram rather than the data it is supposed to convey. As the author points out, some of this is due to the fact that cartograms do not follow any set rules and thus any two cartographers will render the cartogram differently. Also, the fact that it is an innovative and unusual method for conveying the information means that I, and others like me, will be unaccustomed to interpreting this sort of illustration. My judgment may be clouded by this fact, but personally, for its good points I think it would be better to use other methods to convey the information.

On the one hand, it offers a remedy to the problem of unnaturally equating physical geographic space with an actual measure of population, intensity, movement or any other variable. On the other hand, if we are trying to overcome the problem of geographic misrepresentation, why bother using a map at all? Surely, the data can be conveyed in a better fashion: contiguous cartograms drift dangerously close to becoming a mass of chartjunk. Additionally, as we have already seen, humans are not very good at measuring area or volume even relative to another object of the same scale; hence, the cartogram is really mostly useful to say "hmm, Rhode Island is bigger than it should be, in fact it is bigger than South Carolina", but we cannot accurately say by how much. Putting this one-dimensional data into a 1-dimensional chart would be more appropriate. Even worse, the non-contiguous charts remove even the ability to see if a geographic region has been modified from its default size. In figure 11.3b, perhaps you can recognize that AL is smaller than it should be, perhaps not, but I certainly would not immediately say "hey, LA looks bigger than it should be". You can see that it is still smaller than Texas, but why bother encoding the data in such a confusing fashion?

James Hamlin - Oct 04, 2008 06:21:12 pm

I don't mean to seem sycophantic, but Multi-Scale Banking to 45 Degrees struck me as an exemplary paper. It takes a result from human perceptual research, identifies some shortcomings in its previous application, and develops technically interesting techniques for its automated exploitation.

After lauding Lakoff's work on metaphor and suggesting metaphor's central role in visualization, I can't let the tail end of the Pad++ paper, "Physics and Metaphor", go unanswered. The distinction the authors make between physics-based and metaphor-based interfaces is certainly useful, but what they mean by "metaphor" here is overt metaphor - concepts like "files, menus, and windows." But the physics-based interface still necessarily operates as a metaphor. How could it not? How are we to understand the "physics" of this information presentation other than metaphorically? There's no literal physics here. What the authors are in fact recommending is a shift from a certain class of metaphors to a wholly different one. Also, this focus on "uniform application of sets of simple laws," for some reason, reminds me vaguely of the tight coupling concept.

Ljuba - Oct 05, 2008 11:25:49 am

I wanted to correct a mistake that I made in class when critiquing the government payroll chart. I very confidently assumed that a small percent variation in spending would be insignificant, or at the very least, not worth stretching the chart out so that it looks like a major spending increase had occurred. Maybe I'm just on edge about things like misrepresenting government spending these days on account of this major election coming up.

Also, the chart had other problems which may have biased me against it. After thinking about it some more, it seems fair (if poorly implemented here) to emphasize a small percentage growth if the absolute growth is significant. The problem here, of course, is that we don't know what constitutes a significant spending increase. If we did, we'd be much more likely to critique this graph fairly.

Matt Gedigian - Oct 05, 2008 04:55:26 pm

Borden Dent hammers the point that shape is absolutely essential for cartograms.

"Preservation of the general shape of the enumeration units is so crucial to communication that the cartogram form should not be used unless some approximation of true shape can be achieved".

"Of the qualities mentioned (shape, order, and contiguity), shape is bar far the most important."

But I found the the Danny Dorling-style cartograms (example), which do not preserve shape, to be better than many of the shape-preserving ones. Granted, these may create lookup challenges for users who are trying to find specific entries. But they do not seem to demand familiarity with the geography (a weakness of cartograms cited above) and they facilitate area comparisons (mentioned in class).

Chris - Oct 05, 2008 08:05:18 pm

I really like the spectral analysis done in "Banking to 45 Degrees." Filtering the input to extract the meaningful trend, and then setting visualization parameters based on this trend seems like the right tool for the job. Some "intermediate results" which I'm curious about are

  • What would have the results looked like if you had used a notch filter for the clump of interest of the spectrum to decide the aspect ratio? For example, on the "aspect ratio = 7.87" plot on page 6, it seems like the right filter for the signal being examined would be one which removes everything except the annual fluctuations (a notch filter on that frequency), rather that one which keeps the annual fluctuations as well as the long-term trend.
  • What would the results have been if the aspect ratio were determined directly from the are of interest of the data's spectrum? That is, what if we looked at the power spectrum, decided the frequency which is of the most interest to us, and then decided the aspect ratio based on that frequency directly, rather than filtering the data to include only that frequency (and some nearby ones) and then deciding the aspect ratio from the filtered data? It may be that the results of this filter-blind analysis would be worse, but I would be curious to see what they would be.

