Information Technology Reference
In-Depth Information
Figure 9.7
Generalized interpolative biplot in two-dimensional space.
must be scaled in the same way as were the original variables. The vector
d
n
+
1
is
calculated with the chosen Euclidean embeddable distance measures, for example those
described in Section 9.2. For a categorical variable, the matrix
G
can be appended with
an (
n
+
1)th row denoting the category levels for the new sample
x
∗
.Forinstance,
when using Pythagorean distance and the EMC the
i
th element in the vector
d
n
+
1
is
obtained by
p
1
2
d
n
+
1,
i
f
k
(
x
ik
,
x
k
)
−
=
k
=
1
−
0
1
.
p
(
1
)
p
L
k
1
1
2
I
(
g
(
k
)
=
g
∗
(
k
)
2
(
x
ik
−
x
k
)
2
=
1
−
+
)
ih
n
+
1,
h
k
=
k
=
p
(
1
)
+
1
h
=
1
Several new samples can be interpolated by repeated use of this method, forming a new
matrix
G
∗
:
m
L
for the
m
new samples, with each row corresponding to a sample and
the columns corresponding to the category levels similar to the matrix
G
. Combining
G
×
