Clustering Contextual Neural Gas: A New Approach for Spatial Planning and Analysis Tasks - Computational Approaches for Urban Environments - page 83

identified the five clusters of the synthetic data set. It is notable that the middle
cluster consists of more vertices than the other clusters, even though the middle
cluster consists of the same number of data points as the clusters in the corner. The
reason for this is that, because of the low value of the l -parameter, the distribution
of the CNG's neurons depends heavily on the spatial distribution of observations.
Hence, since the spatial extent of the middle cluster is four times that of the clusters
in the corners, it is mapped by more neurons.
Finally, it can be seen that three of the graph's clusters in the corners are
connected, which is likely due to the small distance between them. Because the
MLMO algorithm has taken the weighting of the connections into account, the
corner clusters are correctly distinguished.

4.4.2 Practical Application

To evaluate the practical applicability of the proposed method, it is used for
delineating homogeneous regions in the city of Philadelphia, Pennsylvania. The city
is situated in the northeastern United States along the Delaware and Schuylkill rivers
and consists of an area of approximately 369 km 2 . Philadelphia is currently the fifth
largest city in the United States with an estimated population in 2012 of 1.5 million
people. Philadelphia is the economic and cultural center of the Delaware Valley,
the sixth largest metropolitan area of the United States. The city is of particular
interest because it has experienced dramatic changes in its ethnic and racial makeup
in the last two decades (The Philadelphia Research Initiative 2011 ). Hence, dynamic
approaches to outline homogeneous regions are essential in this context. However,
the validation of the results is difficult because there is no correct solution to the
problem in a formal sense. The results of the proposed method are evaluated in
this experiment by comparing them with the planning analysis sections (PAS) of
the Philadelphia City Planning Commission (PCPC; Philadelphia City Planning
Commission 2004 ) and linking them to existing demographic knowledge. Each
section of the PAS contains a number of census tracts that roughly correspond to
general socioeconomic divisions existing within the city (Wolfgang et al. 1987 ).
Even though the PAS were designed for administrative purposes decades ago, they
are still currently used for planning and analysis tasks (e.g., Pearsall and Christman
2012 ). Figure 4.4 shows the 12 regions of the PAS.
The experiment uses tract-level data about ethnicity, race, age, housing, and
households in Philadelphia from the 2010 US Census (see Fig. 4.5 ). Tracts without
a significant population are removed from the data set and all attributes are
standardized to zero mean and unit variance to make them comparable. Overall,
the study site consists of 380 census tracts.
Similar to the previous experiment, it is unclear how much spatial dependence
should be incorporated into the CNG's learning process to obtain reasonable results.
Figure 4.6 shows the mean modularity scores of 100 runs for different settings of l .