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Dynamics and topographic organization of recursive self-organizing maps
Peter Tino1, Igor Farkas, Jort van Mourik
1School of Computer Science, University of Birmingham, Birmingham B15 2TT, UK. P.Tino@cs.bham.ac.uk
Neural Computation
|August 16, 2006
Summary
Researchers analyzed the recursive self-organizing map (RecSOM) for sequential data processing. They found that trainable feedback connections enhance memory depth and topography preservation in Markovian topographic maps.
Area of Science:
- Neurocomputation
- Dynamical Systems
- Machine Learning
Background:
- Extending topographic maps to sequential data is an active research area.
- Current models lack clear understanding of representational capabilities and internal representations.
- General consensus on optimal sequence processing with topographic maps is missing.
Purpose of the Study:
- To rigorously analyze the recursive self-organizing map (RecSOM) for sequential data.
- To investigate the conditions for generating Markovian organizations of receptive fields.
- To explore methods for improving memory depth and topography preservation in sequential data mapping.
Main Methods:
- Analysis of RecSOM as a nonautonomous dynamical system with fixed input maps.
- Derivation of parameter bounds for guaranteeing contractiveness of fixed-input maps.
- Comparison of fixed dynamic modules versus trainable feedback connections in RecSOM.
Main Results:
- Contractive fixed-input maps are likely to produce Markovian organizations.
- Bounds for parameter beta ensuring contractiveness were derived.
- Trainable feedback connections yield superior memory depth and topography preservation compared to fixed modules.
Conclusions:
- RecSOM provides a framework for Markovian topographic maps of sequential data.
- Fixed dynamic modules can create Markovian maps, but trainable feedback offers enhanced performance.
- Non-Markovian organizations are important for advanced sequential data topographic mapping.
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