Recursive self-organizing map as a contractive iterative function system

Peter Tiňo, Igor Farkaš, Jort van Mourik

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Recently, there has been a considerable research activity in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, 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 [1]), as a non-autonomous dynamical system consisting off a set of fixed input maps. We show that contractive fixed input maps are likely to produce Markovian organizations of receptive fields o the RecSOM map. We derive bounds on parameter $\beta$ (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed input maps is guaranteed.
Original languageEnglish
Title of host publicationIntelligent Data Engineering and Automated Learning - IDEAL 2005
EditorsMarcus Gallagher, James Hogan, Frederic Maire
Place of PublicationBerlin (DE)
PublisherSpringer
Pages327-334
Number of pages8
ISBN (Print)978-3-540-26972-4
DOIs
Publication statusPublished - 20 Jun 2005

Publication series

NameLecture Notes in Computer Science
PublisherSpringer-Verlag
Volume3578

Keywords

  • topographic maps
  • vectorial data
  • contractive fixed input map
  • Markovian organization
  • receptive fields
  • RecSOM map

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    Tiňo, P., Farkaš, I., & van Mourik, J. (2005). Recursive self-organizing map as a contractive iterative function system. In M. Gallagher, J. Hogan, & F. Maire (Eds.), Intelligent Data Engineering and Automated Learning - IDEAL 2005 (pp. 327-334). (Lecture Notes in Computer Science; Vol. 3578). Springer. https://doi.org/10.1007/11508069_43