Graphics Reference
In-Depth Information
Factorial Plans and Dendrograms:
the Challenge for Visualization
4.7
hesynergy between computergraphics andvisual perceptionpermitsone todesign
statistical tools for the interactive visual exploration of statistical data (Unwin et al.,
).Data visualization is becoming an increasingly important tool in scientific re-
search. Nowadays, the availability of high-performance computing has definitively
changed the role of statistical graphics: they are not only a static view of the past but
also a dynamic partner and a guide to the future (Wainer and Velleman,
). Mo-
tivated readers are encouraged to visit the Web site managed by Friendly and Denis
(Visited on Oct.
),whichpresents a historical overview of advances in statistical
graphics and most of the widely used data representations (Friendly,
).
Based on psychometric experiments andanatomical considerations, Wegman has
pointed out the human eye's capabilities in visually processing data. More specifi-
cally, Wegman's (
) “recipe” is based on three ingredients: a geometric support,
a projecting function of original data into a suitable graphical space, and interaction
tools. Wegman's analysis strategy is based on a system of parallel coordinates as visu-
alization support (Inselberg,
),a high-dimensional rotation algorithm (Asimov,
; Cook et al.,
; Buja et al.,
), and saturation brushing and color design
(Wegman,
).
Linking original data with graphical representation allows the user to have an in-
novative viewofthedata:byquerying objects onthegraph,theuserdirectlyinteracts
with the data and with the analysis parameters.
According to Wegman's recipe, but using different ingredients, we propose an-
other way to handle data visualization in a statistical context; we like to consider our
approach as a little more statistical and a little less computational.
Parallel-coordinate systems are replaced with Cartesian systems (where axes take
on a very special statistical meaning because they are factors);the similarity between
statistical units in R
p
is evaluated in terms of distances by the use of dendrograms;
classical brushing and other more or less classical interactive tools that are presented
below ensure a smooth man-machine interaction.
here are many sotware programs and packages that allow the user to interact
with data: users can select groups of units and change the appearance of the plot.
With respect to classical interactions, the approach proposed by Wegman allows the
user to affect visualization support by changing the analysis parameters.
Inother words,the data displaychanges, either whentherearechanges inthedata
(adding or deleting variables or units) orwhen the analysis parameters are modified.
In both cases the visualization satisfies a (statistical) criterion.
Interaction capabilities in the visual data exploration phase complete the interac-
tivity analysis toolkit. Results are presented in some visual forms providing insight
into the data, drawing conclusions, and interacting with the data.
Ausefultask-oriented criterion forpursuinganexploratory approachisthe visual
information-seeking mantra (Shneiderman,
;Cardetal.,
).hebasicstepsfor
this kind of approach are listed in order of execution below:
