A review of methods for spike sorting : the detection and classification of neural action potentials
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paper_title: An Iterative Spike Separation Technique

paper_content:

A spike separation technique which combines data processing methods with extracellular probing techniques to allow simultaneous observation of multiple neural events is presented. A preparation, the locust ventral cord, allows spike separation. Experimental results and simulation indicate the usefulness of the method for this preparation. A feature of the data processing method allows the experimenter to direct the machine classification by an initial classification. Subsequently, the machine returns an indication of the quality of classification, allowing a reclassification or termination.
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paper_title: Simultaneous Studies of Firing Patterns in Several Neurons.

paper_content:

A tungsten microelectrode with several small holes burnt in the vinyl insulation enables the action potentials from several adjacent neurons to be observed simultaneously. A digital computer is used to separate the contributions of each neuron by examining and classifying the waveforms of the action potentials. These methods allow studies to be made of interactions between neurons that lie close together.
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paper_title: A Comparison of Techniques for Classification of Multiple Neural Signals

paper_content:

A number ofmultiunit neural signal classification techniques are compared in their theoretical separation properties and in their empirical performance in classifying two channel recordings from the ventral nerve cord of the cockroach. The techniques include: the use of amplitude and conduction time measures, template matching, the principal components method, optimal filtering, and maximin discrimination. The noise encountered under different situations is characterized, permitting the comparisons to be made as functions of the experimental conditions. Recommendations are made as to the appropriate use of the techniques.
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paper_title: The real-time sorting of neuro-electric action potentials in multiple unit studies

paper_content:

Abstract Description of a method by which action potentials recorded simultaneously can be sorted in a moderate size machine in real-time and on-line.
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paper_title: Real-Time Classification of Multiunit Neural Signals Using Reduced Feature Sets

paper_content:

Classification of characteristic neural spike shapes in multi-unit recordings is performed in real time using a reduced feature set. A model of uncorrelated signal-related noise is used to reduce the feature set by choosing a subset of aperiodic samples which is effective for discrimination between signals by a nearest-mean algorithm. Initial signal classes are determined by an unsupervised clustering algorithm applied to the reduced features of the learning set events. Classification is carried out in real time using a distance measure derived for the reduced feature set. Examples of separation and correlation of multiunit activity from cat and frog visual systems are described.
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paper_title: A Comparison of Techniques for Classification of Multiple Neural Signals

paper_content:

A number ofmultiunit neural signal classification techniques are compared in their theoretical separation properties and in their empirical performance in classifying two channel recordings from the ventral nerve cord of the cockroach. The techniques include: the use of amplitude and conduction time measures, template matching, the principal components method, optimal filtering, and maximin discrimination. The noise encountered under different situations is characterized, permitting the comparisons to be made as functions of the experimental conditions. Recommendations are made as to the appropriate use of the techniques.
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paper_title: A totally automated system for the detection and classification of neural spikes

paper_content:

A system for neural spike detection and classification is presented which does not require a priori assumptions about spike shape or timing. The system is divided into two parts: a learning subsystem and a real-time detection and classification subsystem. The learning subsystem, comprising of feature learning phase and a template learning phase, extracts templates for each separate spike class. The real-time detection and classification subsystems identifies spikes in the noisy neural trace and sorts them into classes, based on the templates and the statistics of the background noise. Comparisons are made among three different schemes for the real-time detection and classification subsystem. Performance of the system is illustrated by using it to classify spikes in segments of neural activity recorded from monkey motor cortex and from guinea pig and ferret auditory cortexes. >
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paper_title: Automatic nerve impulse identification and separation.

paper_content:

Abstract A heuristic method was developed to identify and to separate automatically unit nerve impulses from a multiunit recording. Up to 20 distinct units can be identified. The method can sequentially decompose superimposed nerve impulses if the rapidly changing region of at least one of them is relatively undistorted. The identification and separation procedure has been successfully applied to the extracellularly recorded neural activity associated with the shadow reflex pathway of the barnacle. The limitations of the procedure are discussed and additional applications of the technique are presented.
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paper_title: Automatic sorting of multiple unit neuronal signals in the presence of anisotropic and non-Gaussian variability

paper_content:

