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A model-based spike sorting algorithm for removing correlation artifacts in multi-neuron recordings.

Pillow JW, Shlens J, Chichilnisky EJ, Simoncelli EP - PLoS ONE (2013)

Bottom Line: Combining this measurement model with a Bernoulli prior over binary spike trains yields a posterior distribution for spikes given the recorded data.We introduce a greedy algorithm to maximize this posterior that we call "binary pursuit".The algorithm allows modest variability in spike waveforms and recovers spike times with higher precision than the voltage sampling rate.

View Article: PubMed Central - PubMed

Affiliation: Center for Perceptual Systems, Department of Psychology and Section of Neurobiology, The University of Texas at Austin, Austin, Texas, USA. pillow@mail.utexas.edu

ABSTRACT
We examine the problem of estimating the spike trains of multiple neurons from voltage traces recorded on one or more extracellular electrodes. Traditional spike-sorting methods rely on thresholding or clustering of recorded signals to identify spikes. While these methods can detect a large fraction of the spikes from a recording, they generally fail to identify synchronous or near-synchronous spikes: cases in which multiple spikes overlap. Here we investigate the geometry of failures in traditional sorting algorithms, and document the prevalence of such errors in multi-electrode recordings from primate retina. We then develop a method for multi-neuron spike sorting using a model that explicitly accounts for the superposition of spike waveforms. We model the recorded voltage traces as a linear combination of spike waveforms plus a stochastic background component of correlated Gaussian noise. Combining this measurement model with a Bernoulli prior over binary spike trains yields a posterior distribution for spikes given the recorded data. We introduce a greedy algorithm to maximize this posterior that we call "binary pursuit". The algorithm allows modest variability in spike waveforms and recovers spike times with higher precision than the voltage sampling rate. This method substantially corrects cross-correlation artifacts that arise with conventional methods, and substantially outperforms clustering methods on both real and simulated data. Finally, we develop diagnostic tools that can be used to assess errors in spike sorting in the absence of ground truth.

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Geometric picture of failures in clustering-based spike sorting, with multi-electrode retinal data [29].(A) Synchronous spike waveforms on a single extracellular electrode from two different neurons (black and red), which sum linearly to form a new waveform (blue) when these neurons fire synchronously. (B) Spike waveforms from these same two neurons projected into a two-dimensional linear feature space. Each point in this space corresponds to a single recorded waveform. Black and red vectors indicate the waveforms shown in (A), and the corresponding clusters of colored points around each vector indicate the samples that were assigned to each neuron. Synchronous spikes from these two neurons give rise to voltage waveforms that lie near the sum of these two vectors (blue vector), and these points (gray) are generally discarded as outliers. (C–D) More generally, overlapping spikes with different temporal offsets produce different waveforms (example, with second waveform offset −0.45 ms relative to first, shown in (C). These summed waveforms lie along a trajectory in the feature space, parameterized by their temporal offset. Several examples (blue points) are shown in (D), along with their associated waveforms.
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pone-0062123-g001: Geometric picture of failures in clustering-based spike sorting, with multi-electrode retinal data [29].(A) Synchronous spike waveforms on a single extracellular electrode from two different neurons (black and red), which sum linearly to form a new waveform (blue) when these neurons fire synchronously. (B) Spike waveforms from these same two neurons projected into a two-dimensional linear feature space. Each point in this space corresponds to a single recorded waveform. Black and red vectors indicate the waveforms shown in (A), and the corresponding clusters of colored points around each vector indicate the samples that were assigned to each neuron. Synchronous spikes from these two neurons give rise to voltage waveforms that lie near the sum of these two vectors (blue vector), and these points (gray) are generally discarded as outliers. (C–D) More generally, overlapping spikes with different temporal offsets produce different waveforms (example, with second waveform offset −0.45 ms relative to first, shown in (C). These summed waveforms lie along a trajectory in the feature space, parameterized by their temporal offset. Several examples (blue points) are shown in (D), along with their associated waveforms.

Mentions: Clustering methods are generally successful when each neuron's spike waveform is sufficiently distinct from background noise and from those of other neurons, or when spikes occur primarily in isolation. However, these methods generally fail when spike waveforms from multiple neurons are superimposed [4], [10], [11], [30]. Specifically, if two neurons fire synchronously, the resulting voltage trace will resemble the sum of the individual waveforms [31]. The sum of the two spike waveforms forms a pattern that is distinct from the waveforms considered separately, and clustering methods will either assign the composite spike waveform to a distinct cluster–thus “hallucinating” a fictitious neuron–or discard the observation as an outlier that does not match any neuron. Figure 1 demonstrates the systematic failure to identify the near-synchronous spikes of two neurons recorded in primate retina [29], [32]. Figure 1A–B shows the superposition of synchronous spike waveforms, which a clustering method fails to identify. The problem is not limited to synchronous spikes, as shown in Fig. 1 C–D: any spikes whose waveforms exhibit non-zero dot product can give rise to an unrecognizable composite waveforms when superimposed. The feature-space trajectory of overlapping spikes can trace out regions of feature space distinct from the waveforms of each constituent neuron. These points will also typically be discarded as outliers by traditional clustering methods.


