Knowledge Discovery in Spatial Planning Data: A Concept for Cluster Understanding - Computational Approaches for Urban Environments - page 65

Tabl e 3. 3 Performance of
the generated rules (own
source)

U-matrix cluster

Rules UC1 UC2 UC3 UC4 UC5 UC6 UC7

R1 35 4 0 0 1 0 0

R2 0 23 2 1 0 0 0

R3 0 0 12 0 0 0 0

R4 0 1 0 8 0 2 0

R5 0 0 0 0 7 0 0

R6 0 0 1 0 0 3 0

R7 0 2 0 0 0 2 3

3.3.7.1 Rediscovering Known Structures

If the procedures above are applied correctly to a data set, it should be possible to
rediscover structures which are already known. For example, the spatial monitoring
system of the Federal Institute for Research on Building, Urban Affairs and
Spatial Development (Federal Institute for Research on Building, Urban Affairs and
Spatial Development 2013 ) captures the attribute geographical position (German:
räumliche Lage), of which there are four types: highly peripheral, peripheral,
central, and highly central . The BBSR spatial typology classifies 51 % of the UD
data as highly central . The U-matrix cluster UC1 contains 35 data points, of which
18 (51 %) should, statistically speaking, belong to the class highly central . In fact 31
of the 35 urban districts in Cluster UC1 are labeled highly central (i.e., 89 %). An
urn model can be used to calculate the probability of Cluster UC1 containing at least
31 highly central districts by pure chance (p-value). Applying the hypergeometric
distribution (Rice 2007 ,p. 42ff.), we calculate a p-value of 2.8441*10-9. Thus, it
can be safely assumed that Cluster UC1 largely consists of highly central districts.
The city of Leverkusen was found to be the most representative urban district for
this cluster. The generated rule for Cluster UC1 is as follows:

UD data belongs to Cluster UC1, if
log . SealedSurfaces / 48:3179 and
log . OpenSpaceMeshSize / 72:6255 and
log . BuildingArea / < 65:4549

This enables a possible characterization of Cluster UC1: “ highly central districts
with a large proportion of sealed surfaces, substantial fragmentation, and dense
building areas ”. In summary, Cluster UC1 basically coincides with the known type
of the prior classification (Federal Institute for Research on Building, Urban Affairs
and Spatial Development 2013 ) highly central district. The proposed clustering has
defined a particular subset of this type of urban district. This can eventually indicate
paths for further research into these urban districts, for example, regarding effective
land usage, ecological impacts of soil sealing, and fragmentation of the urban
area.