Geography Reference
In-Depth Information
classes forming narrow bands, even though all classes have equal width for that attribute.
Those narrow bands correspond to the dominant linear separation features in the point
display. None of this would be problematic, if the wind speed variable, as observed in
nature, indeed shows such a staggered structure as opposed to the pattern mostly being
an artefact of some data transformation process. Unfortunately, the latter turned out to be
largely the case here. The correspondence between block group locations and wind speed
prompted us to look more closely into that variable. It turned out that average wind speed in
this data set had a very small absolute range of values when compared with other variables.
That should not cause any problems, since all variables were scaled to a 0-1 range. However,
in the process of interpolation all 11 attributes had become represented as integer raster grids
in order to limit data volumes for rasters spanning all of the contiguous United States at a
1km 2 resolution. For attributes with small absolute range the combination of integer storage
and 0-1 scaling meant the introduction of wide gaps along that attribute dimension, when
compared with attributes with larger absolute ranges. Effectively, the SOM represents these
gaps existing in the source data correctly (see lower right corner of Figure 8.6), although
they were introduced through preprocessing rather than being representative of an actual
climatic phenomenon.
8.4.4 Juxtaposition of visualizations in geographic space
and attribute space
One argument raised earlier in this chapter was that high-resolution spatialization of geo-
graphic features based on their attributes may provide a useful alternative perspective on
geographic phenomena. For instance, one would be able to juxtapose geographic and at-
tribute space visualizations in a more equitable manner. Synchronization of symbology takes
semiotic choices out of the equation and lets the two-dimensional layout speak for itself.
However, such synchronization may first require further transformation of the spatializa-
tion geometry. This is where the rich set of out-of-the-box tools available in GIS software
becomes especially handy. For example, when the goal is to create an alternative map of
the lower 48 states, one can start with point locations for census block groups (Figure 8.6),
create a two-dimensional Voronoi region for each block group, and then dissolve boundaries
between Voronoi regions of block groups within the same state. With identical symbology
attached to state polygons, the two maps can now juxtaposed (Figure 8.7).
Given the regular, predictable geographic patterns of climate derived from a coarse set
of geographic samples, one would expect the SOM map (bottom of Figure 8.7) to mirror
many of the structures found in the geographic map (top of Figure 8.7). Owing to the
nature of the SOM update rule - with similar training vectors being attracted to and up-
dating nearby neuron regions - major topological relationships will tend to get replicated
in the low-dimensional neuron lattice. One would thus expect that states are represented as
contiguous polygons in SOM space. In many cases, this does in fact come true in the SOM
map, as in the case of such states as Florida (FL), Louisiana (LA) or California (CA). As
another consequence of the preservation of topology, one would expect that states sharing a
boundary in geographic space will also be neighbours in the SOM space. For example, notice
how the clock-wise order of neighbours of the state of Indiana (IN) is replicated in the SOM
(KY-IL-MI-OH). Topology preservation is sometimes even able to bridge the earlier men-
tioned chasms caused by the preprocessing of data. For example, the large polygon depicting
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