Neuronal noise sources and systematic variability in the shape of a spike limit the ability to sort multiple unit waveforms recorded from nervous tissue into their single neuron constituents. Here we present a procedure to efficiently sort spikes in the presence of noise that is anisotropic, i.e., dominated by particular frequencies, and whose amplitude distribution may be non-Gaussian, such as occurs when spike waveforms are a function of interspike interval. Our algorithm uses a hierarchical clustering scheme. First, multiple unit records are sorted into an overly large number of clusters by recursive bisection. Second, these clusters are progressively aggregated into a minimal set of putative single units based on both similarities of spike shape as well as the statistics of spike arrival times, such as imposed by the refractory period. We apply the algorithm to waveforms recorded with chronically implanted micro-wire stereotrodes from neocortex of behaving rat. Natural extensions of the algorithm may be used to cluster spike waveforms from records with many input channels, such as those obtained with tetrodes and multiple site optical techniques.
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paper_title: Efficient Approximations for the Marginal Likelihood of Bayesian Networks with Hidden Variables

paper_content:

We discuss Bayesian methods for model averaging and model selection among Bayesian-network models with hidden variables. In particular, we examine large-sample approximations for the marginal likelihood of naive-Bayes models in which the root node is hidden. Such models are useful for clustering or unsupervised learning. We consider a Laplace approximation and the less accurate but more computationally efficient approximation known as the Bayesian Information Criterion (BIC), which is equivalent to Rissanen's (1987) Minimum Description Length (MDL). Also, we consider approximations that ignore some off-diagonal elements of the observed information matrix and an approximation proposed by Cheeseman and Stutz (1995). We evaluate the accuracy of these approximations using a Monte-Carlo gold standard. In experiments with artificial and real examples, we find that (1) none of the approximations are accurate when used for model averaging, (2) all of the approximations, with the exception of BIC/MDL, are accurate for model selection, (3) among the accurate approximations, the Cheeseman–Stutz and Diagonal approximations are the most computationally efficient, (4) all of the approximations, with the exception of BIC/MDL, can be sensitive to the prior distribution over model parameters, and (5) the Cheeseman–Stutz approximation can be more accurate than the other approximations, including the Laplace approximation, in situations where the parameters in the maximum a posteriori configuration are near a boundary.
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paper_title: A Comparison of Techniques for Classification of Multiple Neural Signals

paper_content:

A number ofmultiunit neural signal classification techniques are compared in their theoretical separation properties and in their empirical performance in classifying two channel recordings from the ventral nerve cord of the cockroach. The techniques include: the use of amplitude and conduction time measures, template matching, the principal components method, optimal filtering, and maximin discrimination. The noise encountered under different situations is characterized, permitting the comparisons to be made as functions of the experimental conditions. Recommendations are made as to the appropriate use of the techniques.
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paper_title: Optimal discrimination and classification of neuronal action potential waveforms from multiunit, multichannel recordings using software-based linear filters

paper_content:

Describes advanced protocols for the discrimination and classification of neuronal spike waveforms within multichannel electrophysiological recordings. The programs are capable of detecting and classifying the spikes from multiple, simultaneously active neurons, even in situations where there is a high degree of spike waveform superposition on the recording channels. The protocols are based on the derivation of an optimal linear filter for each individual neuron. Each filter is tuned to selectively respond to the spike waveform generated by the corresponding neuron, and to attenuate noise and the spike waveforms from all other neurons. The protocol is essentially an extension of earlier work (S. Andreassen et al., 1979; W.M. Roberts and D.K. Hartline, 1975; R.B. Stein et al., 1979). However, the protocols extend the power and utility of the original implementations in two significant respects. First, a general single-pass automatic template estimation algorithm was derived and implemented. Second, the filters were implemented within a software environment providing a greatly enhanced functional organization and user interface. The utility of the analysis approach was demonstrated on samples of multiunit electrophysiological recordings from the cricket abdominal nerve cord. >
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paper_title: Multidimensional binary search trees used for associative searching

paper_content:

