This investigation addresses the problem of the neural waveform classification. The chemical activity of a neuron creates a varying potential (action potential) which is the primary source of the communication with other neurons. Scientists record, analyze, and decode such activities; results from such analyses can be used in many applications such as neural prosthetics, brain-machine interfaces, and pharmacology.
In extracellular recordings, the electrodes are positioned outside the neurons themselves. Such recordings usually contain the activities of more than one neuron, resulting in multi-neuron (or multi-unit) activity recordings. The multi-unit activity is processed by a technique called spike sorting to distinguish between the activity of each neuron.
Spike sorting is often defined as an unsupervised three-stage process where, first, the spiking events are detected in the digitized signal, and second, the detected spike waveforms are projected into a lower-dimensional feature space, and third, the number of neurons generating those spikes is determined, and each spiking event is assigned to its originating neuron.
The current investigation proposes effective algorithms for improving the unsupervised spike sorting performance for feature extraction and clustering stages.
Principal Components Analysis (PCA) is the most commonly-used dimensionality reduction technique employed for the feature extraction of neural spikes. We investigate other dimensionality reduction techniques such as projection pursuit, normalized and unnormalized spectral clustering, graph-cuts, kernel principal components analysis, locally linear embedding, etc. and show that PCA works more desirably in producing feature space compared to other techniques in spike sorting problem. To improve the PCA feature extraction performance, we propose a graph-spectrum-based feature extraction method (which we call Graph Laplacian Features, GLF) which simultaneously incorporates minimizing the graph Laplacian and maximizing the variance at different feature space dimensions. The GLF method produces feature points that are compact when they belong to the same group, and are isolated when from different groups. The algorithm is compared with Principal Components Analysis and wavelet-coefficient-based feature points using simulated and real single-electrode neural data. The GLF application is extended to multi-channel recordings such as stereotrode and tetrode, and its performance is evaluated by comparing with PCA and spike height features in simulated and real steretrode and tetrode recordings. The results show that the proposed algorithm produces more compact and well-separated clusters compared to the other approaches.
In this work, we also investigate the third stage of spike sorting, i.e. the clustering of the feature space and the classification of spikes. A brief look at K-means, fuzzy C-means, and expectation maximization for mixture of Gaussians shows that such algorithms may not be the best choice for the unsupervised spike sorting. Thus, we investigate the mean-shift clustering approach, and propose a modified and fast version of the mean-shift clustering algorithm for neural spike sorting. Mean-shift is a robust hill-climbing approach for feature space clustering. The basic mean-shift algorithms including the blurring mean-shift (BMS) and the variable bandwidth mean-shift (VBMS) methods are briefly described, and then modifications are proposed to improve the algorithm convergence rate and reduce the algorithm’s need to supervision. To reach such goal, we propose using a quantized-space version of the algorithm with appropriate weighting functions. The proposed Mean-Shift process evolves by eliminating the feature points of lower density and keeping the high-density points in order to converge to the high-density area of each cluster. These strategies help our algorithm converge automatically without a need to stop it manually. The proposed clustering algorithm is then tested and compared to BMS and VBMS which shows its efficacy. The proposed method is used to cluster the feature spaces of simulated neural recordings produced by PCA and GLF method to compare such feature spaces based on clustering performances. Also, the same labeled simulated dataset is used to compare the performance of the fuzzy C-means with the proposed modified mean-shift algorithm.
In addition, other signal-processing issues of spike-sorting are investigated to address the robustness of the sorting procedure to variations in sampling rate and the number of quantization bit depth. The effects of different signal-to-noise ratios (SNRs) on clustering are studied when using PCA and GLF features. Such features are shown to be robust to quantization bit depth variations while they are quite sensitive to the sampling rate even when it exceeds the Nyquist rate.