Geography Reference
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quickly run into limits determined by available RAM. Resolution of interpolated raster grids
was eventually reduced to 10
10 km, which made overlay operations feasible. Failure of
block groups to contain any pixel centroids was solved by assigning attributes of the nearest
point features.
Every block group thus had a set of 11 climate attributes associated with it. These were then
normalized to a 0-1 range and the order of block groups was randomized. This accounts for
the fact that the standard SOM training algorithm takes one input vector at a time, presents
it to the lattice of SOM neurons, finds the most similar neuron and then updates weights of
that neuron and its neighbourhood. The size of that neighbourhood is larger early during
training and then begins to shrink and the magnitude of changes made to neuron weights
likewise decreases over time. Input vectors presented early thus have more influence on the
training process than later vectors.
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8.4.2 SOM training and transformation
An ASCII text file containing normalized climate attributes for block groups, with random
order of block groups, was presented as input to SOM training. The number of block groups
was the principal factor in determining the number of neurons. Ideally, we would like
to obtain a unique two-dimensional point location for each of the 200 000 block groups.
Therefore there should be at least as many neurons as block groups. Despite the expected
density effects, with denser attribute space regions being represented with more neurons,
there will still be a fair number of neurons capturing multiple input vectors. This is mostly
due to the fact that some neurons will have to represent empty portions of the input space,
although in highly contracted form. In addition, there is the problem of edge neurons, where
the expanded/contracted representation of input space tends to be less reliable and many
input vectors tend to get captured. Given these concerns and computational resources,
it was decided to train a SOM consisting of 250 000 neurons (500
500). This will not
translate into a square SOM, but into a rectangular two-dimensional lattice, due to the use of
a hexagonal neighbourhood, with rows dropping into the 'gaps' below (see also Figure 8.5).
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Figure 8.5
Neuron geometry in a high-resolution SOM with hexagonal neighbourhood (10 000
neurons)
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