Nicholas Kong - Oct 05, 2008 09:24:17 pm

@Matt I agree that Dent's emphasis on shape was a little extreme, although I do think he was perhaps correct at a certain level of shape. Dent does mention that cartograms are only useful when the viewer is able to construe the meaning of the visualization, and so applying cartographic principles to county-level maps may not be a good idea as most are unfamiliar with county shapes. With the Dorling cartograms we obtain an understanding of the purpose of the map due to its juxtaposition with a geographically-accurate representation of California and the cartogram's overall resemblance to California. The shapes of the counties themselves are not so important because we are not familiar with them at the onset; we are not really losing any information through the transformation.

Maxwell Pretzlav - Oct 05, 2008 10:32:16 pm

I, too, had a strong response to the chapter on cartograms. I immediately thought of a design I had seen in a book I own of work by famous graphic designer Tibor Kalman. I couldn't find an image online, so I scanned the two facing pages (originally from Colors magazine):

from Tibor Kalman: Perverse Optimist, pp 264-265 (click for bigger)

I think this is an example of a very successful cartogram. Its goal is not to relay specific numbers to the viewer, but to give a general view of the difference between two sets of geographical data. By using a world map, which should be familiar to almost all viewers, and by showing two different maps, it helps the viewer not get lost in the geographical deformities but to have a direct emotional reaction to the data being shown. The pronounced differences between locations, and how the data happens to group on continents, causes smaller locations to almost fall behind the larger and create perspective, which helps emphasize the point being made.

David Poll - Oct 06, 2008 01:11:27 am

As I mentioned in class, Pad++ reminds me very much of some of the more innovative "DeepZoom" interfaces I've seen. Granted, DeepZoom is really about making transitions from low-res to higher-res/zoomed-in images smoother, but the rudiments of the zooming UI are definitely there. Among the cool DeepZoom implementations: "Hard Rock's Memorabilia". Some of the DeepZoom uses I've seen are pretty mindblowing: an advertisement for a car in the newspaper where zooming in on the sticker gives a full, high-resolution brochure for the vehicle. DeepZoom right now is mostly static, but it's not hard to see the similarities, and it's not too big of a stretch of the imagination to see how this idea could be easily applied for more interactive user interfaces a la Pad++. This might be an interesting framework to build as part of a final project... It wouldn't be too hard with some of the existing UI frameworks out there, and then the question would be how it could best be applied.

Witton Chou - Oct 06, 2008 04:36:47 am

I really like the idea of banking to 45 degrees. It is actually something I never noticed before - I never noticed how much easier and more accurate the eye/brain is in discerning data from a graph. I found that these banking techniques really point us in a better direction to various trends depending on the banking technique used.

NickDoty - Oct 06, 2008 02:20:29 pm

I'd just like to add my two cents that I both really enjoyed the banking to 45 degrees concept and was surprised by it. It seems to make an aesthetic improvement in addition to improving our ability to evaluate slopes. I had thought that this was a new and revolutionary way to work with Sparklines, but it looks like Tufte mentions this 45 degree research in his Beautiful Evidence book.

Calvin Ardi - Oct 06, 2008 02:26:16 pm

The cartogram reading covered the topic in good detail; I've certainly seen it's use in various media and graphics, but haven't read the background or the general idea of creating one. As Ketrina said, they are a welcome change from the figures and "plain" graphics that are usually displayed, but Michael brings up a good point about needing to know the general geography beforehand. It's probably reasonable (in my opinion) that the general reader has a good sense of where the major countries in the world are, but if it were something more detailed (perhaps the United States for readers in Europe or Asia, or vice versa), perhaps another, smaller map of the country would be helpful. I find that these maps work to gauge a value relative to another, but take figure 11.9 (page 10) for example: the shades and colors are a bit hard to distinguish, and though countries are scaled, it's a bit difficult for me to gauge what Mexico's or Argentina's percent of the world population precisely, other than that they are significantly smaller than India or Japan.

