Objective. Recent advancements in electrode designs and micro-fabrication technology has allowed existence of microelectrode arrays with hundreds of channels for single-cell recordings. In such electrophysiological recordings, each implanted micro-electrode can record the activities of more than one neuron in its vicinity. Recording the activities of multiple neurons may also be referred to as multiple unit activity. However, for any further analysis, the main goal is to isolate the activity of each recorded neuron and thus called single-unit activity. This process may also be referred to as spike sorting or spike classification. Recent approaches to extract SUA are time consuming, mainly due to the requirement of human intervention at various stages of spike sorting pipeline. Lack of standardization is another drawback of the current available approaches. Therefore, in this study we proposed a standard spike sorter: SpikeDeep-Classifier, a fully automatic spike sorting algorithm. Approach. We proposed a novel spike sorting pipeline, based on a set of supervised and unsupervised learning algorithms. We used supervised, deep learning-based algorithms for extracting meaningful channels and removing background activities (noise) from the extracted channels. We also showed that the process of clustering becomes straight-forward, once the noise/artifact is completely removed from the data. Therefore, in the next stage, we applied a simple clustering algorithm (K-mean) with predefined maximum number of clusters. Lastly, we used a similarity-based criterion to keep distinct clusters and merge similar-looking clusters. Main results. We evaluated our algorithm on a dataset collected from two different species (humans and non-human primates (NHPs)) without any retraining. We also validated our algorithm on two publicly available labeled datasets.
Across many areas, from neural tracking to database entity resolution, manual assessment of clusters by human experts presents a bottleneck in rapid development of scalable and specialized clustering methods. To solve this problem we develop C-FAR, a novel method for Fast, Automated and Reproducible assessment of multiple hierarchical clustering algorithms simultaneously. Our algorithm takes any number of hierarchical clustering trees as input, then strategically queries pairs for human feedback, and outputs an optimal clustering among those nominated by these trees. While it is applicable to large dataset in any domain that utilizes pairwise comparisons for assessment, our flagship application is the cluster aggregation step in spike-sorting, the task of assigning waveforms (spikes) in recordings to neurons. On simulated data of 96 neurons under adverse conditions, including drifting and 25\% blackout, our algorithm produces near-perfect tracking relative to the ground truth. Our runtime scales linearly in the number of input trees, making it a competitive computational tool. These results indicate that C-FAR is highly suitable as a model selection and assessment tool in clustering tasks.
Developing electrophysiological recordings of brain neuronal activity and their analysis provide a basis for exploring the structure of brain function and nervous system investigation. The recorded signals are typically a combination of spikes and noise. High amounts of background noise and possibility of electric signaling recording from several neurons adjacent to the recording site have led scientists to develop neuronal signal processing tools such as spike sorting to facilitate brain data analysis. Spike sorting plays a pivotal role in understanding the electrophysiological activity of neuronal networks. This process prepares recorded data for interpretations of neurons interactions and understanding the overall structure of brain functions. Spike sorting consists of three steps: spike detection, feature extraction, and spike clustering. There are several methods to implement each of spike sorting steps. This paper provides a systematic comparison of various spike sorting sub-techniques applied to real extracellularly recorded data from a rat brain basolateral amygdala. An efficient sorted data resulted from careful choice of spike sorting sub-methods leads to better interpretation of the brain structures connectivity under different conditions, which is a very sensitive concept in diagnosis and treatment of neurological disorders. Here, spike detection is performed by appropriate choice of threshold level via three different approaches. Feature extraction is done through PCA and Kernel PCA methods, which Kernel PCA outperforms. We have applied four different algorithms for spike clustering including K-means, Fuzzy C-means, Bayesian and Fuzzy maximum likelihood estimation. As one requirement of most clustering algorithms, optimal number of clusters is achieved through validity indices for each method. Finally, the sorting results are evaluated using inter-spike interval histograms.