This paper develops the multidimensional binary search tree (or k -d tree, where k is the dimensionality of the search space) as a data structure for storage of information to be retrieved by associative searches. The k -d tree is defined and examples are given. It is shown to be quite efficient in its storage requirements. A significant advantage of this structure is that a single data structure can handle many types of queries very efficiently. Various utility algorithms are developed; their proven average running times in an n record file are: insertion, O (log n ); deletion of the root, O ( n ( k -1)/ k ); deletion of a random node, O (log n ); and optimization (guarantees logarithmic performance of searches), O ( n log n ). Search algorithms are given for partial match queries with t keys specified [proven maximum running time of O ( n ( k - t )/ k )] and for nearest neighbor queries [empirically observed average running time of O (log n ).] These performances far surpass the best currently known algorithms for these tasks. An algorithm is presented to handle any general intersection query. The main focus of this paper is theoretical. It is felt, however, that k -d trees could be quite useful in many applications, and examples of potential uses are given.
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paper_title: Automatic sorting of multiple unit neuronal signals in the presence of anisotropic and non-Gaussian variability

paper_content:

Neuronal noise sources and systematic variability in the shape of a spike limit the ability to sort multiple unit waveforms recorded from nervous tissue into their single neuron constituents. Here we present a procedure to efficiently sort spikes in the presence of noise that is anisotropic, i.e., dominated by particular frequencies, and whose amplitude distribution may be non-Gaussian, such as occurs when spike waveforms are a function of interspike interval. Our algorithm uses a hierarchical clustering scheme. First, multiple unit records are sorted into an overly large number of clusters by recursive bisection. Second, these clusters are progressively aggregated into a minimal set of putative single units based on both similarities of spike shape as well as the statistics of spike arrival times, such as imposed by the refractory period. We apply the algorithm to waveforms recorded with chronically implanted micro-wire stereotrodes from neocortex of behaving rat. Natural extensions of the algorithm may be used to cluster spike waveforms from records with many input channels, such as those obtained with tetrodes and multiple site optical techniques.
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paper_title: Fast K-dimensional tree algorithms for nearest neighbor search with application to vector quantization encoding

paper_content:

Fast search algorithms are proposed and studied for vector quantization encoding using the K-dimensional (K-d) tree structure. Here, the emphasis is on the optimal design of the K-d tree for efficient nearest neighbor search in multidimensional space under a bucket-Voronoi intersection search framework. Efficient optimization criteria and procedures are proposed for designing the K-d tree, for the case when the test data distribution is available (as in vector quantization application in the form of training data) as well as for the case when the test data distribution is not available and only the Voronoi intersection information is to be used. The criteria and bucket-Voronoi intersection search procedure are studied in the context of vector quantization encoding of speech waveform. They are empirically observed to achieve constant search complexity for O(log N) tree depths and are found to be more efficient in reducing the search complexity. A geometric interpretation is given for the maximum product criterion, explaining reasons for its inefficiency with respect to the optimization criteria. >
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paper_title: Recognition of multiunit neural signals

paper_content:

An essential step in studying nerve cell interaction during information processing is the extracellular microelectrode recording of the electrical activity of groups of adjacent cells. The recording usually contains the superposition of the spike trains produced by a number of neurons in the vicinity of the electrode. It is therefore necessary to correctly classify the signals generated by these different neurons. This problem is considered, and a new classification scheme is developed which does not require human supervision. A learning stage is first applied on the beginning portion of the recording to estimate the typical spike shapes of the different neurons. As for the classification stage, a method is developed which specifically considers the case when spikes overlap temporally. The method minimizes the probability of error, taking into account the statistical properties of the discharges of the neurons. The method is tested on a real recording as well as on synthetic data. >
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paper_title: Detection, classification, and superposition resolution of action potentials in multiunit single-channel recordings by an on-line real-time neural network

paper_content:

