Information Technology Reference
In-Depth Information
−
0.04
−
0.02
0
0.02
0.04
0.06
11
1sd
0.08
0.1
Figure 2.9
Calibrating a biplot axis in the case of normalized data. Biplot drawn by
plotting
(
U
)
2
versus
V
2
.
We now need the scaffolding coordinates of points on the biplot axis to be labelled
with the above 'nice' values. Therefore we have to express
markers.x
in terms of the
scaffolding using the transformation
>
markers.v <- (markers.x - mean(X[,1]))/sqrt(var(X[,1]))
Next, (2.10) is applied to the transformed markers,
markers.v
, to obtain the required
coordinates:
>
coords.horizontal <- (markers.v / sum(V[1,1:2]^2)) * V[1,1]
>
coords.vertical <- (markers.v / sum(V[1,1:2]^2)) * V[1,2]
The two vectors
coords.horizontal
and
coords.vertical
provide the coordinates
of the markers on the biplot axis to be labelled with the 'nice' values 0.00, 0.02, 0.04,
0.06, 0.08.
As an exercise, the reader can construct a biplot axis similar to the one in Figure 2.9
but equipped with a scale in terms of 5
+
log
(
X
Norm
)
.
Hints
: Firstly, calculate nice scale
values using
>
markers.x <- pretty(range(5+log(scale(X[,1]))), n = 5)
