The urban sprawl dynamics: does a neural network understand the spatial logic better than a cellular automata?

approach has been reversed: the state at t and t+1 of cell becoming urbanized during the
observed time lag represents a “model” which other cells will follow during the time lag
t+1, t+2.

5. The classification of the land use dynamics with SOM

The NN SOM, a powerful tool of classification, have been developed mainly by
Kohonen (1995) between 1979 and 1982. As said before SOM are AutoPoietic NN,
where the target is not predefined, but dynamically built up during the learning phase.
Their architecture comprises two layers: an input one, acting simply as a buffer, that
doesn’t modify the data, and an output one, known as Kohonen layer (or matrix), which
is formed by units regularly organized in the space and which evolves during the
training following a spatial organization process of the data characteristics, named
Feature Mapping (Fig. 1a). The construction of these maps allow a close examination of
the relationships between the items in the training set.

INPUT LAYER

KOHONEN layer

(a)

Figure 1 - the SOM topology (a) and the weight update function (b)

When the training phase has calculated the weight matrix, the classification maps each
input vector to the output unit with the minimum Euclidean distance from the codebook.
The SOM attitude to “classify” makes possible to perform a mapping with two main
peculiarities:

• Clustering: the net performs a logical division of the input space into regions
(cluster), associating a point in the N-dimensional input space to the two-
dimensional output matrix. In the dimension reduction process the principal
components discriminating data are dominant.

• Self-organisation: before the training the weights vectors topology depends only on
the initialising criterion: if it is random weights will be casually organised into their
hyper-cube. The learning criterion tends to move the weights vectors toward the
input vectors seen during the training. The vector moving affects not only the winner

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