Introduction- Identifying the potential firing patterns following different brain regions under normal and abnormal conditions increases our understanding of events at the level of neural interactions in the brain. The Izhikevich model is one of the simplest biologically plausible models, i.e. capable of capturing the most recognized firing patterns of neurons. This property makes the model efficient in simulating the large-scale networks of neurons. Improving the Izhikevich model for adapting to the neuronal activity of the rat brain with great accuracy would make the model effective for future neural network implementations. Methods- Data sampling from two brain regions, the HIP and BLA, was performed by the extracellular recordings of male rats, and spike sorting was conducted by Plexon offline sorter. Further analyses were performed through NeuroExplorer and MATLAB. To optimize the Izhikevich model parameters, a genetic algorithm was used. The process of comparison in each iteration leads to the survival of better populations until achieving the optimum solution. Results- In the present study, the possible firing patterns of the real single neurons of the HIP and BLA were identified. Additionally, an improved Izhikevich model was achieved. Accordingly, the real neuronal spiking pattern of these regions neurons and the corresponding cases of the Izhikevich neuron spiking pattern were adjusted with great accuracy. Conclusion- This study was conducted to elevate our knowledge of neural interactions in different structures of the brain and accelerate the quality of future large-scale neural network simulations, as well as reducing the modeling complexity. This aim was achievable by performing the improved Izhikevich model, and inserting only the plausible firing patterns, and eliminating unrealistic ones.
Short-and-sparse deconvolution (SaSD) is the problem of extracting localized, recurring motifs in signals with spatial or temporal structure. Variants of this problem arise in applications such as image deblurring, microscopy, neural spike sorting, and more. The problem is challenging in both theory and practice, as natural optimization formulations are nonconvex. Moreover, practical deconvolution problems involve smooth motifs (kernels) whose spectra decay rapidly, resulting in poor conditioning and numerical challenges. This paper is motivated by recent theoretical advances, which characterize the optimization landscape of a particular nonconvex formulation of SaSD. This is used to derive a $provable$ algorithm which exactly solves certain non-practical instances of the SaSD problem. We leverage the key ideas from this theory (sphere constraints, data-driven initialization) to develop a $practical$ algorithm, which performs well on data arising from a range of application areas. We highlight key additional challenges posed by the ill-conditioning of real SaSD problems, and suggest heuristics (acceleration, continuation, reweighting) to mitigate them. Experiments demonstrate both the performance and generality of the proposed method.
Given a continuous-time signal that can be modeled as the superposition of localized, time-shifted events from multiple sources, the goal of Convolutional Dictionary Learning (CDL) is to identify the location of the events--by Convolutional Sparse Coding (CSC)--and learn the template for each source--by Convolutional Dictionary Update (CDU). In practice, because we observe samples of the continuous-time signal on a uniformly-sampled grid in discrete time, classical CSC methods can only produce estimates of the times when the events occur on this grid, which degrades the performance of the CDU. We introduce a CDL framework that significantly reduces the errors arising from performing the estimation in discrete time. Specifically, we construct an expanded dictionary that comprises, not only discrete-time shifts of the templates, but also interpolated variants, obtained by bandlimited interpolation, that account for continuous-time shifts. For CSC, we develop a novel computationally efficient CSC algorithm, termed Convolutional Orthogonal Matching Pursuit with interpolated dictionary (COMP-INTERP). We benchmarked COMP-INTERP to Contiunuous Basis Pursuit (CBP), the state-of-the-art CSC algorithm for estimating off-the-grid events, and demonstrate, on simulated data, that 1) COMP-INTERP achieves a similar level of accuracy, and 2) is two orders of magnitude faster. For CDU, we derive a novel procedure to update the templates given sparse codes that can occur both on and off the discrete-time grid. We also show that 3) dictionary update with the overcomplete dictionary yields more accurate templates. Finally, we apply the algorithms to the spike sorting problem on electrophysiology recording and show their competitive performance.
