Topographic Maps for Clustering and Data Visualization

Topographic maps (also known as topology-preserving mappings) are projections of a data set which attempt to capture some underlying structure therein. These are essentially unsupervised mappings (though supervised versions do exist), and so the algorithms must be structured in some way so that the final projection reveals some underlying structure in the data.

A more recent development is the Generative Topographic Mapping (GTM) developed by [1] in the late 1990s. This was a very active research area for a few years but the field seems to have lost some of its vitality recently. Some of this is no doubt due to the fact that the GTM is much more complex than the SOM and so researchers more interested in viewing their data sets rather than innovating in the field of topographic mappings have tended to use the SOM rather than the GTM. Also, the emphasis of GTM publications tended to be on the fact that it was a ‘principled alternative’ to the SOM. If researchers feel bound to stick to principled approaches, their research processes are limited in ways that do not happen in more application-oriented research. Also the quasi-religious Bayesian approach does not appeal to all researchers.

The rest of this Chapter is structured as follows: in Sect. 3, we discuss the basic competitive learning paradigm and the extension which leads to the SOM. In Sect. 4, we review the GTM and illustrate its use. Finally we review some of our recent work in this area.