I also found the multi-scale banking paper's diagrams and figures to be very well presented; much more so than the generic graphics and sometimes ambiguous figures that are presented in other papers and presentations. Specifically, the sparklines generated for stocks were rather efficient in it's use of space while still providing the overall trends of each stock. It was a bit confusing, at first, when glancing at the sparklines presented, regarding the left and right graphs. I'm wondering whether the sparklines of the stocks presented would be used separately inline, or if they would be clumped together as done in the paper. If the latter, I feel like a legend of some sort would be useful.

Yuta Morimoto

Insight of line chart without zero is very interesting. I have not consider how to effectively use graph with out zero. For a long time, I have been told that I should not use line charts without zero point, because they sometime cause misleading.

However, as we saw in class, examining a graphs carefully and not forgetting to check the axis, I would never lead the misunderstanding. In fact, putting zero may be trade off between detail understanding and quick recognition of them. Some graphs in statistics are hard to understand, because they are not enlarged enough or have too much blank space to place zero. To facilitate understanding of charts, a graph with out zero seems a one of good choices. Does anyone know about research on how to make a line chart with out zero?

Simon Tan - Oct 06, 2008 11:41:32 pm

I was looking at some Google Finance stock plots the other day and realized that they, too, followed the "banking to 45 degrees" rule. The thing about those charts is that they are also interactive, so you can drag the chart left or right to move forward or backward respectively in time. As you drag the charts, the scale changes dynamically so that there is always a maximum amount of resolution in the data being shown. This interaction seemed disconcerting at first ("Why is the scale changing constantly?"), but I realized it actually emphasized the large dips and peaks of the stock's chart more. As you scroll past a particular point where a stock dives, the quick slide upwards of the rest of the graph gives you perspective of how much it's struggling to maintain that banking to 45 degrees. The faster and more dramatic the jumps, the more volatile you know the stock price is.

Zoomable UIs like Pad++ and interfaces made with Silverlight's DeepZoom technology are quite fascinating. However, I feel that the thing to note about zoomable interfaces is that there have to be shortcuts to jump between points on the 'infinite canvas' quickly. I get frustrated when I have to zoom all the way out for perspective and then have to zoom all the way back in to a different point, when I already know exactly where I want to go. Panning there from a within a deep zoom level isn't very efficient, either.

Sarah Van Wart - Oct 07, 2008 05:48:26 am

I really liked the metaphor of infinite space that Pad++ offered. It seems to provide a real sense of continuity by allowing you to back-track and remember the steps that you took to get from point A to point B. The notion that various tasks could be separated spatially (instead of the traditional directory structure or heirarchial database) could certainly be a more powerful way to organize certain information spaces. It's almost hard to conceptualize a different way of thinking about organizating information, as I feel almost programmed to think in terms of directories, subdirectories, windows, and a finite desktop, but I find it fascinating that research is being done to provide alternate ways to organize information in systems.

I also liked the concept of hypertext when browsing the internet. The parent-child relationship as the user clicks from link to link seems to be an extremely useful as a replacement to the "Back" button. Whereas the "Back" button only allows a user to page through search results linearly, Pad++ allows you not only to recall the meandering path you may have taken to get to a particular page, but also allows you to visualize the way in which you arrived at the page. Interesting.

@Simon: I agree that it seems that it might be easy to get lost, but I think that there's an "overview" thumbnail image that you can click on to pan the space or navigate somewhere else. This being said, I wonder if the overview panning feature would be useful in all cases -- especially for spaces countaining lots of information.

Calvin Ardi - Oct 07, 2008 07:55:49 pm

I was reading the New York Times online and came across a few graphics that fit our readings:

  • What Your Global Neighbors Are Buying - a cartogram depicting how people spend their discretionary income. Mouse over the boxes to get a more precise amount. There are also tabs at the top for the different categories of discretionary spending: the changes in scaling is a neat effect as you can tell from the motion how much difference in spending a country does between two categories.
  • A Year of Heavy Losses - A treemap of various financial firms and their market capitalization. Colors are used for nominal variables, area of the box representing the percentage of the market value, with a mouseover detail of their market capitalization in 2007 and 2008 (along with a sentence or two about the company's status).

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