Geoscience Reference
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l
Fig. 4.6
Mean modularity scores of 100 runs for different settings of l for the real-world data set
In order to compare the nonspatial characteristics of the clustering results and
of the PAS, their mean homogeneity with respect to the different attributes is
compared. The homogeneity of a cluster is calculated as the sample standard
deviation of the differences between the cluster's center and the data that is assigned
to it. Table 4.1 shows the mean homogeneity values of the attributes for the different
clusterings. Notably, the homogeneity for all attributes decreases with increasing
l . Furthermore, even though the PAS consists of double as much clusters as the
clustering for l D 13, its mean homogeneity is mostly equal or worse. However,
in contrast to the other clusterings, the PAS is perfectly spatially contiguous. The
clustering for l D 2 is nearly as spatially contiguous as the PAS, but it is less
homogeneous than the PAS with respect to the attributes 65older, black, hispanic,
and occup. However, for the majority of the attributes, the clustering for l
D
2 is
still more homogeneous than the PAS.
Philadelphia is one of the most segregated cities in the United States; even
the most affluent Blacks live in neighborhoods that are close to majority black
(Logan 2011 ). Hence, it can be expected that these neighborhoods emerge as distinct
clusters in the clustering results. Comparing Fig. 4.4 with Fig. 4.5 reveals that the
predominantly Black neighborhoods, especially in North Philadelphia, are mixed
with non-black neighborhoods or are separated by the outlines of the PAS (e.g.,
Sects. 7, 9, and 11 in Fig. 4.4 ). Also the clustering for l D 2 (compare Fig. 4.7
with Fig. 4.5 ) does not clearly identify the predominantly Black neighborhoods.
However, these neighborhoods are clearly outlined by cluster 3 of the clustering
for l
D 10 and cluster 5 of the clustering for l
D 13.
 
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