Visualization of clusters in geo-referenced data using three-dimensional self-organizing maps

Abstract

The Self-Organizing Map (SOM) is an artificial neural network that performs simultaneously vector quantization and vector projection. Due to this characteristic, the SOM is an effective method for clustering analysis via visualization. The SOM can be visualized through the output space, generally a regular two-dimensional grid of nodes, and through the input space, emphasizing the vector quantization process. Among all the strategies for visualizing the SOM, we are particularly interested in those that allow dealing with spatial dependency, linking the SOM to the geographic visualization with color. One possible approach, commonly used, is the cartographic representation of data with label colors defined from the output space of a two-dimensional SOM. However, in the particular case of geo-referenced data, it is possible to consider the use of a three-dimensional SOM for this purpose, thus adding one more dimension in the analysis. In this dissertation is presented a method for clustering geo-referenced data that integrates the visualization of both perspectives of a three dimensional SOM: linking its output space to the cartographic representation through a ordered set of colors; and exploring the use of frontiers among geo-referenced elements, computed according to the distances in the input space between their Best Matching Units.