Information Technology Reference
In-Depth Information
X
6
a
c
5
2
3
4
4
5
3
6
d
7
b
8
Y
2
Figure 5.24
Nonlinear biplot with back-projection prediction biplot trajectories.
Details
In principle,
Nonlinbipl
will accept any allowable Euclidean embeddable distance
measure that is additive. Nearly all that is needed is to add to
Nonlinbipl
a one-line
specification of a typical term of the distance function. The following specifications serve
as examples of how this should be done for Pythagoras distance, square root of Manhattan
(5.5) and Clark distance (5.6):
{ if (dist == "Pythagoras") dist.expr <- function (xik, xjk)
{ (xik-xjk)^2 }
if (dist == "SqrtL1") dist.expr <- function (xik, xjk)
{ abs(xik-xjk) }
if (dist == "Clark") dist.expr <- function (xik, xjk)
{ ((xik-xjk)/(xik+xjk))^2 }
}
Nonlinbipl
then uses the above specification to calculate the matrix
D
to allow the
computations required by (5.7), (5.9), (5.13) and (5.16). In order to perform the integration
in (5.19) for the currently included distance functions, the derivative in (5.16) is first
symbolically expressed in terms of an R expression with the following function defined
within
Nonlinbipl
:
