Kalman filter mixture model for spike sorting of non-stationary data

Nonstationarity in extracellular recordings can present a major problem during in vivo experiments. In this paper we present automatic methods for tracking time-varying spike shapes. Our algorithm is based on a computationally efficient Kalman filter model; the recursive nature of this model allows for on-line implementation of the method. The model parameters can be estimated using a standard expectation-maximization approach. In addition, refractory effects may be incorporated via closely related hidden Markov model techniques. We present an analysis of the algorithm's performance on both simulated and real data.     

Spike sorting with hidden Markov models

The ability to detect and sort overlapping spike waveforms in extracellular recordings is key to studies of neural coding at high spatial and temporal resolution. Most spike-sorting algorithms are based on initial spike detection (e.g. by a voltage threshold) and subsequent waveform classification. Much effort has been devoted to the clustering step, despite the fact that conservative spike detection is notoriously difficult in low signal-to-noise conditions and often entails many spike misses. Hidden Markov models (HMMs) can serve as generative models for continuous extracellular data records. These models naturally combine the spike detection and classification steps into a single computational procedure. They unify the advantages of independent component analysis (ICA) and overlap-search algorithms because they blindly perform source separation even in cases where several neurons are recorded on a single electrode. We apply HMMs to artificially generated data and to extracellular signals recorded with glass electrodes. We show that in comparison with state-of-art spike-sorting algorithms, HMM-based spike sorting exhibits a comparable number of false positive spike classifications but many fewer spike misses.     

Spike sorting based on discrete wavelet transform coefficients

Using the novel mathematical technique known as wavelet analysis, a new method (WSC) is presented to sort spikes according to a decomposition of neural signals in the time-frequency space. The WSC method is implemented by a pyramidal algorithm that acts upon neural signals as a bank of quadrature mirror filters. This algorithm is clearly explained and an overview of the mathematical background of wavelet analysis is given. An artificial spike train, especially designed to test the specificity and sensibility of sorting procedures, was used to assess the performance of the WSC method as well as of methods based on principal component analysis (PCA) and reduced feature set (RFS). The WSC method outperformed the other two methods. Its superior performance was largely due to the fact that spike profiles that could not be separated by previous methods (because of the similarity of their temporal profile and the masking action of noise) were separable by the WSC method. The WSC method is particularly noise resistant, as it implicitly eliminates the irrelevant information contained in the noise frequency range. But the main advantage of the WSC method is its use of parameters that describe the joint time-frequency localization of spike features to build a fast and unspecialized pattern recognition procedure.     

Robust Bayesian clustering.

A new variational Bayesian learning algorithm for Student-t mixture models is introduced. This algorithm leads to (i) robust density estimation, (ii) robust clustering and (iii) robust automatic model selection. Gaussian mixture models are learning machines which are based on a divide-and-conquer approach. They are commonly used for density estimation and clustering tasks, but are sensitive to outliers. The Student-t distribution has heavier tails than the Gaussian distribution and is therefore less sensitive to any departure of the empirical distribution from Gaussianity. As a consequence, the Student-t distribution is suitable for constructing robust mixture models. In this work, we formalize the Bayesian Student-t mixture model as a latent variable model in a different way from Svensén and Bishop [Svensén, M., & Bishop, C. M. (2005). Robust Bayesian mixture modelling. Neurocomputing, 64, 235-252]. The main difference resides in the fact that it is not necessary to assume a factorized approximation of the posterior distribution on the latent indicator variables and the latent scale variables in order to obtain a tractable solution. Not neglecting the correlations between these unobserved random variables leads to a Bayesian model having an increased robustness. Furthermore, it is expected that the lower bound on the log-evidence is tighter. Based on this bound, the model complexity, i.e. the number of components in the mixture, can be inferred with a higher confidence.     

Spike detection II: automatic, perception-based detection and clustering.

OBJECTIVES: We developed perception-based spike detection and clustering algorithms. METHODS: The detection algorithm employs a novel, multiple monotonic neural network (MMNN). It is tested on two short-duration EEG databases containing 2400 spikes from 50 epilepsy patients and 10 control subjects. Previous studies are compared for database difficulty and reliability and algorithm accuracy. Automatic grouping of spikes via hierarchical clustering (using topology and morphology) is visually compared with hand marked grouping on a single record. RESULTS: The MMNN algorithm is found to operate close to the ability of a human expert while alleviating problems related to overtraining. The hierarchical and hand marked spike groupings are found to be strikingly similar. CONCLUSIONS: An automatic detection algorithm need not be as accurate as a human expert to be clinically useful. A user interface that allows the neurologist to quickly delete artifacts and determine whether there are multiple spike generators is sufficient.     

