Information Technology Reference
In-Depth Information
Although the interpolation axes provide us with a method of graphical interpolation,
the highly nonlinear nature of the axes for Clark's distance makes the use of these axes
quite difficult in practice. As mentioned before, it is intuitive to use axes to read off
values and therefore we recommend that these biplots are fitted with prediction biplot
axes. In the following section we do provide an example of the vector-sum interpolation
method with a different data set.
5.7.3 Interpolating a new point into a nonlinear biplot
To illustrate the application of the vector-sum method for interpolating a new sample
into a nonlinear biplot we consider the soils data described by Gower and Harding
(1988). This data set consists of 12 trace elements (in the logarithm of parts per million)
measured at 15 sites in Glamorganshire. Interpolative biplots of this data set are shown
in Figure 5.27. The function calls for constructing these biplots are:
Nonlinbipl(soils.data, ax.type = "interpolative",
dist = "SqrtL1")
Nonlinbipl(soils.data, ax.type = "interpolative",
dist = "SqrtL1", zoomval = 0.1)
Nonlinbipl(soils.data, ax.type = "interpolative",
dist = "SqrtL1", ax = c(5,7,9,12), scale.axes = TRUE)
Nonlinbipl(soils.data, ax.type = "interpolative", dist = "SqrtL1",
ax = c(5,7,9,12), scale.axes = TRUE, zoomval = 0.15)
We illustrate the vector-sum method for interpolating a new point into a nonlinear
biplot in Figure 5.28. Notice that the blue arrow originates in the point of concurrency, O,
and not in the position of the grey cross. This process involves the R code given below.
Note that the coordinates of the point of concurrency are returned by
Nonlinbipl
.These
coordinates are assigned to the argument
from
in the call to
vectorsum.interp
.Note
also that the argument
p
in the latter call is assigned the value 1 and not 4, since the
factor of 4 has already been included in the construction of the biplot.
> out <- Nonlinbipl(soils.data, ax.type = "interpolative",
dist = "SqrtL1", scale.axes = TRUE, ax = c(5,7,9,12))
> draw.arrow(col = "green", angle = 30, length = 0.3, lwd = 2.5)
#(four times)
> vectorsum.interp(vertex.points = 4, p = 1, from = out$O.co,
pch.centroid = "", col.centroid = "blue",
pch.interp = "", border = "red", length = 0.25, angle = 30)
> draw.text(string = "P", cex = 1.5, col = "blue")
5.7.4 Nonlinear predictive biplot with Clark's distance
From the distance function
x
ik
−
x
jk
x
ik
+
x
jk
2
p
d
ij
=
k
=
1
