Information Technology Reference
In-Depth Information
45
50
55
60
65
70
75
LGAN
Figure 2.31
Scatterplot (biplot) of variables
LTN
and
LGAN
of the head dimensions
data set described by Flury (1988).
2.9.1 Spanning ellipse
Constructing an ellipse surrounding chosen observations is a simple method for enclosing
the data region. A spanning ellipse is defined as the smallest ellipse that covers all the
objects. An algorithm for constructing such an ellipse is provided by Titterington (1976)
and Silvey
et al
. (1978). The function
clusplot
of Pison
et al
. (1999) for drawing
ellipses encircling clusters found in a cluster analysis incorporates the Titterington algo-
rithm. This function is available in the R package
cluster
.The
clusplot
function is
slightly modified into the function
MinSpanEllipse
included in
UBbipl
for enclosing
the points in a two-dimensional scatterplot with a minimum spanning ellipse. Figure 2.32
shows a minimum spanning ellipse enclosing the scatterplot of the head dimensions data.
This figure is a result of using the code
> library(cluster)
> MinSpanEllipse(Headdimensions.data[,5:6], asp = 1,
clus = rep(1,259), col.p = "blue", col.clus = "red",
pch.points = 16)
Perusal of Figure 2.32 shows the observations roughly to fall between 45 and 75 for
LGAN
and between 105 and 135 for
LTN
. The shape of the spanning ellipse also
suggests some degree of positive relationship between these variables.
