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Global Visualization of Neural Dynamics

Global Visualization of Neural Dynamics. Krzysztof Dobosz, Włodzisław Duch Department of Informatics Nicolaus Copernicus University , Toruń, Poland Google: W. Duch Neuromath , Jena, April 2008. Brain Spirography. Example of a pathological signal analysis. Motivation.

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Global Visualization of Neural Dynamics

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  1. Global Visualization of Neural Dynamics Krzysztof Dobosz, Włodzisław Duch Department of Informatics Nicolaus Copernicus University, Toruń, Poland Google: W. Duch Neuromath, Jena, April 2008

  2. Brain Spirography Example of a pathological signal analysis

  3. Motivation • Analysis of multi-channel, non-stationary, time series data. • Neural respiratory rhythm generator (RRG): hundreds of neurons, what is the system doing? • Information is in the trajectories, how to see them? • Component-based analysis. • Time-frequency analysis. • Recurrence plots. Fuzzy Symbolic Dynamics (FSD), visualize + understand. • Understand FSD mappings using model data. • First look at RRG data. • First look at real EEG data.

  4. Fuzzy Symbolic Dynamics (FSD) Trajectory of dynamical system (neural activities, av. rates): 1. Standardize data. 2. Find cluster centers (e.g. by k-means algorithm): m1, m2 ... 3. Use non-linear mapping to reduce dimensionality: Localized probe function: sharp indicator functions => symbolic dynamics; soft membership functions => fuzzy symbolic dynamics.

  5. Model, radial/linear sources Sources generate waves on a grid Flat wave Radial wave Relatively simple patterns arise, but slow sampling shows numerical artifacts. Ex: one and two radial waves.

  6. Respiratory Rhythm Generator 3 layers, spiking neurons, output layer with 50 neurons

  7. Sensitive differences?

  8. FSD development • Optimization of parameters of probe functions to see more structure from the point of view of relevant task. • Learning: supervised clustering, projection pursuit based on quality of clusters => projection on interesting directions. • Measures to characterize dynamics: position and size of basins of attractors, transition probabilities, types of oscillations around each attractor. • Visualization in 3D and higher (lattice projections etc). • Tests on model data and on the real data.

  9. Complex logic What is needed to understand data with complex logic? • cluster non-local areas in the X space, use projections W.X • capture local clusters after transformation, use G(W.X-q) SVMs fail because the number of directions W that should be considered grows exponentially with the size of the problem n. What will solve it? • A class of constructive neural network solution with G(W.X-q) functions with special training algorithms. • Maximize the leave-one-out error after projection: take localized function G, count in a soft way cases from the same class as X. Projection may be done directly to 1D, 2D or higher.Examples: parity, monks.

  10. Parity n=9 Pursuite of the best “point of view” using simple gradient learning; cluster quality index shown below. No problem with large variance noise in 6 channels.

  11. EEG example • Data from two electrodes, BCI IIIa

  12. Alcoholics vs. controls Colors: from blue at the beginning of the sequence, to red at the end. Left: normal subject; right: alcoholic; task: two matched stimuli, 64 channels (3 after PP), 256 Hz sampling, 1 sec, 10 trials; single stalc.

  13. What can we learn? • FSD shows global mapping of the whole trajectory. • Pairs of probe functions show different aspects. • Where is the trajectory most of the time? Low/high energy synchronization. • Supervised clustering for characterization of the basins of attractors, transition probabilities, types of oscillations around each attractor. • Clear differences between different conditions, perhaps useful in classification and diagnosis, if standardized. • More tests on real data needed.

  14. Future plans • More complex models to understand how to interpret the FSD plots. • Effects of various component-based transformations. • Projection pursuit is important, raw signals quite messy. • Identifying interesting segments: projection pursuit in space and time. • Learning of parameters of probe functions that show interesting structures. • Analysis of types of behavior using the models of spiking networks (RRG and other models). • BCI applications? Many other things …

  15. Thank youfor lending your ears ... Google: W. Duch => Papers & presentationsSee also http:www.e-nns.org

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