# 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 language English Intelligent Data Engineering and Automated Learning - IDEAL 2005 Marcus Gallagher, James Hogan, Frederic Maire Berlin (DE) Springer 327-334 8 978-3-540-26972-4 https://doi.org/10.1007/11508069_43 Published - 20 Jun 2005

### Publication series

Name Lecture Notes in Computer Science Springer-Verlag 3578

### Keywords

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

• ## Cite this

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