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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 spikes estimated using clustering and binary pursuit.Each row shows results for one example neuron. Each plot depicts the 2D linear feature space used for clustering (see Fig. 1 ). Left column: Black and gray points indicate spikes obtained by clustering for two cells. Additional spikes obtained for the black cell by binary pursuit (but ignored as outliers by clustering), are scattered in various directions relative to this ellipse (red points). Note that some points do not appear to be outliers within the two dimensions shown, but are outliers in other dimensions. Middle column: When the spikes of these two cells overlap in time, the resulting superimposed waveform is predicted to lie along a trajectory (see Fig. 1 ). Filled black and gray ellipses correspond to the location of isolated spikes for the primary and secondary cells, respectively. Size and shape of ellipses corresponds to the level curve (at one standard deviation) of the estimated (Gaussian) noise distribution. Colored ellipses indicate predicted locations of noisy superimposed waveforms, with color indicating their temporal offset. Right column: Subset of spikes identified by binary pursuit that were either isolated (black and gray points), or overlapping (colored points, with color indicating the temporal offset of the two spikes).
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pone-0062123-g003: Comparison of spikes estimated using clustering and binary pursuit.Each row shows results for one example neuron. Each plot depicts the 2D linear feature space used for clustering (see Fig. 1 ). Left column: Black and gray points indicate spikes obtained by clustering for two cells. Additional spikes obtained for the black cell by binary pursuit (but ignored as outliers by clustering), are scattered in various directions relative to this ellipse (red points). Note that some points do not appear to be outliers within the two dimensions shown, but are outliers in other dimensions. Middle column: When the spikes of these two cells overlap in time, the resulting superimposed waveform is predicted to lie along a trajectory (see Fig. 1 ). Filled black and gray ellipses correspond to the location of isolated spikes for the primary and secondary cells, respectively. Size and shape of ellipses corresponds to the level curve (at one standard deviation) of the estimated (Gaussian) noise distribution. Colored ellipses indicate predicted locations of noisy superimposed waveforms, with color indicating their temporal offset. Right column: Subset of spikes identified by binary pursuit that were either isolated (black and gray points), or overlapping (colored points, with color indicating the temporal offset of the two spikes).

Mentions: We compared spike train estimates obtained with traditional clustering and with binary pursuit. The most immediate difference was that binary pursuit identified a larger number of spikes for every cell. These additional identified spikes generally overlapped the spikes of other cells, as illustrated in Fig. 3. The left column shows the spikes of four example cells obtained using a clustering method.


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 spikes estimated using clustering and binary pursuit.Each row shows results for one example neuron. Each plot depicts the 2D linear feature space used for clustering (see Fig. 1 ). Left column: Black and gray points indicate spikes obtained by clustering for two cells. Additional spikes obtained for the black cell by binary pursuit (but ignored as outliers by clustering), are scattered in various directions relative to this ellipse (red points). Note that some points do not appear to be outliers within the two dimensions shown, but are outliers in other dimensions. Middle column: When the spikes of these two cells overlap in time, the resulting superimposed waveform is predicted to lie along a trajectory (see Fig. 1 ). Filled black and gray ellipses correspond to the location of isolated spikes for the primary and secondary cells, respectively. Size and shape of ellipses corresponds to the level curve (at one standard deviation) of the estimated (Gaussian) noise distribution. Colored ellipses indicate predicted locations of noisy superimposed waveforms, with color indicating their temporal offset. Right column: Subset of spikes identified by binary pursuit that were either isolated (black and gray points), or overlapping (colored points, with color indicating the temporal offset of the two spikes).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3643981&req=5

pone-0062123-g003: Comparison of spikes estimated using clustering and binary pursuit.Each row shows results for one example neuron. Each plot depicts the 2D linear feature space used for clustering (see Fig. 1 ). Left column: Black and gray points indicate spikes obtained by clustering for two cells. Additional spikes obtained for the black cell by binary pursuit (but ignored as outliers by clustering), are scattered in various directions relative to this ellipse (red points). Note that some points do not appear to be outliers within the two dimensions shown, but are outliers in other dimensions. Middle column: When the spikes of these two cells overlap in time, the resulting superimposed waveform is predicted to lie along a trajectory (see Fig. 1 ). Filled black and gray ellipses correspond to the location of isolated spikes for the primary and secondary cells, respectively. Size and shape of ellipses corresponds to the level curve (at one standard deviation) of the estimated (Gaussian) noise distribution. Colored ellipses indicate predicted locations of noisy superimposed waveforms, with color indicating their temporal offset. Right column: Subset of spikes identified by binary pursuit that were either isolated (black and gray points), or overlapping (colored points, with color indicating the temporal offset of the two spikes).
Mentions: We compared spike train estimates obtained with traditional clustering and with binary pursuit. The most immediate difference was that binary pursuit identified a larger number of spikes for every cell. These additional identified spikes generally overlapped the spikes of other cells, as illustrated in Fig. 3. The left column shows the spikes of four example cells obtained using a clustering method.

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