Igor TETKO
Institute of Bioorganic and Petroleum Chemistry of NAS of Ukraine,
Kyiv, UKRAINE;
Institute for Bioinformatics, Ingolstraedter Lanstrasse 1,
D-85764, Neuherberg, GERMANY
E-mail: itetko@vvclab.org

Symmetry analysis in spikes (bursts) recognition and classifications

Abstract:
The present study introduces an approach for automatic classification of extracellularly recorded action potentials of neurons based on geometrical approach. Neuronal spikes (bursts) are considered as geometrical objects, namely trajectories in phase space. It is shown that for spikes, generated by the same neuron, it is possible to find such symmetry transformation under which their trajectories are invariant in phase space. On the other hand, the phase trajectories of spikes generated by other neurons change significantly under action of that transformation. Thus it is possible to define a special symmetry transformation (including Lie symmetry) that only typifies the spikes of the given neuron.  The proposed algorithm is explained and an overview of the mathematical background is given. The method was tested on simulated data and showed good results in real experiments. New problems and applications are also discussed.