# Recursive self-organizing map as a contractive iterative function system

## 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.

Publication DOI: https://doi.org/10.1007/11508069_43 College of Engineering & Physical Sciences > School of Informatics and Digital Engineering > MathematicsCollege of Engineering & Physical Sciences > Systems analytics research institute (SARI) topographic maps,vectorial data,contractive fixed input map,Markovian organization,receptive fields,RecSOM map,Computer Science (miscellaneous) 978-3-540-26972-4 http://www.scop ... tnerID=8YFLogxK (Scopus URL) http://www.spri ... 8-3-540-26972-4 (Publisher URL) Chapter 2005-06-20 Tiňo, Peter Farkaš, Igor van Mourik, Jort ( 0000-0002-3172-2714)