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Fig. 6.25
"Ideal" connections for the spiral dataset of Fig. 6.24a.
As can be seen in Fig. 6.24b, the first layer connections take no account
of the local structuring direction of the dataset. In Fig. 6.25 we present what
one usually thinks should be the "ideal" connections, reflecting the local
structuring directions of the data.
With classical distance measures, this behavior is not achieved. With an
entropic dissimilarity measure the connections will follow the local structure
of the dataset as we shall briefly see.
Example 6.7.
Figure 6.26 shows the first layer connections for the dataset
of Fig. 6.21, where one can see the difference between using a dissimilarity
matrix based on Euclidian distance (Fig. 6.26a) or based on the LEGClust
entropic measure (Fig. 6.26b). First layer connections, when using an entropic
measure, clearly follow an horizontal line
5
and, despite the fact that point
k
1
is the closest one, the stronger connection for point
Q
is the connection
between
Q
(11) and
P
(10), as expected and shown in Table 6.17.
(a)
(b)
Fig. 6.26 First layer connections using a dissimilarity matrix based on Euclidian
distance (a) and on entropic measure (b).
5
The first connections shown in Fig. 6.26a are horizontal because in case of ties
the algorithm chooses the first position of the tied points list. Points 2 and 8 are
at the same distance to point 1 but the algorithm chose point 2 because it is the
closest to point 1 in the list of points.
