On the use of three-dimensional self-organizing maps for visualizing clusters in georeferenced data

The self-organizing map (SOM) is an artificial neural network that is very effective for clustering via visualization. Ideally, so as to produce a good model, the output space dimension of the SOM should match the intrinsic dimension of the data. However, because it is very difficult or even impossible to visualize SOMs with more than two dimensions, the vast majority of applications use SOM with a regular two-dimensional (2D) grid of nodes. For complex problems, this poses a limitation on the quality of the results obtained. There are no theoretical problems in generating SOMs with higher dimensional output spaces, but the 3D SOMs have met limited success. In this chapter, we show that the 3D SOM can be used successfully for visualizing clusters in georeferenced data. To overcome the problem of visualizing the 3D grid of units, we start by assigning one primary color (of the RGB color scheme) to each of the three dimensions of the 3D SOM. We then use those colors when representing, on a geographic map, the georeferenced elements that are mapped to each SOM unit. We then provide a comparison of a 2D and 3D SOM for a concrete problem. The results obtained point to a significant increase in the clustering quality due to use of 3D SOMs.