Dynamics and Topographic Organization of Recursive Self-Organizing Maps

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. However, at present, there is no general consensus as to how best to process sequences using topographic maps and this topic remains a very active focus of current neurocomputational research. The representational capabilities and internal representations of the models are not well understood. We rigorously analyze a generalization of the Self-Organizing Map (SOM) for processing sequential data, Recursive SOM (RecSOM) (Voegtlin, 2002), as a non-autonomous dynamical system consisting of a set of fixed input maps. We argue that contractive fixed input maps are likely to produce Markovian organizations of receptive fields on the RecSOM map. We derive bounds on parameter (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed input maps is guaranteed. Some generaliz...

• Type: Journal
• Year: 2006
• Where: NECO
• Authors: Peter Tiño, Igor Farkas, Jort van Mourik
• Keywords: Input Maps, NECO 2006, Topographic Maps, Vectorial Data