Information Technology Reference
In-Depth Information
mu = 4
mu = 3
mu = 2
a
c
O
d
b
Figure 5.18
Orthogonal projection of point O onto each of the intersection spaces for
µ
=
2, 3, 4.
everything necessary for prediction or interpolation. The circular prediction of Figure 5.20
is illustrated in Figure 5.21. The point P is predicted by constructing the circle with
diameter OP and the value '2' is predicted for original variable
Y
. This circle also gives
the predicted value for original variable
X
as '5.6'.
In Section 5.4 we discuss how the user can perform circular prediction with the
function
Nonlinbipl
.
5.4.2.3 Back-projection
A third possibility for obtaining prediction biplot trajectories is based on finding the
point on
L
∩
N
, nearest to the marker
µ
on the embedded original variable axis,
that is, utilizing the back-projection mechanism we discussed when deriving the linear
prediction biplot axes for PCA and CVA biplots. The nearest point is found by projecting
the embedded axis
(
ξ
k
(µ)
,
ξ
k
,
m
+
1
(µ))
onto
L
∩
N
(
µ)
. Similar to Figure 5.16, we
translate the intersection space to the origin and project
ξ
k
(µ)
0
0
ξ
k
,
m
+
1
(µ)
+
t
(µ)
l
2
(µ)
,
−
0
...
0
)
to obtain
onto
(
l
2
(µ)
−
l
1
(µ)
l
2
(µ)ξ
k
,1
(µ)
−
l
1
(µ)
l
2
(µ)ξ
k
,2
(µ)
+
l
1
(µ)
t
(µ)
l
1
(µ)
t
(µ)
l
2
(µ)
−
l
1
(µ)
l
2
(µ)ξ
k
,1
(µ)
+
l
1
(µ)ξ
k
,2
(µ)
−
and, after translating back with
t
(µ)/
l
2
(µ)
units in the second direction, the marker
µ
is
l
(µ))
ξ
k
,
r
(µ)
+
given by
(
I
r
−
l
(µ)
t
(µ)
l
(µ)
.
