Information Technology Reference
In-Depth Information
Figure 3.3
Three-dimensional representation of data from Table 3.3.
However, the figure resulting from the call to
PCAbipl
will differ in two important
respects from Figure 3.7: there will be three biplot axes (unless their printing is suppressed
by using the argument
ax = NULL
; printing of the scaffolding axes (V
1
and V
2
together
with their calibrations) is always suppressed.
3.2.2 Interpolation biplot axes
However, the scatter diagram in Figure 3.7 is not a biplot since it only contains informa-
tion on the sample points. No information is visible on the variables
X
,
Y
and
Z
from
Table 3.3. To add information on the variables in Figure 3.7, biplot axes are added to
the display. Interpolation axes are used to interpolate (new) sample points. Any (new)
sample
x
∗
:
p
×
1 can be interpolated by orthogonal projection onto the biplot space
L
using (3.4) to give
z
∗
=
x
∗
V
r
. In order to construct interpolation biplot axes, note that
p
p
x
k
e
k
and
z
∗
=
x
∗
V
r
=
x
k
e
k
V
r
,
x
=
(3.6)
k
=
1
k
=
1
so that the interpolant
z
∗
is obtained as the weighted sum of the orthogonal projections
onto
L
of the unit points
(
e
k
)
of the Cartesian axes.
