Effects of Irregular Topology in Spherical Self-Organizing Maps

Effects of Irregular Topology in Spherical Self-Organizing Maps

is part of the Paper Session:
Special Session to honor Manfred M Fischer's contributions to Geography: Spatial Analysis and Modeling.

scheduled on Friday, 4/18/08 at 16:40 PM.

Author(s):
Charles Schmidt - San Diego State University (charles.r.schmidt@asu.edu)
Serge Rey* - San Diego State University
Andre Skupin - San Diego State University

Abstract:
A regular network topology is one in which every node
on the network has exactly the same number of adjacent nodes. Any
topology involving an edge is irregular. Arranging our lattice on the
surface of a sphere seems to be an obvious way to overcome the edge.
However, there exist only five arrangements on the sphere which are
completely regular; these are the five platonic solids (Ritter, 1999;
Harris et al., 2000). Any other arrangement of neurons on the surface
of the sphere will result in an irregular topology, as not all neurons
will have the same number of neighbors. The classic method for
minimizing this irregularity is to generate the spherical lattice by
tessellating the sides of the icosahedron (Nishio et al., 2006). While
this method will always result in a highly regular spherical topology,
the main drawback is that the number of neurons in the network (the
network size), N, grows exponentially as tessellations are applied.
That results in only very coarse control over network size.  A topology
which yields a more flexible network size may be desirable. However, in
order to address this issue of network size, we must first determine
the degree to which irregularity effects the SOM. The objective of this
research is to determine the utility of certain irregular spherical
topologies beyond offering greater control over network size. Toward
that end, we will develop and test new diagnostics to measure and
visualize topology-induced errors in SOM

Keywords:

Self-Organizing Maps, GeoVisualization