Information Technology Reference
In-Depth Information
Ta b l e 3 . 2 0
Overall quality attained associated with Figure 3.34 biplot in all
dimensions.
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
1
2
3
4
5
6
7
8
9
10
11
12
13
14
37.8
59.8
74.9
82.7
89.7
94.6
97.5
98.6
99.4
99.7
99.9
100.0
100.0
100.0
The sample predictivity of the target is calculated as 0.46. This moderate value
indicates that the distance from the biplot space to the target in the full space is relatively
large. Since the biplot space is 'as close as possible' to the sample points, this suggests
that overall the sample points are not very close to the target.
3.8.3 Using axis predictivities in biplots
Axis predictivities can be used as a criterion for selecting axes to be shown in a predictive
PCA biplot. In the mail order catalogue data shown as a PCA biplot in Figure 2.8 there
are several axes with very low axis predictivity. In Figure 3.35 we again show the PCA
biplot of the scaled mail order catalogue data but we use argument
ax
of
PCAbipl
to
suppress plotting of all axes with predictivity less than 0.45. In addition, we specify
predictivity.print = TRUE
for including in the label of each axis its predictivity.
A PCA biplot can be rotated so that the axis with maximum predictivity is drawn in a
horizontal position by calling
PCAbipl
with argument
specify.xaxis = "maxpred"
.
If in this call the argument
select.origin
is set to TRUE then the origin of this biplot
can be interactively changed to any desired position. This is shown in Figure 3.36 for
the
Ocotea
data.
In Figure 3.37 we show how to carry out individual orthogonal parallel translation
of the biplot axes so that the biplot axes are moved to peripheral positions that do not
interfere with the sample points. This leads to a biplot with approximately orthogonal
predictive axes similar to conventional scatterplots. The function call to
PCAbipl
result-
ing in Figure 3.37 needs the settings
orthog.transy = c(-4.9, -4.2, -5.5, -4,
5.3, 5.5)
and
select.origin = FALSE
.
3.8.4 One-dimensional PCA biplots
As an example of a one-dimensional biplot we consider mining data from a copper
flotation plant. The complete data set of nearly 500 samples is described by Aldrich
et al.
(2004) and is available as
CopperFroth.data
in library
UBbipl
. In this section
we ignore the group structure but in Section 4.10 we will revisit
CopperFroth.data
by considering biplots that take into account predefined groups in the data.
One problem with one-dimensional biplots is that all sample points and all the biplot
axes appear on a single straight line.
PCAbipl
shifts all the biplot axes parallel to the line
containing the samples, as shown in Figure 3.38. The axes are calibrated in the usual way
to allow for predictions to be made. We illustrate this in Figure 3.38 for samples
s20
,
s50
and
s250
. Compare these graphically determined values with the algebraically computed
