Information Technology Reference
In-Depth Information
The above code produces Figure 2.10 by changing
USigma
and
V
to
USigmaHalf
and
VSigmaHalf,
respectively, by setting
>
USigmaHalf <- X.scaled.svd$u %*% diag(sqrt(X.scaled.svd$d))[,1:2]
*lambda
>
VSigmaHalf <- X.scaled.svd$v %*% diag(sqrt(X.scaled.svd$d))[,1:2]
/lambda
together with the changes
add = c(2,6)
,
exp.factor = 1.2
and
shift = 0.5
.
Note that in Figure 2.10 the same predicted value for
11
is obtained as in Figure 2.9 but
the red arrow is lengthened to extend beyond the one standard deviation marker.
Scaling (lambda and sigma), rotation and axis shifts (Section 2.4) are all devices that
can be used to enhance the visual quality of the display. These devices are best used
interactively after the initial construction of a biplot, and we have taken advantage of
them throughout the topic to edit the final biplot.
The above calibration procedure and R code are incorporated in several functions in
our library
UBbipl
.
2.4 Refining the biplot display
Figure 2.5 can be improved. In conventional scatterplots there is some freedom, which
can be used to advantage, in positioning the axes. This freedom carries over to biplots.
6
5
4
3
2
(a, b)
1
0
6
5
4
3
2
1
0
Figure 2.11
Orthogonal parallel translation. The upper axis is scaled in the same way
as the lower parallel axis and equal-valued scale markers are on lines orthogonal to both
axes. Projection onto either scale delivers the same result. Orthogonal axes through an
origin O are shown as dotted lines; these are used solely for plotting purposes and would
be deleted in any biplot. A point (a, b) relative to these plotting axes is shown.