Determination of single-unit spike trains from multiunit recordings obtained during extracellular recording has been the focus of many studies over the last two decades. In multiunit recordings, superpositions can occur with high frequency if the firing rates of the neurons are high or correlated, making superposition resolution imperative for accurate spike train determination. In this work, a connectionist neural network (NN) was applied to the spike sorting challenge. A novel training scheme was developed which enabled the NN to resolve some superpositions using single-channel recordings. Simulated multiunit spike trains were constructed from templates and noise segments that were extracted from real extracellular recordings. The simulations were used to determine the performances of the NN and a simple matched template filter (MTF), which was used as a basis for comparison. The network performed as well as the MTF in identifying nonoverlapping spikes, and was significantly better in resolving superpositions and rejecting noise. An on-line, real-time implementation of the NN discriminator, using a high-speed digital signal processor mounted inside an IBM-PC, is now in use in six laboratories.
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paper_title: Tetrodes markedly improve the reliability and yield of multiple single-unit isolation from multi-unit recordings in cat striate cortex

paper_content:

The majority of techniques for separating multiple single-unit spike trains from a multi-unit recording rely on the assumption that different cells exhibit action potentials having unique amplitudes and waveforms. When this assumption fails, due to the similarity of spike shape among different cells or to the presence of complex spikes with declining intra-burst amplitude, these methods lead to errors in classification. In an effort to avoid these errors, the stereotrode (McNaughton et al., 1983) and later the tetrode (O'Keefe and Reece, 1993; Wilson and McNaughton, 1993) recording techniques were developed. Because the latter technique has been applied primarily to the hippocampus, we sought to evaluate its performance in the neocortex. Multi-unit recordings, using single tetrodes, were made at 28 sites in area 17 of 3 anesthetized cats. Neurons were activated with moving bars and square wave gratings. Single units were separated by identification of clusters in 2-D projections of either peak-to-peak amplitude, spike width, spike area, or the 1st versus 2nd principal components of the waveforms recorded on each channel. Using tetrodes, we recorded a total of 154 single cells (mean = 5.4, max = 9). By cross-checking the performance of the tetrode with the stereotrode and electrode, we found that the best of the 6 possible stereotrode pairs and the best of 4 possible electrodes from each tetrode yielded 102 (mean = 3.6, max = 7) and 95 (mean = 3.4, max = 6) cells, respectively. Moreover, we found that the number of cells isolated at each site by the tetrode was greater than the stereotrode or electrode in 16/28 and 28/28 cases, respectively. Thus, both stereotrodes, and particularly electrodes, often lumped 2 or more cells in a single cluster that could be easily separated by the tetrode. We conclude that tetrode recording currently provides the best and most reliable method for the isolation of multiple single units in the neocortex using a single probe.
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paper_title: The stereotrode: A new technique for simultaneous isolation of several single units in the central nervous system from multiple unit records

paper_content:

A new method is described for the recording and discrimination of extracellular action potentials in CNS regions with high cellular packing density or where there is intrinsic variation in action potential amplitude during burst discharge. The method is based on the principle that cells with different ratios of distances from two electrode tips will have different spike-amplitude ratios when recorded on two channels. The two channel amplitude ratio will remain constant regardless of intrinsic variation in the absolute amplitude of the signals. The method has been applied to the rat hippocampal formation, from which up to 5 units have been simultaneously isolated. The construction of the electrodes is simple, relatively fast, and reliable, and their low tip impedances result in excellent signal to noise characteristics.
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paper_title: Blind separation of auditory event-related brain responses into independent components

paper_content:

Averaged event-related potential (ERP) data recorded from the human scalp reveal electroencephalographic (EEG) activity that is reliably time-locked and phase-locked to experimental events. We report here the application of a method based on information theory that decomposes one or more ERPs recorded at multiple scalp sensors into a sum of components with fixed scalp distributions and sparsely activated, maximally independent time courses. Independent component analysis (ICA) decomposes ERP data into a number of components equal to the number of sensors. The derived components have distinct but not necessarily orthogonal scalp projections. Unlike dipole-fitting methods, the algorithm does not model the locations of their generators in the head. Unlike methods that remove second-order correlations, such as principal component analysis (PCA), ICA also minimizes higher-order dependencies. Applied to detected—and undetected—target ERPs from an auditory vigilance experiment, the algorithm derived ten components that decomposed each of the major response peaks into one or more ICA components with relatively simple scalp distributions. Three of these components were active only when the subject detected the targets, three other components only when the target went undetected, and one in both cases. Three additional components accounted for the steady-state brain response to a 39-Hz background click train. Major features of the decomposition proved robust across sessions and changes in sensor number and placement. This method of ERP analysis can be used to compare responses from multiple stimuli, task conditions, and subject states.
---
paper_title: Automatic sorting of multiple unit neuronal signals in the presence of anisotropic and non-Gaussian variability

paper_content:

