An unsupervised automatic method for sorting neuronal spike waveforms in awake and freely moving animals.

The present study introduces an approach to automatic classification of extracellularly recorded action potentials of neurons. The classification of spike waveform is considered a pattern recognition problem of special segments of signal that correspond to the appearance of spikes. The spikes generated by one neuron should be recognized as members of the same class. The spike waveforms are described by the nonlinear oscillating model as an ordinary differential equation with perturbation, thus characterizing the signal distortions in both amplitude and phase. It is shown that the use of local variables reduces the problem of spike recognition to the separation of a mixture of normal distributions in the transformed feature space. We have developed an unsupervised iteration-learning algorithm that estimates the number of classes and their centers according to the distance between spike trajectories in phase space. This algorithm scans the learning set to evaluate spike trajectories with maximal probability density in their neighborhood. Following the learning, the procedure of minimal distance is used to perform spike recognition. Estimation of trajectories in phase space requires calculation of the first- and second-order derivatives, and integral operators with piecewise polynomial kernels were used. This provided the computational efficiency of the developed approach for real-time application as required by recordings in behaving animals and in human neurosurgical operations. The new method of spike sorting was tested on simulated and real data and performed better than other approaches currently used in neurophysiology.