Geoscience Reference
In-Depth Information
of these tools is for unsupervised classification and feature extraction purposes, such items can also
be used as modelling tools, for example, where inputs are mapped onto a response surface in an
optimal manner (Openshaw and Openshaw 1997). However, a supervised SOFM is also available,
and one possible realisation of an appropriate training algorithm can be found in Kasabov (1996).
The underlying basis for such networks is rooted deep in vector quantisation theory, and their emer-
gence as an operational geographical tool has arisen from the spatial data explosion and our associ-
ated need for large-scale multidimensional data reduction capabilities. In simple conceptual terms,
an SOFM consists of two layers, an input layer and an output layer, called a feature map, which
represents the output vectors of the output space. The task of each SOFM is to map input vectors
from the input units onto the output units or feature map (which under normal circumstances takes
the form of a 1D or 2D array) and to perform this adaptive transformation in an ordered topological
fashion, such that topological relationships between the input vectors are preserved and represented
in the final product via the spatial distribution or pattern of unit activations. Thus, the more related
two vectors are in terms of input space, the closer will be the position of the two corresponding units
that represent these input patterns in the feature map. The overall idea then is to develop a topologi-
cal map of input vectors such that similar input vectors would trigger both their own units and other
similar units in proportion to their topological closeness. Thus, a global organisation of the units
and associated data is expected to emerge for the training programme.
In more detail, the essential characteristics of SOFM networks can be summarised as follows:
Network properties
A two-layer architecture where the input layer is fully connected to the output layer
(Kohonen layer) and whose units are arranged in a 2D grid (map). The map units have
local interaction capabilities, which means that changes in the behaviour of one unit
will have a direct effect on the behaviour of other units in its immediate neighbourhood.
PE properties
Each output unit is characterised by an
n
-dimensional weight vector and contains a
linear PE. Each feature map unit computes its net input on a linear basis and non-
linearities come into being when the selection is made as to which unit
ires
.
Learning properties
Unsupervised learning in a network is the adaptive modification of the connection
weights associated with local interacting units in response to input excitations and in
accordance with a competitive learning rule (i.e. weight adjustment of the winning unit
and its neighbours). The weight adjustment of the neighbouring units is instrumental in
preserving the topological ordering of the input space.
SOFM networks can also be used for front-end pattern classification purposes or for other impor-
tant decision-making processes, for example, in cartographic generalisation (Allouche and Moulin
2005; Sester 2005). It is also possible to have output values from the feature map layer passed into
the hidden layer of a backpropagation network on a direct feed basis.
13.8
ADVANTAGES, APPLICATION DOMAINS AND EXAMPLES
13.8.1 a
dVantageS
The attraction of CNN-based GC extends far beyond the high computation rates provided by mas-
sive parallelism, and the numerous advantages that are now on offer for us to exploit are perhaps
best considered under the following points (see Fischer 2005):
•
Greater representational flexibilities and freedom from linear model design constraints
•
Built-in network capabilities (via representation, training, etc.) to incorporate rather than to
ignore the special nature of spatial data
•
Greater degrees of robustness, or fault tolerance, to deal with noisy data and missing or
fuzzy information
