The Analytic Hierarchy Process (AHP), a decision-making method
based upon division of problem spaces into hierarchies, is visualized
through the use of treemaps, which pack large amounts of hierarchical
information into small screen spaces. Two direct manipulation
tools, presented metaphorically as a ìpumpî and a
ìhook,î were developed and applied to the treemap
to support AHP sensitivity analysis. The problem of construction
site selection is considered in this video. Apart from its traditional
use for problem/ information space visualization, the treemap
also serves as a potent visual tool for "what if" type
Visualization, treemap, analytic hierarchy process, AHP, decision
* Current address: Kansai C&C Research Lab., NEC Corporation,
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Treemaps graphically represent hierarchical information via a
two-dimensional rectangular map, providing compact visual representations
of complex data spaces through both area and color [2-5]. Their
efficiency for particular data searching tasks has been tested
through controlled studies [4,5] with primary benefits seen for
two types of tasks: location of outliers in mass hierarchies and
identification of cause-effect relationships within hierarchies.
By extending the treemap into a "read/write" graphic
through direct manipulation tools, the user is given the capability
to massage the data and perform the outlier and cause-effect tasks
much more effectively. Analytic Hierarchy Process (AHP) , given
its decision tree hierarchy and inherent need for large-scale
data visualization and user manipulation, is an appropriate choice
for treemap visualization.
AHP was developed to promote improved decision-making for a specific
class of problems that involve prioritization of potential alternate
solutions through evaluation of a set of criteria elements. These
elements may be divided into sub-elements and so on, thus forming
a hierarchical decision tree. Once the hierarchical problem definition
has been established, these criteria are weighted individually
at every level relative to each other; prioritization of the alternate
solutions can then be obtained via evaluation of these weights.
The treemap can represent both hierarchical structure and each
elementsí quantitative information simultaneously in a
two-dimensional rectangular space; 100% of the designated screen
area is utilized. Application arenas for treemaps have included
computer directory browsing, stock market portfolio visualizations,
an NBA player statistical browser, and a US budget viewer.
Treemaps are generated using a straightforward algorithm known
as ìslice-and-dice.î The root node of a hierarchy
is represented by the entire screen area. For the root nodeís
children, the screen area is sliced (either horizontally or vertically)
to create smaller rectangles with area dependent upon the value
of a particular weighting attribute. Each node is then
processed recursively, with the direction of the slicing switched
by 90 degrees for each level.
Since the decision-making processes are represented by hierarchical
trees in AHP, these trees translate directly to the treemap visualization
method. Figure 1 is an example of a treemap generated with our
prototype AHP application. A base rectangle representing the goal
of decision-making is divided into small rectangular areas proportional
to their relative importances. Users can identify any criterion
by labels displayed in the offset areas (offset areas are also
helpful for users to recognize the hierarchical structure). The
hook and pump tools (upper right in Figure 1) enable users to
adjust the size of areas by pulling on a boundary or by pumping
up an area. Since areas represent preferences among the alternatives,
the users can quickly grasp the relative impact of each component
and understand which components most influence the outcome. On
the bottom of the display, a horizontal histogram shows the aggregate
result, and as users hook or pump areas the histogram changes
within a few hundred milliseconds. This dynamic approach enables
users to explore many alternatives in seconds as opposed the many
minutes required to input a fresh set of preferences using the
current keyboard entry approach. The treemap, which till now has
been used as a way of displaying large amounts of data, now becomes
a powerful input strategy.
A usability test was conducted with six business or management
majors who were already familiar with the AHP. They performed
five tasks and then rated the interface highly on all 12 criteria.
Improvements were suggested, but the basic concept was strongly
1. Saaty, T.L. The Analytic Hierarchy Process. McGraw-Hill, New York, 1980.
2. Shneiderman, B. Tree Visualization with Tree-maps: A 2-D space-filling approach. ACM Transactions on Graphics 11, 1 (Jan. 1992), pp. 92-99.
3. Turo, D. and Johnson, B. Improving the visualization with treemaps: Design issues and experimentation. Proceedings of Visualization ë92, IEEE Computer Society Press, 1992, pp. 124-131.
4. Turo, D. and Johnson, B. Improving the visualization with treemaps: Design issues and experimentation. Proceedings of Visualization ë92, IEEE Computer Society Press, 1992, pp. 124-131.
5. Turo, D., Enhancing treemap displays via distortion and animation: Algorithms and experimental evaluation, Unpublished Masters Thesis, Department of Computer Science, University of Maryland, 1993.
6. Asahi, T., Turo, D., and Shneiderman, B., Using treemaps to
visualize the Analytic Hierarchy Process, University of Maryland
Department of Computer Science Technical Report CS-TR-3293 (June
Figure 1: Screen design for treemap representation of Analytic Hierarchy Process
with user interface tools for adjusting the treemap.