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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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Comparison of spike trains estimated using binary pursuit and clustering.Three different summary statistics are computed and compared for 293 retinal ganglion cells. For each statistic, the data are shown as “Q–Q” plots: Each line spans the range of quantiles from 5% to 95%, and points are plotted at corresponding deciles of the distributions from 10% to 90%. Different colored lines correspond to different Bernoulli spike rate priors: values in legend indicate a multiplicative factor on the log-prior, relative to the firing rate estimated from clustering. (A) Spike rate. (B) Cross-correlation function artifact index measures the depth of the “notch” at the origin of the cross-correlation function between a pair of cells, a measure of missed spikes. (C) Refractory period contamination rate, which is a measure of false positives. Note that the purple curves (which arise from using a prior for each cell that is six times the firing rate of spikes estimated using clustering) show a reduction in both contamination and CCF artifacts relative to clustering.
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pone-0062123-g005: Comparison of spike trains estimated using binary pursuit and clustering.Three different summary statistics are computed and compared for 293 retinal ganglion cells. For each statistic, the data are shown as “Q–Q” plots: Each line spans the range of quantiles from 5% to 95%, and points are plotted at corresponding deciles of the distributions from 10% to 90%. Different colored lines correspond to different Bernoulli spike rate priors: values in legend indicate a multiplicative factor on the log-prior, relative to the firing rate estimated from clustering. (A) Spike rate. (B) Cross-correlation function artifact index measures the depth of the “notch” at the origin of the cross-correlation function between a pair of cells, a measure of missed spikes. (C) Refractory period contamination rate, which is a measure of false positives. Note that the purple curves (which arise from using a prior for each cell that is six times the firing rate of spikes estimated using clustering) show a reduction in both contamination and CCF artifacts relative to clustering.

Mentions: The black curves in the panels of Fig. 5 summarize the relative behavior of the two spike sorting methods. Figure 5 A shows that binary pursuit identifies more spikes for every cell in our population (N = 293 cells). Figure 5 B shows a comparison of the magnitude of the CCF artifact. The spike trains obtained using binary pursuit are seen to have little or no artifact. From these two plots, one might be tempted to believe that binary pursuit has solved the spike sorting problem. But further examination reveals a new problem: an increase in refractory-period violations, which provide another indicator of spike-sorting errors [4], [15], [24], [41]–[43]. We quantify these errors in terms of the “contamination rate” for each neuron, defined as the ratio of the frequency of occurrence of spikes within the refractory period ( ms) to the baseline frequency of spikes outside this window. (A contamination rate of 50% indicates that the rate of spikes detected during the refractory window is equal to half the rate of spikes detected outside this window). Figure 5 C shows a comparison of the contamination rate for spikes sorted by clustering and binary pursuit. We see that for a large proportion of the cells, binary pursuit has a significantly higher contamination rate than clustering, and thus some of the increase in spike rate seen in these cells is likely due to inclusion of erroneous spikes.


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)

Comparison of spike trains estimated using binary pursuit and clustering.Three different summary statistics are computed and compared for 293 retinal ganglion cells. For each statistic, the data are shown as “Q–Q” plots: Each line spans the range of quantiles from 5% to 95%, and points are plotted at corresponding deciles of the distributions from 10% to 90%. Different colored lines correspond to different Bernoulli spike rate priors: values in legend indicate a multiplicative factor on the log-prior, relative to the firing rate estimated from clustering. (A) Spike rate. (B) Cross-correlation function artifact index measures the depth of the “notch” at the origin of the cross-correlation function between a pair of cells, a measure of missed spikes. (C) Refractory period contamination rate, which is a measure of false positives. Note that the purple curves (which arise from using a prior for each cell that is six times the firing rate of spikes estimated using clustering) show a reduction in both contamination and CCF artifacts relative to clustering.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3643981&req=5

pone-0062123-g005: Comparison of spike trains estimated using binary pursuit and clustering.Three different summary statistics are computed and compared for 293 retinal ganglion cells. For each statistic, the data are shown as “Q–Q” plots: Each line spans the range of quantiles from 5% to 95%, and points are plotted at corresponding deciles of the distributions from 10% to 90%. Different colored lines correspond to different Bernoulli spike rate priors: values in legend indicate a multiplicative factor on the log-prior, relative to the firing rate estimated from clustering. (A) Spike rate. (B) Cross-correlation function artifact index measures the depth of the “notch” at the origin of the cross-correlation function between a pair of cells, a measure of missed spikes. (C) Refractory period contamination rate, which is a measure of false positives. Note that the purple curves (which arise from using a prior for each cell that is six times the firing rate of spikes estimated using clustering) show a reduction in both contamination and CCF artifacts relative to clustering.
Mentions: The black curves in the panels of Fig. 5 summarize the relative behavior of the two spike sorting methods. Figure 5 A shows that binary pursuit identifies more spikes for every cell in our population (N = 293 cells). Figure 5 B shows a comparison of the magnitude of the CCF artifact. The spike trains obtained using binary pursuit are seen to have little or no artifact. From these two plots, one might be tempted to believe that binary pursuit has solved the spike sorting problem. But further examination reveals a new problem: an increase in refractory-period violations, which provide another indicator of spike-sorting errors [4], [15], [24], [41]–[43]. We quantify these errors in terms of the “contamination rate” for each neuron, defined as the ratio of the frequency of occurrence of spikes within the refractory period ( ms) to the baseline frequency of spikes outside this window. (A contamination rate of 50% indicates that the rate of spikes detected during the refractory window is equal to half the rate of spikes detected outside this window). Figure 5 C shows a comparison of the contamination rate for spikes sorted by clustering and binary pursuit. We see that for a large proportion of the cells, binary pursuit has a significantly higher contamination rate than clustering, and thus some of the increase in spike rate seen in these cells is likely due to inclusion of erroneous spikes.

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