On Non-markovian Topographic Organization of Receptive Fields in Recursive Self-organizing Map

Recently, there has been an outburst of interest in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. The representational capabilities and internal representations of the models are not well understood. We concentrate on a generalization of the Self-Organizing Map (SOM) for processing sequential data – the Recursive SOM (RecSOM [1]). We argue that contractive fixed-input dynamics of RecSOM is likely to lead to Markovian organizations of receptive fields on the map. We show that Markovian topographic maps of sequential data can be produced using a simple fixed (non-adaptable) dynamic module externally feeding a standard topographic model designed to process static vectorial data of fixed dimensionality (e.g. SOM). We elaborate upon the importance of non-Markovian organizations in topographic maps of sequential data.