Graphics Reference
In-Depth Information
multivariate procedures like outlier detection, clustering, or classification in a highly
multivariate context.
Although parallel coordinate plots can handle many variables at a time, their ren-
dering limits are reached very soon when plotting more than only a few hundreds of
lines. his is due to overplotting, which is far worse than with scatterplots, since par-
allel coordinate plots only use one dimension to plot the information and the glyph
used (a line) prints far more ink than the glyphs in a scatterplot (points). One solu-
tion to coping with overplotting is touse α-blending. When α-blending isused,each
polygon is plotted with only α% opacity, i.e.,
% transparency. With smaller α
values, areas of high line density are more visible and hence are better contrasted to
areas with a small density.
Figures
.
to
.
use α-blending to make the plots better readable or to empha-
size the highlighted cases. In the cars data set we only look at fewer than
cases,
and one can imagine how severe the overplotting will get once thousands of poly-
lines are plotted.
Figures
.
and
.
show two examples of how useful α-blending can be. he
so-called “Pollen” data used in Fig.
.
come from an ASA data competition in the
late
s. he data are completely artificial and have the word “E U R E K A” woven
into the center of the simulated normal distributions. he almost
cases in five
dimensions produceasolid black band without any α-blendingapplied.Goingdown
to an alpha value of as little as
.
will reveal a more solid thin line in the center of
the data. Zooming in on these cases will find the word “Eureka,” which just increases
the simulated density in the center enough to be visible.
hedata in Fig.
.
are real data fromForina et al.(
)on the fatty acid content
of Italian olive oil samples from nine regions. he three graphics show the same plot
of all eight fatty acids with α-values of
.
,
.
, and
.
. Depending on the amount
of α-blending applied,the group structure of some of the nine regions ismoreor less
visible.
Note that it is hard to give general advice on how much α-blending should be
applied because the rendering system and the actual size of the plot may change its
(
−
α
)
Figure
.
.
he “Pollen” data with α
(let)andα
.
(right)
=
=
