Fuzzy Symbolic Dynamics for Neurodynamical Systems

  • Authors:
  • Krzysztof Dobosz;Włodzisław Duch

  • Affiliations:
  • Faculty of Mathematics and Computer Science,;Department of Informatics, Nicolaus Copernicus University, Toruñ, Poland

  • Venue:
  • ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part II
  • Year:
  • 2008

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Abstract

Neurodynamical systems are characterized by a large number of signal streams, measuring activity of individual neurons, local field potentials, aggregated electrical (EEG) or magnetic potentials (MEG), oxygen use (fMRI) or concentration of radioactive traces (PET) in different parts of the brain. Various basis set decomposition techniques try to discover components that carry meaningful information are used to analyze such signals, but these techniques tell us little about the activity of the whole system. Fuzzy Symbolic Dynamics (FSD) may be used for dimensionality reduction of high-dimensional signals, defining non-linear mapping for visualization of trajectories that shows various aspects of signals that are difficult to discover looking at individual components, or to notice observing dynamical visualizations. FSD can be applied to raw signals, transformed signals (for example, ICA components), or to signals defined in the time-frequency domain. Visualization of a model system with artificial radial oscillatory sources, and of the output layer (50 neurons) of a neural Respiratory Rhythm Generator model (RRG) that includes 300 spiking neural units, are presented to illustrate the method.