Recursive self-organizing map as a contractive iterative function system


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.

Publication DOI:
Divisions: College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
Uncontrolled Keywords: topographic maps,vectorial data,contractive fixed input map,Markovian organization,receptive fields,RecSOM map,Computer Science (miscellaneous)
ISBN: 978-3-540-26972-4
Last Modified: 27 Jun 2024 12:05
Date Deposited: 07 Jan 2010 14:21
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
http://www.spri ... 8-3-540-26972-4 (Publisher URL)
PURE Output Type: Chapter
Published Date: 2005-06-20
Authors: Tiňo, Peter
Farkaš, Igor
van Mourik, Jort (ORCID Profile 0000-0002-3172-2714)



Version: Accepted Version

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