Motivation for a genetically-trained topography-preserving map

It is often observed that the lattice of a well-trained self-organizing map (SOM) preserves the topology of the data set. In this paper, we examine what is meant by this claim and discuss a related goal for a dimension-reducing mapping. We term this goal "topography preservation", and attempt to fulfill it using a two-stage training method called genetically-trained topographic mapping. In the first stage of training, a clustering algorithm is used to map sets of input data points to each neuron. In the second stage, a genetic algorithm assigns adjacencies between the neurons of the output lattice according to the fitness defined by the topography preservation goal. Stock market data and an artificial data set are used to illustrate the relative strengths of the standard SOM and the new algorithm.