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C l us te r 1
Cluster 2
Clus t er 3
Cluster 4
Cluster 5
0.0
0.2
0.4
0.6
0.8
1.0
x
Fig. 4.1 Synthetic data set. The attribute values of the data points of cluster 1 are 0, the attribute
values of the other clusters 1
to fail to correctly identify the spatial clusters. Additionally, the clustering of the
data set becomes much more difficult, if the actual number of clusters is not known
beforehand.
The results for the synthetic data set depend on parameter l .Ifl is set too low,
differences in the observations' attribute values are neglected and the resulting graph
therefore exhibits no distinct clusters. Otherwise, if l is set too high, the clustering
does not consider the spatial configuration of the data set, resulting in a graph with
only two clusters that represent the data points with the values 0 and 1.However,
because of the clearly defined cluster structure of the data set, it can be assumed that
l is chosen correctly, when the modularity of the resulting graph is maximal.
Figure 4.2 plots the mean modularity scores of 100 runs for different settings of
l .Forl>16, the mean modularity score is basically constant and at its minimum.
Hence, for large l values, the spatial configuration of the data set has no significant
effect on the clustering of the resulting graph. Furthermore, the plot shows multiple
local maxima; the highest mean modularity score (0:724) is achieved with l D 7.
Figure 4.3 exemplarily shows the graph resulting from a CNG that has been
trained with l D 7 and its clustering, indicated by the colored vertices. At first, it is
notable that the depicted graph consists of only 17 vertices, although CNG consists
of 25 neurons. Generally, the number of neurons which map no data at all increases
rapidly if l is increased, because of the simple clustering structure of the data set.
The large number of vertices present indicates that the incorporated degree of spatial
dependence is significant. Moreover, the figure reveals that the MLMO algorithm
 
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