Neuronal noise sources and systematic variability in the shape of a spike limit the ability to sort multiple unit waveforms recorded from nervous tissue into their single neuron constituents. Here we present a procedure to efficiently sort spikes in the presence of noise that is anisotropic, i.e., dominated by particular frequencies, and whose amplitude distribution may be non-Gaussian, such as occurs when spike waveforms are a function of interspike interval. Our algorithm uses a hierarchical clustering scheme. First, multiple unit records are sorted into an overly large number of clusters by recursive bisection. Second, these clusters are progressively aggregated into a minimal set of putative single units based on both similarities of spike shape as well as the statistics of spike arrival times, such as imposed by the refractory period. We apply the algorithm to waveforms recorded with chronically implanted micro-wire stereotrodes from neocortex of behaving rat. Natural extensions of the algorithm may be used to cluster spike waveforms from records with many input channels, such as those obtained with tetrodes and multiple site optical techniques.
---
paper_title: Recognition of multiunit neural signals

paper_content:

An essential step in studying nerve cell interaction during information processing is the extracellular microelectrode recording of the electrical activity of groups of adjacent cells. The recording usually contains the superposition of the spike trains produced by a number of neurons in the vicinity of the electrode. It is therefore necessary to correctly classify the signals generated by these different neurons. This problem is considered, and a new classification scheme is developed which does not require human supervision. A learning stage is first applied on the beginning portion of the recording to estimate the typical spike shapes of the different neurons. As for the classification stage, a method is developed which specifically considers the case when spikes overlap temporally. The method minimizes the probability of error, taking into account the statistical properties of the discharges of the neurons. The method is tested on a real recording as well as on synthetic data. >
---
paper_title: Automatic sorting of multiple unit neuronal signals in the presence of anisotropic and non-Gaussian variability

paper_content:

Neuronal noise sources and systematic variability in the shape of a spike limit the ability to sort multiple unit waveforms recorded from nervous tissue into their single neuron constituents. Here we present a procedure to efficiently sort spikes in the presence of noise that is anisotropic, i.e., dominated by particular frequencies, and whose amplitude distribution may be non-Gaussian, such as occurs when spike waveforms are a function of interspike interval. Our algorithm uses a hierarchical clustering scheme. First, multiple unit records are sorted into an overly large number of clusters by recursive bisection. Second, these clusters are progressively aggregated into a minimal set of putative single units based on both similarities of spike shape as well as the statistics of spike arrival times, such as imposed by the refractory period. We apply the algorithm to waveforms recorded with chronically implanted micro-wire stereotrodes from neocortex of behaving rat. Natural extensions of the algorithm may be used to cluster spike waveforms from records with many input channels, such as those obtained with tetrodes and multiple site optical techniques.
---
paper_title: Tetrodes markedly improve the reliability and yield of multiple single-unit isolation from multi-unit recordings in cat striate cortex

paper_content:

The majority of techniques for separating multiple single-unit spike trains from a multi-unit recording rely on the assumption that different cells exhibit action potentials having unique amplitudes and waveforms. When this assumption fails, due to the similarity of spike shape among different cells or to the presence of complex spikes with declining intra-burst amplitude, these methods lead to errors in classification. In an effort to avoid these errors, the stereotrode (McNaughton et al., 1983) and later the tetrode (O'Keefe and Reece, 1993; Wilson and McNaughton, 1993) recording techniques were developed. Because the latter technique has been applied primarily to the hippocampus, we sought to evaluate its performance in the neocortex. Multi-unit recordings, using single tetrodes, were made at 28 sites in area 17 of 3 anesthetized cats. Neurons were activated with moving bars and square wave gratings. Single units were separated by identification of clusters in 2-D projections of either peak-to-peak amplitude, spike width, spike area, or the 1st versus 2nd principal components of the waveforms recorded on each channel. Using tetrodes, we recorded a total of 154 single cells (mean = 5.4, max = 9). By cross-checking the performance of the tetrode with the stereotrode and electrode, we found that the best of the 6 possible stereotrode pairs and the best of 4 possible electrodes from each tetrode yielded 102 (mean = 3.6, max = 7) and 95 (mean = 3.4, max = 6) cells, respectively. Moreover, we found that the number of cells isolated at each site by the tetrode was greater than the stereotrode or electrode in 16/28 and 28/28 cases, respectively. Thus, both stereotrodes, and particularly electrodes, often lumped 2 or more cells in a single cluster that could be easily separated by the tetrode. We conclude that tetrode recording currently provides the best and most reliable method for the isolation of multiple single units in the neocortex using a single probe.
---
paper_title: A Comparison of Techniques for Classification of Multiple Neural Signals

