Beyond the topological map : developing alternate mappings in self organisation

The self organising map is a well established unsupervised
learning technique which is able to form sophisticated representations of an input data set. However, conventional Self Organising Map (SOM) algorithms are limited to the production of topological maps — that is, maps where distance between points on the map have a direct relationship to the Euclidean distance between the training vectors corresponding to those points.

It would be desirable to be able to create maps which form clusters on primitive attributes other than Euclidean distance; for example, clusters based upon orientation or shape. Such maps could provide a novel approach to pattern recognition tasks by providing a new method to associate groups of data.

In this paper, it is shown that the type of map produced by SOM algorithms is a direct consequence of the lateral connection strategy employed. Given this knowledge, a technique is required to establish the feasability of using an alternative lateral connection strategy. Such a technique is presented. Using this technique, it is possible to rule out lateral connection strategies that will not produce output states useful to the organisation process. This technique is demonstrated using conventional Laplacian interconnection as well as a number of novel interconnection strategies.