Graphics Reference
In-Depth Information
partofthedatadisplaydefinitionanddescribeexactlytheamountofinformationthat
is to be visualized. he histogram of a quantitative variable, for example, is based on
the categorization model. his model is determined by a vector C
of
real values that segments the range of a variable A. For each segment the frequencies
of observations that fall into the category are counted and stored. he scale compo-
nent of the histogram model consists of the categorization vector C,theorderingπ
c
of the values in C (due to the ordered nature of real values only two orderings make
sense, ascending or descending, and the ascending one is the standard used for his-
togram representations), and the maximum number of counts for any bin. his also
implicitly assumesthat thevertical axisof the histogramstarts at
andshowsthe full
range ofvalues from
tothemaximumnumber ofcounts inacategory. Notationally,
the categorization model can be written as:
=(
C
,...,C
c
)
=
A
C
C
, C
,
C
, C
,...,
C
c
−
, C
c
;
[
]
(
]
(
]
)=
)
count
(
AC
count
(
A
i
)
,...,
count
(
A
i
i
C
A
i
C
i
C
c
−
<
A
i
C
c
s
X
=(
C, π
c
,max
(
count
(
AC
)))
.
Amodellinkforthisexamplecannowbeestablishedeitherviathesetofobservations
A
C or the scale s
X
. Linking scales for the above example of the categorization
operator yields three different cases: linking the categorization vector C,linkingthe
ordering of the categorization values, and linking the maximum count for one bin.
Assuming that the categorization operator model is represented by a histogram, the
third case basically links the scales used for the vertical axes of the histograms, and
the other two link the scales of the horizontal axes, in particular, the bin width and
the anchor point.
Linking histogram scales is implemented, for example, in Manet. In Fig.
.
two
histogram scales are linked. he plot to the right is the active plot that propagates its
scale to the one at the let. For the plot at the let also the frame size is adjusted. he
Figure
.
.
Two histograms with linked scales. Both histograms start with the same anchor point, have
thesamebinwidth,andusethesamescalingfortheverticalaxes.heplotontheright does not fully
extend to the upper border of the plot because the maximum number of counts for a bin is smaller than
the one for the let plot. Hence it becomes clear that in this instance, the let plot is the active plot.
Otherwise, the largest bins of the let plot would exceed the frame boundaries of the plot