Spike sorting is a fundamental preprocessing step in neuroscience that is central to access simultaneous but distinct neuronal activities and therefore to better understand the animal or even human brain. But numerical complexity limits studies that require processing large scale datasets in terms of number of electrodes, neurons, spikes and length of the recorded signals. We propose in this work a novel active set algorithm aimed at solving the Lasso for a classical convolutional model. Our algorithm can be implemented efficiently on parallel architecture and has a linear complexity w.r.t. the temporal dimensionality which ensures scaling and will open the door to online spike sorting. We provide theoretical results about the complexity of the algorithm and illustrate it in numerical experiments along with results about the accuracy of the spike recovery and robustness to the regularization parameter.
Determining the positions of neurons in an extracellular recording is useful for investigating functional properties of the underlying neural circuitry. In this work, we present a Bayesian modelling approach for localizing the source of individual spikes on high-density, microelectrode arrays. To allow for scalable inference, we implement our model as a variational autoencoder and perform amortized variational inference. We evaluate our method on both biophysically realistic simulated and real extracellular datasets, demonstrating that it is more accurate than and can improve spike sorting performance over heuristic localization methods such as center of mass.
Probabilistic clustering models (or equivalently, mixture models) are basic building blocks in countless statistical models and involve latent random variables over discrete spaces. For these models, posterior inference methods can be inaccurate and/or very slow. In this work we introduce deep network architectures trained with labeled samples from any generative model of clustered datasets. At test time, the networks generate approximate posterior samples of cluster labels for any new dataset of arbitrary size. We develop two complementary approaches to this task, requiring either O(N) or O(K) network forward passes per dataset, where N is the dataset size and K the number of clusters. Unlike previous approaches, our methods sample the labels of all the data points from a well-defined posterior, and can learn nonparametric Bayesian posteriors since they do not limit the number of mixture components. As a scientific application, we present a novel approach to neural spike sorting for high-density multielectrode arrays.
Understanding the coordinated activity underlying brain computations requires large-scale, simultaneous recordings from distributed neuronal structures at a cellular-level resolution. One major hurdle to design high-bandwidth, high-precision, large-scale neural interfaces lies in the formidable data streams that are generated by the recorder chip and need to be online transferred to a remote computer. The data rates can require hundreds to thousands of I/O pads on the recorder chip and power consumption on the order of Watts for data streaming alone. We developed a deep learning-based compression model to reduce the data rate of multichannel action potentials. The proposed model is built upon a deep compressive autoencoder (CAE) with discrete latent embeddings. The encoder is equipped with residual transformations to extract representative features from spikes, which are mapped into the latent embedding space and updated via vector quantization (VQ). The decoder network reconstructs spike waveforms from the quantized latent embeddings. Experimental results show that the proposed model consistently outperforms conventional methods by achieving much higher compression ratios (20-500x) and better or comparable reconstruction accuracies. Testing results also indicate that CAE is robust against a diverse range of imperfections, such as waveform variation and spike misalignment, and has minor influence on spike sorting accuracy. Furthermore, we have estimated the hardware cost and real-time performance of CAE and shown that it could support thousands of recording channels simultaneously without excessive power/heat dissipation. The proposed model can reduce the required data transmission bandwidth in large-scale recording experiments and maintain good signal qualities. The code of this work has been made available at https://github.com/tong-wu-umn/spike-compression-autoencoder
Given a convolutional dictionary underlying a set of observed signals, can a carefully designed auto-encoder recover the dictionary in the presence of noise? We introduce an auto-encoder architecture, termed constrained recurrent sparse auto-encoder (CRsAE), that answers this question in the affirmative. Given an input signal and an approximate dictionary, the encoder finds a sparse approximation using FISTA. The decoder reconstructs the signal by applying the dictionary to the output of the encoder. The encoder and decoder in CRsAE parallel the sparse-coding and dictionary update steps in optimization-based alternating-minimization schemes for dictionary learning. As such, the parameters of the encoder and decoder are not independent, a constraint which we enforce for the first time. We derive the back-propagation algorithm for CRsAE. CRsAE is a framework for blind source separation that, only knowing the number of sources (dictionary elements), and assuming sparsely-many can overlap, is able to separate them. We demonstrate its utility in the context of spike sorting, a source separation problem in computational neuroscience. We demonstrate the ability of CRsAE to recover the underlying dictionary and characterize its sensitivity as a function of SNR.
