Towards High-resolution Self-organizing Maps of Geographic Features - Geographic Visualization: Concepts, Tools and Applications - page 179

(e.g. movement between block groups 12 and 13) or via bridge block groups that are tran-
sitional in terms of both geographic and attribute space location (e.g. block group 23).
8.5 Summary and outlook
This chapter proposes the creation of high-resolution spatializations from the attributes
of geographic features. Its main aim is to generate an alternative to the standard approach
in geovisualization, where the geographic map tends to be the only stable element, while
other visualizations are characterized by fluid geometry, topology and visual appearance. It
is argued that the self-organizing map could be one method able to generate more stable
base maps onto which various types of other data could be mapped through a series of
geometric and attribute-based transformations. This approach is decidedly different from
the current use of such tools as scatter plots, parallel coordinate plots and even of the SOM
method itself.
We demonstrated this approach by first training a SOM consisting of 250 000 neurons
with climate data generated for more than 200 000 geographic features, performing various
transformations, and finally juxtaposing SOM-base maps with geographic maps. Numerous
challenges were encountered, beginning with the difficulty of performing geographic over-
lays involving several hundred thousand objects in standard GIS software. Training using
SOM PAK was unproblematic, but a number of artefacts in the visualization - in particular
the break-up of k -means clusters after projection onto the SOM - suggest that more train-
ing cycles should be applied, beyond the 120 000 cycles used in our experiment (20 000 and
100 000 in the two training stages, respectively).
Future work will include a more formal investigation of the distortions incurred by the
training of a SOM consisting of several hundred thousand neurons with an equally large
number of training vectors. On one hand, there is a need to develop recommendations for
how to use standard SOM tools (e.g. SOM PAK ) in the context of high-resolution SOM.
This must occur in recognition of the fact that geometric distortion as such is unavoidable
when high-dimensional data are represented by low-dimensional geometry and that the
SOM method is in fact able to bridge large dimensional gaps between source data and
display space through density-driven effects of expansion and compression. On the other
hand, overall distortion characteristics can be addressed by recent variations of the SOM
method. For example, edge effect distortions are caused by topological heterogeneity in
the neuron structure, with edge neurons having fewer neighbours than neurons further
inside of the SOM. This source of distortions could be diminished by arranging neurons
on a closed surface. A number of spherical SOM approaches have been proposed (Sangole
and Knopf, 2002; Wu and Takatsuka, 2005), but have not yet been used much in practical
SOM applications and have not involved large numbers of neurons. Another interesting
question in the context of high-resolution SOMs is how the total number of neurons is
to be determined. The standard SOM algorithm used in our climate experiment as well
as spherical and other variants take the number of neurons as an input parameter, which
therefore allows user control of SOM granularity. A very different, alternative approach
involves the deletion or addition of neurons in response to certain threshold functions. This
leads to so-called growing SOMs (Fritzke, 1999). Apart from these approaches addressing
problems observed in both low- and high-resolution SOMs, there may be issues arising