Clustering Contextual Neural Gas: A New Approach for Spatial Planning and Analysis Tasks - Computational Approaches for Urban Environments - page 88

Tabl e 4. 1 Mean homogeneity of the attributes for different clusterings

l

D 2 l D 10 l D 13 PA S

pop 1,157.834 1,044.499 1,006.730 1,257.946

0-24 0.055 0.037 0.035 0.071

25-64 0.046 0.033 0.027 0.058

65older 0.041 0.032 0.026 0.026

white 0.122 0.103 0.092 0.184

black 0.119 0.101 0.090 0.090

asian 0.039 0.038 0.038 0.043

hispanic 0.040 0.037 0.033 0.033

avgHHSize 0.241 0.242 0.228 0.295

occup 0.043 0.043 0.040 0.400

renterOccup 0.112 0.113 0.106 0.106

4.5 Conclusion and Further Work

This study presented a new method which combines CNG, topology learning,
and graph clustering to outline homogeneous regions, taking into account spatial
dependence. The proposed method does not require prior knowledge about the
actual number of clusters in the data, because it utilizes the modularity score when
clustering the learned topology. Two experiments, one using a synthetic data set
and another one using a demographic data set of Philadelphia, PA confirmed the
usefulness of the method for delineating homogeneous clusters. Because of this
property, the proposed method is in particular well suited for spatial analysis and
planning tasks.
There are some considerations that must be taken into account when applying
the proposed method. The CNG algorithm uses a nonlocal update scheme, which
prevents it from being easily stuck in local optima. However, repeated runs of the
experiments have shown that the final positions of the neurons and consequently
the learned topology can differ slightly with each run. This difference can possibly
affect the clustering of the topology.
The results of the proposed method depend also on its parametrization. The
method combines multiple algorithms, and each one's parameter setting can crit-
ically affect the final results. It is unclear how to choose the parameters so that
the final results meet the analyst's requirements. In particular, the choice of the
parameter l , which controls the degree of spatial dependence incorporated into the
clustering, has a significant impact on the homogeneity and spatial contiguity of the
clustering. However, although the chance that the resulting clusters are contiguous
increases with high values of l , there is no guarantee that the clusters will ever be
spatially contiguous.
In this study, the proposed method utilizes a modified version of the CHL
algorithm to learn a topology from CNG, but other approaches might also be
reasonable. For example, instead of connecting the first and second neuron of the