Cluster analysis faces two problems in high dimensions: first, the `curse of dimensionality' that can lead to overfitting and poor generalization performance; and second, the sheer time taken for conventional algorithms to process large amounts of high-dimensional data. In many applications, only a small subset of features provide information about the cluster membership of any one data point, however this informative feature subset may not be the same for all data points. Here we introduce a `Masked EM' algorithm for fitting mixture of Gaussians models in such cases. We show that the algorithm performs close to optimally on simulated Gaussian data, and in an application of `spike sorting' of high channel-count neuronal recordings.
We introduce the functional mean-shift algorithm, an iterative algorithm for estimating the local modes of a surrogate density from functional data. We show that the algorithm can be used for cluster analysis of functional data. We propose a test based on the bootstrap for the significance of the estimated local modes of the surrogate density. We present two applications of our methodology. In the first application, we demonstrate how the functional mean-shift algorithm can be used to perform spike sorting, i.e. cluster neural activity curves. In the second application, we use the functional mean-shift algorithm to distinguish between original and fake signatures.
Spike sorting is a fundamental preprocessing step for many neuroscience studies which rely on the analysis of spike trains. In this paper, we present two unsupervised spike sorting algorithms based on discriminative subspace learning. The first algorithm simultaneously learns the discriminative feature subspace and performs clustering. It uses histogram of features in the most discriminative projection to detect the number of neurons. The second algorithm performs hierarchical divisive clustering that learns a discriminative 1-dimensional subspace for clustering in each level of the hierarchy until achieving almost unimodal distribution in the subspace. The algorithms are tested on synthetic and in-vivo data, and are compared against two widely used spike sorting methods. The comparative results demonstrate that our spike sorting methods can achieve substantially higher accuracy in lower dimensional feature space, and they are highly robust to noise. Moreover, they provide significantly better cluster separability in the learned subspace than in the subspace obtained by principal component analysis or wavelet transform.
Diffusion-weighted magnetic resonance imaging (DWI) and fiber tractography are the only methods to measure the structure of the white matter in the living human brain. The diffusion signal has been modelled as the combined contribution from many individual fascicles of nerve fibers passing through each location in the white matter. Typically, this is done via basis pursuit, but estimation of the exact directions is limited due to discretization. The difficulties inherent in modeling DWI data are shared by many other problems involving fitting non-parametric mixture models. Ekanadaham et al. proposed an approach, continuous basis pursuit, to overcome discretization error in the 1-dimensional case (e.g., spike-sorting). Here, we propose a more general algorithm that fits mixture models of any dimensionality without discretization. Our algorithm uses the principles of L2-boost, together with refitting of the weights and pruning of the parameters. The addition of these steps to L2-boost both accelerates the algorithm and assures its accuracy. We refer to the resulting algorithm as elastic basis pursuit, or EBP, since it expands and contracts the active set of kernels as needed. We show that in contrast to existing approaches to fitting mixtures, our boosting framework (1) enables the selection of the optimal bias-variance tradeoff along the solution path, and (2) scales with high-dimensional problems. In simulations of DWI, we find that EBP yields better parameter estimates than a non-negative least squares (NNLS) approach, or the standard model used in DWI, the tensor model, which serves as the basis for diffusion tensor imaging (DTI). We demonstrate the utility of the method in DWI data acquired in parts of the brain containing crossings of multiple fascicles of nerve fibers.