paper_content:

A number ofmultiunit neural signal classification techniques are compared in their theoretical separation properties and in their empirical performance in classifying two channel recordings from the ventral nerve cord of the cockroach. The techniques include: the use of amplitude and conduction time measures, template matching, the principal components method, optimal filtering, and maximin discrimination. The noise encountered under different situations is characterized, permitting the comparisons to be made as functions of the experimental conditions. Recommendations are made as to the appropriate use of the techniques.
---

Title: A review of methods for spike sorting: the detection and classification of neural action potentials

Section 1: Introduction
Description 1: Introduce the challenge of detecting neural spike activity, the importance of spike sorting, and the goals of this review.

Section 2: Measuring neural activity
Description 2: Discuss the historical background and the basic techniques and challenges of measuring neural activity with electrodes.

Section 3: The basic problems in spike sorting
Description 3: Illustrate the fundamental issues in spike sorting, including background noise, overlapping spikes, and the identification of different neurons.

Section 4: Threshold detection
Description 4: Describe the simplest method of spike detection using voltage thresholds and discuss its advantages and limitations.

Section 5: Types of detection errors
Description 5: Discuss the common errors in spike detection, such as false positives and false negatives, and misclassification due to overlaps.

Section 6: Detecting and classifying multiple spike shapes
Description 6: Review methods for detecting and classifying spikes of different shapes, starting from simple feature analysis to more complex techniques.

Section 7: Feature analysis
Description 7: Explain the use and selection of features for spike shape characterization and their role in spike sorting.

Section 8: Principal component analysis
Description 8: Discuss the method of principal component analysis (PCA) for automatically choosing features and its application in spike sorting.

Section 9: Cluster analysis
Description 9: Describe methods for automatically determining cluster boundaries and classifying data into clusters.

Section 10: Bayesian clustering and classification
Description 10: Review the probabilistic approach to clustering and classification using Bayesian methods.

Section 11: Automatic removal of outliers
Description 11: Discuss strategies for minimizing the impact of outliers on spike classification.

Section 12: Bayesian classification
Description 12: Explain the advantages of Bayesian classification in quantifying classification certainty and monitoring isolation quality.

Section 13: Clustering in higher dimensions and template matching
Description 13: Describe how clustering and template matching can be extended to higher dimensions for improved classification accuracy.

Section 14: Choosing the number of classes
Description 14: Discuss the challenges and methods for determining the optimal number of classes in clustering approaches.

Section 15: Estimating spike shapes with interpolation
Description 15: Explain methods involving interpolation and regularization to improve spike shape estimation and classification accuracy.

Section 16: Filter-based methods
Description 16: Describe the usage of optimal filtering methods for spike sorting and their comparative accuracy.

Section 17: Overlapping spikes
Description 17: Review methods specifically designed to handle the classification and decomposition of overlapping spikes.

Section 18: Multiple electrodes
Description 18: Explore the use and advantages of multiple electrode recordings for spike sorting.

Section 19: Independent component analysis
Description 19: Discuss the application of independent component analysis (ICA) for separating mixed signals in multi-electrode recordings.

Section 20: Related problems in spike sorting
Description 20: Identify and explain challenges that can affect spike sorting methods, such as burst-firing neurons, electrode drift, non-stationary background noise, and spike alignment.

Section 21: Summary
Description 21: Summarize the review, compare various methods, and discuss the current state and future direction of spike sorting techniques.