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In-Depth Information
see the default min-max scaling. Except forsome local groups, not much can beseen
from this plot. he middle plot shows the common scaling option for the same data.
Now the times are comparable, but due to the differences in absolute time needed
for a short time trial and a hard mountain stage, the spread between the first and the
last cyclist is almost invisible for most of the stages. Again, except for some outliers,
thereishardlyanything toseeinthisrepresentation. helowerplotinFig.
.
shows
the same data as the upper two plots, but now each axis is aligned at its median (the
median has the nice interpretation of capturing the time of the peloton). Note that
the axes still have the same scale, i.e., time differences are still comparable, but now
are aligned at the individual medians. his display option clearly reveals the most
information.
For a better description of the race as a whole, it is sensible to look at the cumula-
tive times instead of the stage times. Figure
.
,let, shows a parallel coordinate plot
for the cumulative times for each of the
cyclists who completed the tour for the
corresponding stage. he scaling is the typical default scale usually found in parallel
coordinate plots, i.e., individually scaled between minimum and maximum of each
axis. All drivers of the team “Discovery Channel” are selected. Although this scaling
option gives the highest resolution for these data, it is desirable to have a common
scale for all axes. A simple common scale won't do the trick here, as the cumulative
times keep growing, dwarfing the information of the early stages. Figure
.
, right,
usesacommon scale, butadditionally each axis isaligned at the median ofeach vari-
able. (Time differences at early stages are not very interesting for the course of the
race). Figure
.
, right, now shows nicely how the field spreads from stage to stage
and how the mountain stages (e.g., stages
to
are stages in the Alps) spread the
field far more than flat stages. he drivers of the team “Discovery Channel” are also
selected in this plot, showing how the team was separated during the course of the
race, although most of the cyclists remained in good positions, supporting the later
winner of the race.
he development of the race can be compared in Fig.
.
, where the plot from
Fig.
.
, right, is shown along with two profile plots. he upper profile plot shows
the cumulative category of the stage, which is the sum of
minus the category of
a mountain in the stage. he peaks starting at stages
and
nicely indicate the
mountain stages in the Pyrenees and the Alps. he lower profile plot gives the av-
erage speed of the winner of each stage. Obviously both profiles are negatively cor-
related.
Wrap-up
6.4.4
Parallel coordinate plots are not very useful “out of the box,” i.e., without features
like α-blending and scaling options. he examples used in this chapter show how
valuable these additions are in order to get a sensible insight into high-dimensional
continuous data.Highlightingsubgroupscangiveadditionalunderstandingofgroup
structures and outliers.
