Geography Reference
In-Depth Information
method will tend to form contiguous shapes after being projected onto the SOM. To test this,
block groups in both the geographic map and the SOM-based map were joined into larger
polygons based on shared cluster membership and overlaid on top of states (Figure 8.9).
This direct comparison of the mapping of identical cluster solutions onto two different 'base
maps' provides support for the need to perform further training on the high-resolution SOM.
Clusters appear almost completely contiguous when mapped onto the geographic map (top
of Figure 8.9), while some clusters appear broken into several parts in the SOM-based map
(bottom of Figure 8.9). That is surprising, since the SOM and the
k
-means clusters (
k
=
25)
were computed from exactly the same source vectors.
One would further expect that climate clusters and state boundaries should show virtually
no correlation (except for such cases where a state boundary coincides with a physical feature
affecting climate, like the ridge line of a major mountain range). Indeed, that is the case
in the geographic map. It is true in many parts of the SOM as well. For example, notice
how the progression of climate clusters as parallel bands in the southeastern United States
(sequence of clusters 2-6-18-14-1-16) gets represented in both geographic and SOM-based
visualization, virtually independent of state boundaries. However, there are cases in the
SOM-based map where cluster and state boundaries coincide and these correspond to
the same oddly neighbouring states mentioned earlier. For example, the 'northern' and
'western' boundaries of California in the SOM completely coincide with cluster boundaries.
The large gap among two-dimensional block group locations along the same boundaries
therefore seems to indeed be justified (see also bottom-right portion of Figure 8.8). The
earlier mentioned break-up of Pennsylvania (left side of Figure 8.8) is supported by the
association of the large western portion of Pennsylvania (no. 1 in Figure 8.8) with Ohio in
cluster 15 and of the eastern portion (no. 2 in Figure 8.8) with New Jersey in cluster 17.
8.4.6 Mapping extreme weather events onto the climate SOM
All visual transformations illustrated so far were based on the very same input vectors used
to train the SOM. However, it is also possible to map other data onto the SOM that were
not part of the training process, based on two different approaches. One consists of finding
best-matching neurons for non-training vectors, as long as those vectors consist of the same
dimensions as the training vectors and identical preprocessing has been applied (e.g. scaling
to 0-1 range based on the same minimum/maximum values). In our case, one could map
climate data for geographic areas outside of the United States onto the SOM to identify
global similarities. For example, areas along the Mediterranean coast would likely end up
inside of cluster 24 'in' Southern California (see Figure 8.9).
Another option is to use a currently mapped geographic feature as a socket through
which another geography feature can be mapped onto the SOM, based on shared geographic
location. Skupin and Hagelman (2005) demonstrated this by first training a SOM with multi-
temporal census data and then using single-time vectors as temporal vertices that define
the trajectory of a geography feature. Another proposed trajectory mapping technique takes
space-time paths, such as those captured by GPS, and projects them onto a spatialization
based on the sequence of geographic features traversed (Skupin, 2007). We demonstrate
this here for hurricanes that made landfall in the continental United States during the 2005
hurricane season (Figure 8.10). This involves determining the sequence of block groups
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