Spike sorting based upon machine learning algorithms (SOMA)

We have developed a spike sorting method, using a combination of various machine learning algorithms, to analyse electrophysiological data and automatically determine the number of sampled neurons from an individual electrode, and discriminate their activities. We discuss extensions to a standard unsupervised learning algorithm (Kohonen), as using a simple application of this technique would only identify a known number of clusters. Our extra techniques automatically identify the number of clusters within the dataset, and their sizes, thereby reducing the chance of misclassification. We also discuss a new pre-processing technique, which transforms the data into a higher dimensional feature space revealing separable clusters. Using principal component analysis (PCA) alone may not achieve this. Our new approach appends the features acquired using PCA with features describing the geometric shapes that constitute a spike waveform. To validate our new spike sorting approach, we have applied it to multi-electrode array datasets acquired from the rat olfactory bulb, and from the sheep infero-temporal cortex, and using simulated data. The SOMA sofware is available at http://www.sussex.ac.uk/Users/pmh20/spikes.     

Interactive data analysis and clustering of genomic data

In this work a new clustering approach is used to explore a well- known dataset [Whitfield, M. L., Sherlock, G., Saldanha, A. J., Murray, J. I., Ball, C. A., Alexander, K. E., et al. (2002). Molecular biology of the cell: Vol. 13. Identification of genes periodically expressed in the human cell cycle and their expression in tumors (pp. 1977–2000)] of time dependent gene expression profiles in human cell cycle. The approach followed by us is realized with a multi-step procedure: after preprocessing, parameters are chosen by using data sub sampling and stability measures; for any used model, several different clustering solutions are obtained by random initialization and are selected basing on a similarity measure and a figure of merit; finally the selected solutions are tuned by evaluating a reliability measure. Three different models for clustering, K-means, Self-organizing Maps and Probabilistic Principal Surfaces are compared. Comparative analysis is carried out by considering: similarity between best solutions obtained through the three methods, absolute distortion value and validation through the use of Gene Ontology (GO) annotations. The GO annotations are used to give significance to the obtained clusters and to compare the results with those obtained in the work cited above.     

Spike sorting based on automatic template reconstruction with a partial solution to the overlapping problem

A new method for spike sorting is proposed which partly solves the overlapping problem. Principal component analysis and subtractive clustering techniques are used to estimate the number of neurons contributing to multi-unit recording. Spike templates (i.e. waveforms) are reconstructed according to the clustering results. A template-matching procedure is then performed. Firstly all temporally displaced templates are compared with the spike event to find the best-fitting template that yields the minimum residue variance. If the residue passes the chi(2)-test, the matching procedure stops and the spike event is classified as the best-fitting template. Otherwise the spike event may be an overlapping waveform. The procedure is then repeated with all possible combinations of two templates, three templates, etc. Once one combination is found, which yields the minimum residue variance among the combinations of the same number of component templates and makes the residue pass the chi(2)-test, the matching procedure stops. It is unnecessary to check the remaining combinations of more templates. Consequently, the computational effort is reduced and the over-fitting problem can be partly avoided. A simulated spike train was used to assess the performance of the proposed method, which was also applied to a real recording of chicken retina ganglion cells.     

Automated spike sorting using density grid contour clustering and subtractive waveform decomposition

In multiple cell recordings identifying the number of neurons and assigning each action potential to a particular source, commonly referred to as 'spike sorting', is a highly non-trivial problem. Density grid contour clustering provides a computationally efficient way of locating high-density regions of arbitrary shape in low-dimensional space. When applied to waveforms projected onto their first two principal components, the algorithm allows the extraction of templates that provide high-dimensional reference points that can be used to perform accurate spike sorting. Template matching using subtractive waveform decomposition can locate these templates in waveform samples despite the influence of noise, spurious threshold crossing and waveform overlap. Tests with a large synthetic dataset incorporating realistic challenges faced during spike sorting (including overlapping and phase-shifted spikes) reveal that this strategy can consistently yield results with less than 6% false positives and false negatives (and less than 2% for high signal-to-noise ratios) at processing speeds exceeding those previously reported for similar algorithms by more than an order of magnitude.     

Unsupervised clustering algorithm for N-dimensional data

Cluster analysis is an important tool for classifying data. Established techniques include k-means and k-median cluster analysis. However, these methods require the user to provide a priori estimations of the number of clusters and their approximate location in the parameter space. Often these estimations can be made based on some prior understanding about the nature of the data. Alternatively, the user makes these estimations based on visualization of the data. However, the latter is problematic in data sets with large numbers of dimensions. Presented here is an algorithm that can automatically provide these estimates without human intervention based on the inherent structure of the data set. The number of dimensions does not limit it.     

