Dynamics and topographic organization of recursive self-organizing maps

Peter Tino, Igor Farkas, Jort van Mourik

Research output: Contribution to journalArticle

Abstract

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, there is no general consensus as to how best to process sequences using topographicmaps, and this topic remains an active focus of neurocomputational research. The representational capabilities and internal representations of the models are not well understood. Here, we rigorously analyze a generalization of the self-organizingmap (SOM) for processing sequential data, recursive SOM (RecSOM) (Voegtlin, 2002), as a nonautonomous 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 β (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed-input maps is guaranteed. Some generalizations of SOM contain a dynamic module responsible for processing temporal contexts as an integral part of the model. We show that Markovian topographic maps of sequential data can be produced using a simple fixed (nonadaptable) dynamic module externally feeding a standard topographic model designed to process static vectorial data of fixed dimensionality (e.g., SOM). However, by allowing trainable feedback connections, one can obtain Markovian maps with superior memory depth and topography preservation. We elaborate on the importance of non-Markovian organizations in topographic maps of sequential data. © 2006 Massachusetts Institute of Technology.

Original languageEnglish
Pages (from-to)2529-2567
Number of pages39
JournalNeural Computation
Volume18
Issue number10
DOIs
Publication statusPublished - Oct 2006

Bibliographical note

© 2006 Massachusetts Institute of Technology. Dynamics and Topographic Organization of Recursive Self-Organizing Maps
Peter Tiňo, Igor Farkaš, and Jort van Mourik
Neural Computation 2006 Vol. 18, 2529-2567

Keywords

  • topographic maps
  • vectorial data
  • general data structures
  • sequences
  • Self-Organizing Map
  • sequential data
  • Recursive SOM
  • non-autonomous dynamical system
  • Markovian organizations
  • receptive fields

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