Graphics Reference
In-Depth Information
Correlation-driven
7.6.1
Many researchers have proposed using correlation and other similarity measures
to order dimensions for improved visualization. Bertin's reorderable matrix (Bertin,
) showed that by rearranging the rows and columns of a tabular display, groups
of related records and dimensions could be exposed. Ankerst et al. (
) used cross-
correlation and a heuristic search algorithm to rearrange dimensions for improved
interpretability. Friendly and Kwan (
) introduced the notion of effect ordering,
where an ordering of graphical objects or their attributes would be decided based on
the effect or trend that a viewer seeks to expose. In particular, they showed that by
ordering the dimensions of a star glyph based on their angles in a biplot (basically
each dimension is represented by a line whose angle is controlled by the first two
eigenvectors), related dimensions would get grouped together. his is related to the
method reported by Borg and Staufenbiel (
), where they compared traditional
snow flake and star glyphs with what they called factorial suns, which display each
data point using the dimension orientations generated via the first two eigenvectors
rather than uniformly spacedangles. heirexperiments showedsignificant improve-
ment by naive users in interpreting data sets.
Symmetry-driven
7.6.2
Gestalt principles indicate we have a preference for simple shapes, and we are good
at seeing and remembering symmetry. In Peng et al.(
),the shapes of star glyphs
resulting from using different dimension orders were evaluated for two attributes:
monotonicity(thedirectionofchangeisconstant) andsymmetry(similarraylengths
on opposite sides of the glyph). he ordering that maximized the number of simple
and symmetric shapes was chosen as the best. User studies showed a strong prefer-
ence for visualizations using the ordering optimized in this fashion. We conjecture
that simple shapes are easier to recognize and facilitate the detection of minor shape
variations; for example, shapes with only a small number of concavities and con-
vexities might require less effort to visually process than shapes with many features.
Also, if most shapes are simple, it is much more apparent which records correspond
to outliers. More extensive formal evaluations are needed to validate these conjec-
tures, however. See Fig.
.
for an example.
Data-driven
7.6.3
Another option istobase the orderofthe dimensions onthe values of asingle record
(base), using an ascending or descending sorting of the values to specify the global
dimension order. his can allow users to see similarities and differences between the
base record and all other records. It is especially good for time-series data sets to
show the evolution of dimensions and their relationships over time. For example,
sorting the exchange rates of ten countries with the USA by their relative values in
the first year of the time series exposes a number of interesting trends, anomalies,
and periods of relative stability and instability (Fig.
.
). In fact, the original order is
nearly reversed at a point later in the time series (not shown).
