**Roth,S., Mattis,J.**

Roth and Mattis (1990), in their SAGE system, extend Mackinlay's work (APT) in another way, adding more semantic description to the data and their relationships. SAGE is also based on the generate-and-test paradigm. It uses numerous variations and syntheses of 2-D static displays found in business and statistical graphics packages (e.g. bar and and plot charts, node-link graphs, gauges, techniques using shape, color or size, tables). The types of information with which this system is concerned are the relations among data values contained in relational database or frame.based representations.

The system uses several criteria by which it judges the relevance of different data characteristics. To choose an appropriate graphical technique SAGE uses several characteristics of a set which are Set-Ordering, Coordinates Vs. Amounts, Domain of Membership.

**Set-Ordering**. The nature of ordering relationship among a data set's elements is
the predominant criteria used in APT and one criteria in SAGE for choosing graphical
techniques. An ordering technique can be characterized as either quantitative, ordinal or
nominal.

**Coordinates Vs. Amounts**. SAGE can recognize that elements of ordered sets are
coordinates if each element specifies a point or location temporally, spatially, or
otherwise (e.g. calender-date, latitude). In contrast, amounts are not embedded in
particular frames of reference (e.g.number of days, weight).

**Domain of Membership**. SAGE's characterization goes beyond APT's by recognizing that
sets can belong to the different domains of time, space temperature, or mass. This
information helps to preserve subtle stylistic conventions, such as using a horizontal
axis for time coordinates and a vertical axis to temperature.

For SAGE three properties are defined which describe the way relations made from
elements of one set to another:

**Relational Coverage**. This characteristic describes whether every element of a set
can be mapped to at least one element of another.

**Cardinality**. This characteristic expresses the number of elements of a set to which
a relation can map from an element of another set.

**Uniqueness**. This characteristic refers to whether a relation maps to a unique
value(s) for each element of a set.

**Algebraic Dependencies**. Algebraic dependencies among database elements suggest
another dimension which can affect presentation design. Dependencies can occur among
attributes (relations) or among values within data sets. For example, an organizational
database may contain three relations mapping departments to dollar-amounts:
materials-costs, labor-costs, and total-costs, where total-costs= materials-costs +
labor-costs.

One of the most important issues for graphical design not addressed in APT is the role
of an application or user's goals in viewing data. Differences in goals can greatly alter
the effectiveness of graphical techniques or their combinations. A user's immediate goal
may determine the connection of different relations and thereby affect how they should be
integrated in the presentation. SAGE uses a technique of segmenting the total presentation
request into sub-requests to coordinate text and graphics displays by converting a topic
outline prepared by a discourse processor into a serial list of sub-requests. This
indicates to the graphics system that information expressed in contiguous portions of the
text should be considered more related, and therefore displayed together.

More generally, this characteristic provides a vehicle for expressing two, often
competing, informational goals: the need to express as much information as possible and
the need to selected partitions of sets or relations to be easily and cohesively viewed.

*Last modified on March 29, 1999, G. Scott Owen, owen@siggraph.org*

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