A model-based spike sorting algorithm for removing correlation artifacts in multi-neuron recordings.

Pillow JW, Shlens J, Chichilnisky EJ, Simoncelli EP - PLoS ONE (2013)

Geometric picture of failures in clustering-based spike sorting, with multi-electrode retinal data [29].(A) Synchronous spike waveforms on a single extracellular electrode from two different neurons (black and red), which sum linearly to form a new waveform (blue) when these neurons fire synchronously. (B) Spike waveforms from these same two neurons projected into a two-dimensional linear feature space. Each point in this space corresponds to a single recorded waveform. Black and red vectors indicate the waveforms shown in (A), and the corresponding clusters of colored points around each vector indicate the samples that were assigned to each neuron. Synchronous spikes from these two neurons give rise to voltage waveforms that lie near the sum of these two vectors (blue vector), and these points (gray) are generally discarded as outliers. (C–D) More generally, overlapping spikes with different temporal offsets produce different waveforms (example, with second waveform offset −0.45 ms relative to first, shown in (C). These summed waveforms lie along a trajectory in the feature space, parameterized by their temporal offset. Several examples (blue points) are shown in (D), along with their associated waveforms.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3643981&req=5

pone-0062123-g001: Geometric picture of failures in clustering-based spike sorting, with multi-electrode retinal data [29].(A) Synchronous spike waveforms on a single extracellular electrode from two different neurons (black and red), which sum linearly to form a new waveform (blue) when these neurons fire synchronously. (B) Spike waveforms from these same two neurons projected into a two-dimensional linear feature space. Each point in this space corresponds to a single recorded waveform. Black and red vectors indicate the waveforms shown in (A), and the corresponding clusters of colored points around each vector indicate the samples that were assigned to each neuron. Synchronous spikes from these two neurons give rise to voltage waveforms that lie near the sum of these two vectors (blue vector), and these points (gray) are generally discarded as outliers. (C–D) More generally, overlapping spikes with different temporal offsets produce different waveforms (example, with second waveform offset −0.45 ms relative to first, shown in (C). These summed waveforms lie along a trajectory in the feature space, parameterized by their temporal offset. Several examples (blue points) are shown in (D), along with their associated waveforms.
Mentions: Clustering methods are generally successful when each neuron's spike waveform is sufficiently distinct from background noise and from those of other neurons, or when spikes occur primarily in isolation. However, these methods generally fail when spike waveforms from multiple neurons are superimposed [4], [10], [11], [30]. Specifically, if two neurons fire synchronously, the resulting voltage trace will resemble the sum of the individual waveforms [31]. The sum of the two spike waveforms forms a pattern that is distinct from the waveforms considered separately, and clustering methods will either assign the composite spike waveform to a distinct cluster–thus “hallucinating” a fictitious neuron–or discard the observation as an outlier that does not match any neuron. Figure 1 demonstrates the systematic failure to identify the near-synchronous spikes of two neurons recorded in primate retina [29], [32]. Figure 1A–B shows the superposition of synchronous spike waveforms, which a clustering method fails to identify. The problem is not limited to synchronous spikes, as shown in Fig. 1 C–D: any spikes whose waveforms exhibit non-zero dot product can give rise to an unrecognizable composite waveforms when superimposed. The feature-space trajectory of overlapping spikes can trace out regions of feature space distinct from the waveforms of each constituent neuron. These points will also typically be discarded as outliers by traditional clustering methods.

Bottom Line: Combining this measurement model with a Bernoulli prior over binary spike trains yields a posterior distribution for spikes given the recorded data.We introduce a greedy algorithm to maximize this posterior that we call "binary pursuit".The algorithm allows modest variability in spike waveforms and recovers spike times with higher precision than the voltage sampling rate.

View Article: PubMed Central - PubMed

Affiliation: Center for Perceptual Systems, Department of Psychology and Section of Neurobiology, The University of Texas at Austin, Austin, Texas, USA. pillow@mail.utexas.edu

ABSTRACT
We examine the problem of estimating the spike trains of multiple neurons from voltage traces recorded on one or more extracellular electrodes. Traditional spike-sorting methods rely on thresholding or clustering of recorded signals to identify spikes. While these methods can detect a large fraction of the spikes from a recording, they generally fail to identify synchronous or near-synchronous spikes: cases in which multiple spikes overlap. Here we investigate the geometry of failures in traditional sorting algorithms, and document the prevalence of such errors in multi-electrode recordings from primate retina. We then develop a method for multi-neuron spike sorting using a model that explicitly accounts for the superposition of spike waveforms. We model the recorded voltage traces as a linear combination of spike waveforms plus a stochastic background component of correlated Gaussian noise. Combining this measurement model with a Bernoulli prior over binary spike trains yields a posterior distribution for spikes given the recorded data. We introduce a greedy algorithm to maximize this posterior that we call "binary pursuit". The algorithm allows modest variability in spike waveforms and recovers spike times with higher precision than the voltage sampling rate. This method substantially corrects cross-correlation artifacts that arise with conventional methods, and substantially outperforms clustering methods on both real and simulated data. Finally, we develop diagnostic tools that can be used to assess errors in spike sorting in the absence of ground truth.

Show MeSH
Related in: MedlinePlus