Model-based clustering of meta-analytic functional imaging data

We present a method for the analysis of meta-analytic functional imaging data. It is based on Activation Likelihood Estimation (ALE) and subsequent model-based clustering using Gaussian mixture models, expectation-maximization (EM) for model fitting, and the Bayesian Information Criterion (BIC) for model selection. Our method facilitates the clustering of activation maxima from previously performed imaging experiments in a hierarchical fashion. Regions with a high concentration of activation coordinates are first identified using ALE. Activation coordinates within these regions are then subjected to model-based clustering for a more detailed cluster analysis. We demonstrate the usefulness of the method in a meta-analysis of 26 fMRI studies investigating the well-known Stroop paradigm.     

Spike detection: Inter-reader agreement and a statistical Turing test on a large data set

Objective

Compare the spike detection performance of three skilled humans and three computer algorithms.

New methods of time series analysis of non-stationary EEG data: eigenstructure decompositions of time varying autoregressions.

OBJECTIVE: Those who analyze EEG data require quantitative techniques that can be validly applied to time series exhibiting ranges of non-stationary behavior. Our objective is to introduce a new analysis technique based on formal non-stationary time series models. This novel method provides a decomposition of the time series into a set of 'latent' components with time-varying frequency content. The identification of these components can lead to practical insights and quantitative comparisons of changes in frequency structure over time in EEG time series. METHODS: The technique begins with the development of time-varying autoregressive models of the EEG time series. Such models have been previously used in EEG analysis but we extend their utility by the introduction of eigenstructure decomposition methods. We review the basis and implementation of this method and report on the analysis of two channel EEG data recorded during 3 generalized tonic-clonic seizures induced in an individual as part of a course of electroconvulsive therapy for major depression. RESULTS: This technique identified EEG patterns consistent with prior reports. In addition, it quantified a decrease in dominant frequency content over the seizures and suggested for the first time that this decrease is continuous across the end of the seizures. The analysis also suggested that the seizure EEG may be best modeled by the combination of multiple processes, whereas post-ictally there appears to be one dominant process. There was also preliminary evidence that these features may differ as a function of ECT therapeutic effectiveness. CONCLUSIONS: Eigenanalysis of time-varying autoregressive models has promise for improving the analysis of EEG time series.     

Discrete dynamic Bayesian network analysis of fMRI data

We examine the efficacy of using discrete Dynamic Bayesian Networks (dDBNs), a data-driven modeling technique employed in machine learning, to identify functional correlations among neuroanatomical regions of interest. Unlike many neuroimaging analysis techniques, this method is not limited by linear and/or Gaussian noise assumptions. It achieves this by modeling the time series of neuroanatomical regions as discrete, as opposed to continuous, random variables with multinomial distributions. We demonstrated this method using an fMRI dataset collected from healthy and demented elderly subjects (Buckner, et al., 2000: J Cogn Neurosci 12:24-34) and identify correlates based on a diagnosis of dementia. The results are validated in three ways. First, the elicited correlates are shown to be robust over leave-one-out cross-validation and, via a Fourier bootstrapping method, that they were not likely due to random chance. Second, the dDBNs identified correlates that would be expected given the experimental paradigm. Third, the dDBN's ability to predict dementia is competitive with two commonly employed machine-learning classifiers: the support vector machine and the Gaussian naive Bayesian network. We also verify that the dDBN selects correlates based on non-linear criteria. Finally, we provide a brief analysis of the correlates elicited from Buckner et al.'s data that suggests that demented elderly subjects have reduced involvement of entorhinal and occipital cortex and greater involvement of the parietal lobe and amygdala in brain activity compared with healthy elderly (as measured via functional correlations among BOLD measurements). Limitations and extensions to the dDBN method are discussed.     

S-TREE: self-organizing trees for data clustering and online vector quantization.

This paper introduces S-TREE (Self-Organizing Tree), a family of models that use unsupervised learning to construct hierarchical representations of data and online tree-structured vector quantizers. The S-TREE1 model, which features a new tree-building algorithm, can be implemented with various cost functions. An alternative implementation, S-TREE2, which uses a new double-path search procedure, is also developed. The performance of the S-TREE algorithms is illustrated with data clustering and vector quantization examples, including a Gauss-Markov source benchmark and an image compression application. S-TREE performance on these tasks is compared with the standard tree-structured vector quantizer (TSVQ) and the generalized Lloyd algorithm (GLA). The image reconstruction quality with S-TREE2 approaches that of GLA while taking less than 10% of computer time. S-TREE1 and S-TREE2 also compare favorably with the standard TSVQ in both the time needed to create the codebook and the quality of image reconstruction.     

