Information Technology Reference
In-Depth Information
Figure 9.6
Principal axes projection for two dimensional generalized biplot.
from which it follows that
p
p
p
11
/
11
/
−
1
−
1
Z
k
=
1
(
I
−
n
)
D
k
(
I
−
n
)
Y
=
B
k
Y
=
Y
,
k
=
1
k
=
k
=
1
where
B
k
is the double-centred version of
D
k
. These are transition formulae, the first
equation giving the basic points for given coordinates
Y
and the second giving
Y
as a
sum of the basic points. Similar results occur for MCA which can be seen as special
case of this much more general formulation (see Gower and Hand (1996), for details).
For all variables we have
1
Z
k
0
and, in particular, for categorical variables,
Z
k
will have only
L
k
distinct values, so
1
Z
k
=
0
implies that the weighted mean of the
category points is at the centroids of the sample points.
=
9.6 Interpolation
Interpolation in the generalized biplot is achieved similarly to the method described
in Chapter 5 for the nonlinear biplot. Of course, a new numerical observation
x
∗
