Burst Recognition Algorithm Based on Symmetry Properties

The paper covers the problem of recognition of burst-like objects in time series. The new tool in the proposed methodology is a cluster definition based on the invariants of some transformations. A particular case of application of the method to spike recognition in neurophysiology is described in details. Neuronal spikes 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 that only typifies the spikes of the given neuron. The proposed algorithm is explained and an overview of the mathematical background is given.