Partial distortion entropy maximization for online data clustering

Competitive learning neural networks are regarded as a powerful tool for online data clustering to represent a non-stationary probability distribution with a fixed number of weight vectors. One difficulty in practical applications of competitive learning neural networks to online data clustering is that most of them require heuristically-predetermined threshold parameters for balancing a trade-off between convergence accuracy, i.e. error minimization performance, and speed of adaptation to the changes in source statistics. Although adaptation acceleration is achievable by relocating a “useless” node so that it becomes useful, excessive relocation often disturbs error minimization. Hence, both of the adaptation speed and the error minimization performance sensitively depend on threshold parameters to determine whether a node should be relocated or not. In general, it is difficult to know adequate threshold parameters a priori. This paper proposes a novel criterion for decision making of node relocation without heuristically predetermined thresholds. According to the proposed criterion, a node is relocated only if the relocation task improves partial distortion entropy, which is an online optimality metric reliable from the viewpoint of error minimization. Hence, node relocation is carried out without disturbing error minimization. As a result, both quick adaptation and error minimization are simultaneously accomplished without any carefully predefined parameters. Experimental results clarify the validity of the proposed criterion. Competitive learning with the criterion is clearly superior to other representative algorithms in terms of both quick adaptation and error minimization performance.     

Self-organizing maps and clustering methods for matrix data.

In this contribution we present extensions of the Self Organizing Map and clustering methods for the categorization and visualization of data which are described by matrices rather than feature vectors. Rows and Columns of these matrices correspond to objects which may or may not belong to the same set, and the entries in the matrix describe the relationships between them. The clustering task is formulated as an optimization problem: Model complexity is minimized under the constraint, that the error one makes when reconstructing objects from class information is fixed, usually to a small value. The data is then visualized with help of modified Self Organizing Maps methods, i.e. by constructing a neighborhood preserving non-linear projection into a low-dimensional "map-space". Grouping of data objects is done using an improved optimization technique, which combines deterministic annealing with "growing" techniques. Performance of the new methods is evaluated by applying them to two kinds of matrix data: (i) pairwise data, where row and column objects are from the same set and where matrix elements denote dissimilarity values and (ii) co-occurrence data, where row and column objects are from different sets and where the matrix elements describe how often object pairs occur.     

Complex Spike Wars: a New Hope

The climbing fiber–Purkinje cell circuit is one of the most powerful and highly conserved in the central nervous system. Climbing fibers exert a powerful excitatory action that results in a complex spike in Purkinje cells and normal functioning of the cerebellum depends on the integrity of climbing fiber–Purkinje cell synapse. Over the last 50 years, multiple hypotheses have been put forward on the role of the climbing fibers and complex spikes in cerebellar information processing and motor control. Central to these theories is the nature of the interaction between the low-frequency complex spike discharge and the high-frequency simple spike firing of Purkinje cells. This review examines the major hypotheses surrounding the action of the climbing fiber–Purkinje cell projection, discussing both supporting and conflicting findings. The review describes newer findings establishing that climbing fibers and complex spikes provide predictive signals about movement parameters and that climbing fiber input controls the encoding of behavioral information in the simple spike firing of Purkinje cells. Finally, we propose the dynamic encoding hypothesis for complex spike function that strives to integrate established and newer findings.     

Spectral representation--analyzing single-unit activity in extracellularly recorded neuronal data without spike sorting

One step in the conventional analysis of extracellularly recorded neuronal data is spike sorting, which separates electrical signal into action potentials from different neurons. Because spike sorting involves human judgment, it can be subjective and time intensive, particularly for large sets of neurons. Here we propose a simple, automated way to construct alternative representations of neuronal activity, called spectral representation (SR). In this approach, neuronal spikes are mapped to a discrete space of spike waveform features and time. Spectral representation enables us to find single-unit stimulus-related changes in neuronal activity without spike sorting. We tested the ability of this method to predict stimuli using both simulated data and experimental data from an auditory mapping study in anesthetized marmoset monkeys. We find that our approach produces more accurate classification of stimuli than spike-sorted data for both simulated and experimental conditions. Furthermore, this method lends itself to automated analysis of extracellularly recorded neuronal ensembles. Additionally, we suggest ways in which these representations can be readily extended to assist in spike sorting and the evaluation of single-neuron peri-stimulus time histograms.     

Bayesian model selection for mining mass spectrometry data.

A procedure for learning a probabilistic model from mass spectrometry data that accounts for domain specific noise and mitigates the complexity of Bayesian structure learning is presented. We evaluate the algorithm by applying the learned probabilistic model to microorganism detection from mass spectrometry data.