Knowledge Discovery in Spatial Planning Data: A Concept for Cluster Understanding - Computational Approaches for Urban Environments - page 62

350

300

250

200

150

100

50

0

WC6 WC5 WC4 WC3 WC7 WC1 WC8 WC2

Ward Cluster Number for Data Points

Fig. 3.13 Ward clustering of the UD data

Tabl e 3. 2 Comparison of two different cluster partitions (own source)

U-matrix cluster

Ward cl ust er UC1 UC2 UC3 UC4 UC5 UC6 UC7 UC8 UC9

WC1 15 0 0 1 0 0 0 1 0

WC2 10 15 0 0 0 1 0 0 0

WC3 0 7 15 0 0 1 0 0 0

WC4 0 0 0 6 0 0 0 0 0

WC5 1 0 0 2 7 0 0 0 0

WC6 0 4 0 0 0 5 3 0 2

WC7 4 3 0 0 1 0 0 0 0

WC8 5 1 0 0 0 0 0 1 0

point is at the center of a cluster. Zero or negative values indicate that this data point
is on the periphery of the cluster or may even belong to a different cluster. However,
it is very important to bear in mind that the classical silhouette values assume a
hypersphere as the shape of the cluster.
The silhouette plot of Fig. 3.14 shows that all clusters, apart from numbers
UC2 and UC6, can be well modeled as hyperspheres. Some points in cluster UC1
may be outliers. The data points with the largest silhouette values can be used as
good representatives for each cluster. The table in Appendix 2 contains a list of
cluster representatives determined in this way. The process of knowledge generation
produces a clear semantic for each cluster.