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wise relations. Many researchers have studied ways of selecting a useful ordering,
including Bertin's reorderable matrix [12], Seo and Shneiderman's rank-by-feature
techniques [13], and Peng et al.'s reordering for visual clutter reduction [14]. In all
cases, a user should be able to prune orderings to emphasize those that show trends,
groupings, or other discernable patterns. Thus far most research has focused on sim-
ple 1-D orderings, but higher level orderings and structures (e.g., hierarchies) have
also been studied.
3.4
Hardware and Perceptual Limitations
This discussion of information content would not be complete without also consider-
ing the limitations imposed by the visual communication channel (i.e., the display)
and receiver (the human visual perception system). Regarding the channel and its
capacity, modern displays are limited to somewhere on the order of one to nine mil-
lion pixels, although tiled displays can increase this substantially. The color palette
generally has a size of 2
24
possible values, although the limitations of human color
perception take a big chunk out of this. Finally, the refresh rate of the system, typi-
cally between 20 and 30 frames per second, limits how fast the values on the screen
change, though again the human limitations of change detection mean that much of
this capability is moot.
Regarding these human limitations, from the study of human physiology we know
that there are approximately 800k fibers in the optic nerve. We can perceive 8-9 levels
of intensity graduation, and require a 0.1 second accumulation period to register a
visual stimulus. In addition, we have a limited viewable area at any particular time,
and a variable density of receptors (much less dense in the peripheral vision). Studies
have shown we have a limited ability to distinguish and measure size, position, and
color, and the duration of exposure affects our capacity. Finally, it has been shown
that our abilities are also related to the task at hand; we are much better at relative
judgment tasks than absolute judgment ones.
3.5
Measuring Information Content on Visualizations
We now look at methods that have been used in the past for measuring the informa-
tion content in a data or information visualization. For completeness sake, some of
these are quite trivial. For example, simply counting the number of data values shown
is a valid measure. The issue in this case would be how to deal with partial occlusion.
In some cases this would be acceptable if sufficient information remains visible to
make identification or recognition possible. Tufte [15] suggested the data-ink ratio as
an indicator of information content, though tick marks, labels, and axes are often
essential for appropriate identification. Many researchers have used counts of the
number of features or patterns found in a particular amount of time. Ward and Ther-
oux [16] counted the number of clusters and outliers found by users in different visu-
alizations, while Suraiya et al. [9] counted insights discovered. In each case, a ground
truth is needed to verify that what was found was really present. Similar experiments
have been used to measure classification, measurement, and recall accuracy.
There are many other issues when attempting to measure information in a visuali-
zation. As mentioned earlier, distortion and other transformations can improve the
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