Information Technology Reference
In-Depth Information
FibL (0.79)
VesL (0.37)
1600
20
RayH
(0.65)
27
25
24
26
500
10
1400
11
22
23
14
19
21
15
VesD
(0.67)
16
17
13
18
150
400
12
9
400
30
8
1200
40
37
100
36
RayW
(0.75)
34
6
50
10
28
7
5
33
30
35
31
1
300
1000
32
3
4
Obul; n = 20
Oken; n = 7
Opor; n = 10
20
29
2
800
NumVes (0.48)
Figure 5.2
MDS biplot of the normalized
Ocotea
data. 'Regression predictivities' have
been added to the names of the biplot axes.
of (5.1) are then used for the MDS map of the points. Finally, biplot axes are constructed
using (5.3) and (5.4) of the regression method described above. The axes are calibrated
according to the procedure described in Chapter 2. The minimum value for the stress
(5.1) found in 250 random starts of the SMACOF algorithm was 1586.576. This was
achieved after 712 iterations. If we normalize the raw stress value by dividing by
1
D1
/
2
we obtain a value of 0.7327. We compute 'regression predictivities' using the formula
diag(
X
X
) and add these values to the names of the axes in Figure 5.2.
Note that, apart from the variable with the low axis predictivity (
Ve s L
), the MDS biplot
of Figure 5.2 looks remarkably similar to the PCA biplot in Figure 5.1.
Z
Z
)/
diag
(
5.3 Nonlinear biplots
There is one case where the effects of nonlinearity can be analysed and represented by
nonlinear biplot axes. This is when the distances in
D
can be generated as Pythagorean
distances by a set of
n
points in
n
−
1 dimensions. When this is so, the distances are
said to be
Euclidean embeddable
.
