Clustering Contextual Neural Gas: A New Approach for Spatial Planning and Analysis Tasks - Computational Approaches for Urban Environments - page 77

The proposed method is also closely related to the approach by Costa and
Oliveira ( 2007 ). In their approach, they train a growing neural gas (GNG; Fritzke
1995 ) to obtain a topology. The main differences between the basic NG and the
GNG algorithm are that the GNG does not require to specify the number of neurons
beforehand and that it forms a topology in the process of training the network.
However, the GNG also introduces numerous additional parameters, which must
be set appropriately to obtain reasonable results. Then, in a post-processing step,
the authors modify the topology of the GNG by heuristically removing connections
between neurons; disjunctive sections of the topology are considered clusters.
However, which connections are removed depends on arbitrary chosen threshold
levels and critically affects the results. Additionally, complex structural properties
of the topology are totally disregarded. Moreover, their approach is not appropriate
for clustering spatial data, because it merely uses a basic NG algorithm, which does
not take spatial dependency into account.
This study is structured as follows: Sect. 4.2 introduces the algorithms that this
study utilizes, while Sect. 4.3 briefly explains the consecutive steps of which the
proposed method consists of. The usefulness of the method is demonstrated with
two different experiments (Sect. 4.4 ). Finally, the last section concludes with some
remarks and identifies future work.

4.2 Methodical Background

4.2.1 Contextual Neural Gas

Contextual Neural Gas (CNG; Hagenauer and Helbich 2013 ) is a spatial clustering
algorithm that combines the concepts of the GeoSOM with the NG algorithm. Like
basic NG, CNG consists of an arbitrary number of neurons, which are not subject to
any topological restrictions and provides a nonlinear mapping in high-dimensional
data space. In each step of the training process, an input vector is selected from the
input data and each neuron is moved into its direction. The strength of the movement
depends on the neurons' ranking order with respect to the distance to the input
vector, the adaptation rate, and the neighborhood range. Both the neighborhood
range and the adaptation rate are typically chosen to decrease with time.
CNG differs from basic NG in the determination of the neurons' ranking
order, which CNG accomplishes in a two-phase procedure to incorporate spatial
dependence. In the first step, neurons are ordered by spatial closeness. In the second
step, the first l neurons of the resulting spatial ordering are reordered within their
ranks with respect to the similarity of attributes.
The parameter l determines the strength of spatial dependence which is incorpo-
rated into the mapping. If l D 1, the ordering in the second step has no effect on the
final ordering at all. As a consequence, the adaption of the neurons depends solely
on spatial closeness. The attributes of the input data are ignored. If l is increased,