Information Technology Reference
In-Depth Information
Figure
9.3
Pseudo-sample
interpolation
for
variable height
where
τ = 170
and
τ = 172.
and a set of L k CLPs for a categorical variable. Gower (1992) shows that for a PCO
for continuous variables, with a wide class of distance measures in common use, this
choice of pseudo-samples effectively leads to the nonlinear biplot. The only difference
is that the trajectory is parallel to the nonlinear biplot trajectory (see orthogonal parallel
translation: Section 2.4). We note that, unlike nonlinear biplots, τ = 0 is not common
to all the continuous trajectories. In Figure 9.3 the pseudo-samples for variable k = 1,
height , are interpolated where τ = 170 and τ = 172. As an example, the pseudo-samples
for τ = 170 are given by: (170, blue); (170, brown); (170, green); (170, brown).
Since the second and fourth pseudo-samples are identical, their interpolated represen-
tations are at exactly the same point. The centroid of the four interpolated pseudo-samples
is shown as a green sphere.
As explained above, when the assumption of additive distance is valid the biplot
trajectory can be calculated by using the distance between the centroid of the pseudo-
samples and the original samples. Define the matrix
D 11
D 12
D =
(9.9)
D 12
D 22
with D 11 containing ddistances between the samples, D 22 containing ddistances between
the pseudo-samples and D 12 containing ddistances between the i th sample point and the
j th pseudo-sample.
Search WWH ::




Custom Search