Information Technology Reference
In-Depth Information
(a)
(f)
1
2
3
4
5
(b)
small
medium
big
1
2
3
4
5
(c)
12
3
4
5
6
(d)
(g)
1
2
7
6
3
5
4
(e)
small
medium
big
Figure 1.3
Different types of scale. (a) A linear scale with equally spaced calibration as
used in principal component analysis. (b) A linear scale with logarithmic calibration. (c) A
linear scale with irregular calibration. (d) A curvilinear scale with irregular calibration.
(e) A linear scale for an ordered categorical variable. (f) Linear regions for ordered
categorical variables (g) A categorical variable, colour, defined over convex regions.
this is an example of regular but unequally spaced calibration. In Figure 1.3(c) the
axis remains linear but the calibrations are irregularly spaced. In Figure 1.3(d) the axis
is nonlinear and calibrations are irregularly spaced; in principle, nonlinear axes could
have equally spaced calibrations or regularly space calibrations, but in practice such
combinations are unlikely. Figure 1.3(e) shows an ordered categorical variable,
size
, not
recorded numerically but only as
small
,
medium
and
big
. The calibration is indicated
as a set of correctly ordered markers on a linear axis, but this is shown as a dotted line
to indicate that intermediate markers are undefined (i.e. interpolation is not permitted).
In Figure 1.3(f) the ordered categorical variable
size
is represented by linear regions;
all samples in a region are associated with that level of
size
. Figure 1.3(g) shows an
unordered categorical variable,
colour
, with five levels:
blue
,
green
,
yellow
,
orange
and
red
. These levels label convex regions. In general, the levels of unordered categorical
variables may be represented by convex regions in many dimensions. Examples of these
calibrations occur throughout the topic.
1.2 Overview of the topic
The basic steps for constructing many asymmetric biplots are summarized in Figure 1.4.
Starting from a data matrix
X
, first we calculate a distance matrix
D
:
n
×
n
. The essence