We describe a suite of validation metrics that assess the credibility of a given automatic spike sorting algorithm applied to a given electrophysiological recording, when ground-truth is unavailable. By rerunning the spike sorter two or more times, the metrics measure stability under various perturbations consistent with variations in the data itself, making no assumptions about the noise model, nor about the internal workings of the sorting algorithm. Such stability is a prerequisite for reproducibility of results. We illustrate the metrics on standard sorting algorithms for both in vivo and ex vivo recordings. We believe that such metrics could reduce the significant human labor currently spent on validation, and should form an essential part of large-scale automated spike sorting and systematic benchmarking of algorithms.
Approximate inference in high-dimensional, discrete probabilistic models is a central problem in computational statistics and machine learning. This paper describes discrete particle variational inference (DPVI), a new approach that combines key strengths of Monte Carlo, variational and search-based techniques. DPVI is based on a novel family of particle-based variational approximations that can be fit using simple, fast, deterministic search techniques. Like Monte Carlo, DPVI can handle multiple modes, and yields exact results in a well-defined limit. Like unstructured mean-field, DPVI is based on optimizing a lower bound on the partition function; when this quantity is not of intrinsic interest, it facilitates convergence assessment and debugging. Like both Monte Carlo and combinatorial search, DPVI can take advantage of factorization, sequential structure, and custom search operators. This paper defines DPVI particle-based approximation family and partition function lower bounds, along with the sequential DPVI and local DPVI algorithm templates for optimizing them. DPVI is illustrated and evaluated via experiments on lattice Markov Random Fields, nonparametric Bayesian mixtures and block-models, and parametric as well as non-parametric hidden Markov models. Results include applications to real-world spike-sorting and relational modeling problems, and show that DPVI can offer appealing time/accuracy trade-offs as compared to multiple alternatives.
Spikes in the membrane electrical potentials of neurons play a major role in the functioning of nervous systems of animals. Obtaining the spikes from different neurons has been a challenging problem for decades. Several schemes have been proposed for spike sorting to isolate the spikes of individual neurons from electrical recordings in extracellular media. However, there is much scope for improvement in the accuracies obtained using the prevailing methods of spike sorting. To determine more effective spike sorting strategies using well known methods, we compared different types of signal features and techniques for dimensionality reduction in feature space. We tried to determine an optimum or near optimum feature extraction and dimensionality reduction methods and an optimum or near optimum number of features for spike sorting. We assessed relative performance of well known methods on simulated recordings specially designed for development and benchmarking of spike sorting schemes, with varying number of spike classes and the well established method of $k$-means clustering of selected features. We found that almost all well known methods performed quite well. Nevertheless, from spike waveforms of 64 samples, sampled at 24 kHz, using principal component analysis (PCA) to select around 46 to 55 features led to the better spike sorting performance than most other methods (Wilcoxon signed rank sum test, $p < 0.001$).
In this paper authors have presented a power efficient scheme for implementing a spike sorting module. Spike sorting is an important application in the field of neural signal acquisition for implantable biomedical systems whose function is to map the Neural-spikes (N-spikes) correctly to the neurons from which it originates. The accurate classification is a pre-requisite for the succeeding systems needed in Brain-Machine-Interfaces (BMIs) to give better performance. The primary design constraint to be satisfied for the spike sorter module is low power with good accuracy. There lies a trade-off in terms of power consumption between the on-chip and off-chip training of the N-spike features. In the former case care has to be taken to make the computational units power efficient whereas in the later the data rate of wireless transmission should be minimized to reduce the power consumption due to the transceivers. In this work a 2-step shared training scheme involving a K-means sorter and a Spiking Neural Network (SNN) is elaborated for on-chip training and classification. Also, a low power SNN classifier scheme using memristive crossbar type architecture is compared with a fully digital implementation. The advantage of the former classifier is that it is power efficient while providing comparable accuracy as that of the digital implementation due to the robustness of the SNN training algorithm which has a good tolerance for variation in memristance.