Progressive concept formation in Self-organising Maps

We review a technique for creating Self-organising Maps (SOMs) in a Feature space which is nonlinearly related to the original data space. We show that convergence is remarkably fast for this method. The resulting map has two properties which are interesting from a biological perspective: first, the learning forms topology preserving mappings extremely quickly; second, the learning is most refined for those parts of the feature space which is learned first and which have most data. By considering the linear feature space, we show that it is the interaction between the overcomplete basis in which learning takes place and the mixture of one-shot and incremental learning which comprises the method that gives the method its power. Finally, as an engineering application, we show that maps representing time series data are able to successfully extract the time-dependent structure in the series.