Unsupervised clustering of temporal patterns in high-dimensional neuronal ensembles using a novel dissimilarity measure
Precisely timed spike patterns spanning multiple neurons are a ubiquitous feature of both spontaneous and stimulus-evoked brain network activity ., Remarkably , not all patterns are generated with equal probability ., Synaptic connectivity , shaped by development and experience , favors certain spike sequences over others , limiting the portion of the network’s “state space” that is effectively visited 1 , 2 ., The structure of this permissible state space is of the greatest interest for our understanding of neural network function ., Multi-neuron temporal sequences encode information about stimulus variables 3–8 , in some cases “unrolling” non-temporally organized stimuli , such as odors , into temporal sequences 9 ., Recurrent neuronal networks can generate precise temporal sequences 10–14 , which are required for example for the generation of complex vocalization patterns like bird songs 15 ., Temporal spiking patterns may also encode sequences of occurrences or actions , as they take place , or are planned , projected , or “replayed” for memory consolidation in the hippocampus and other structures 16–25 ., Timing information between spikes of different neurons is critical for memory function , as it regulates spike timing dependent plasticity ( STDP ) of synapses , with firing of a post-synaptic neuron following the firing of a pre-synaptic neuron typically inducing synaptic potentiation , and firing in the reverse order typically inducing depotentiation 26–28 ., Thus , the consolidation of memories may rely on recurring temporal patterns of neural activity , which stabilize and modify the synaptic connections among neurons 16–22 , 29–35 ., Storing memories as sequences has the advantage that a very large number of patterns is possible , because the number of possible spike orderings grows exponentially , and different sequences can efficiently be associated to different memory items , as proposed by for instance the reservoir computing theory 36–40 ., Detecting these temporal patterns represents a major methodological challenge ., With recent advances in neuro-technology , it is now possible to record from thousands of neurons simultaneously 41 , and this number is expected to show an exponential growth in the coming years 42 ., The high dimensionality of population activity , combined with the sparsity and stochasticity of neuronal output , as well as the limited amount of time one can record from a given neuron , makes the detection of recurring temporal sequences an extremely difficult computational problem ., Many approaches to this problem are supervised , that is , they take patterns occurring concurrently with a known event , such as the delivery of a stimulus for sensory neurons or the traversal of a running track for hippocampal place fields , as a “template” and then search for repetitions of the same template in spiking activity 20 , 43 , 44 ., Other approaches construct a template by measuring latencies of each neuron’s spiking from a known event , such as the beginning of a cortical UP state 5 , 45 ., While this enables rigorous , relatively easy statistical treatment , it risks neglecting much of the structure in the spiking data , which may contain representations of other items ( e . g . remote memories , presentations of different stimuli , etc . ) ., A more complete picture of network activity may be provided by unsupervised methods , detecting regularities , for example in the form of spiking patterns recurring more often than predicted by chance ., Unsupervised methods proposed so far typically use linear approaches , such as Principal Component Analysis ( PCA ) 24 , 46 , 47 , and cannot account for different patterns arising from permutations of spike orderings ., While approaches like frequent itemset mining and related methods 48–51 can find more patterns than the number of neurons and provide a rigorous statistical framework , they require that exact matches of the same pattern occur , which becomes less and less probable as the number of neurons grows or as the time bins become smaller ( problem of combinatorial explosion ) ., To address this problem , 52 , 53 proposed another promising unsupervised method based on spin glass Ising models that allows for approximate pattern matching while not being linearly limited in the number of patterns; this method however requires binning , and rather provides a method for classifying the binary network state vector in a small temporal neighborhood , while not dissociating rate patterns from temporal patterns ., In this paper we introduce a novel spike pattern detection method called SPOTDisClust ( Fig 1 ) ., We start from the idea that the similarities of two neural patterns can be defined by the trace that they may leave on the synaptic matrix , which in turn is determined by the pairwise cross-correlations between neural activities 26 , 27 ., The algorithm is based on constructing an epoch-to-epoch dissimilarity matrix , in which dissimilarity is defined as SPOTDis , making use of techniques from the mathematical theory of optimal transport to define , and efficiently compute , a dissimilarity between two spiking patterns 54–57 ., We then perform unsupervised clustering on the pairwise SPOTDis matrix ., SPOTDis measures the similarity of two spike patterns ( in two different epochs ) by determining the minimum transport cost of transforming their corresponding cross-correlation matrices into each other ., This amounts to computing the Earth Mover’s Distance ( EMD ) for all pairs of neurons and all pairs of epochs ( see Methods ) ., Through ground-truth simulations , we show that SPOTDisClust has many desirable properties: It can detect many more patterns than the number of neurons ( Fig 2 ) ; it can detect complex patterns that would be invisible with latency-based methods ( Figs 3 and 4 ) ; it is highly robust to noise , i . e . to the ‘insertion’ of noisy spikes , spike timing jitter , or fluctuations in the firing rate , and its performance grows with the inclusion of more neurons given a constant signal-to-noise ratio ( Fig 5 ) ; it can detect sequences in the presence of sparse firing ( Fig 6 ) ; and finally it is insensitive to a global or patterned scaling of the firing rates ( Fig 7 ) ., We apply SPOTDisClust to V1 Utah array data from the awake macaque monkey , and identify different visual stimulus directions using unsupervised clustering with SPOTDisClust ( Fig 8 ) ., Suppose we perform spiking measurements from an ensemble of N neurons , and we observe the spiking output of this ensemble in M separate epochs of length T samples ( in units of the time bin length ) ., Suppose that there are P distinct activity patterns that tend to reoccur in some of the M epochs ., Each pattern generates a set of normalized ( to unit mass ) cross-correlation histograms among all neurons ., Instantiations of the same pattern are different because of noise , but will have the same expectation for the cross-correlation histogram ., The normalized cross-correlation histogram is defined as, s i j ′ ( τ ) ≡ s i j ( τ ) ∑ τ = - T T s i j ( τ ) , ( 1 ), if ∑ τ = - T T s i j ( τ ) > 0 , and s i j ′ ( τ ) = 0 otherwise ., Here , sij ( τ ) ≡ ∑t si ( t ) sj ( t + τ ) is the cross-correlation function ( or cross-covariance ) , and si ( t ) and sj ( t ) are the spike trains of neurons i and j ., In other words , the normalized cross-correlation histogram is simply the histogram of coincidence counts at different delays τ , normalized to unit mass ., We take the N × N × ( 2T + 1 ) matrix of s i j ′ ( τ ) values as a full representation of a pattern , that is , we consider two patterns to have the same temporal structure when all neuron pairs have the same expected value of s i j ′ ( τ ) for each τ ., For simplicity and clarity of presentation , we have written the cross-correlation function as a discrete ( histogram ) function of time ., However , because the SPOTDis , which is introduced below , is a cross-bins dissimilarity measure and requires only to store the precise delays τ at which s i j ′ ( τ ) is non-zero , the sampling rate can be made infinitely large ( see Methods ) ., In other words , the SPOTDis computation does not entail any loss of timing precision beyond the sampling rate at which the spikes are recorded ., The SPOTDisClust method contains two steps ( Fig 1 ) , which are illustrated for five example patterns ( Fig 1A and 1B ) ., The first step is to construct the SPOTDis dissimilarity measure between all pairs of epochs on the matrix of cross-correlations among all neuron pairs ., The second step is to perform clustering on the SPOTDis dissimilarity measure using an unsupervised clustering algorithm that operates on a dissimilarity matrix ., Many algorithms are available for unsupervised clustering on pairwise dissimilarity matrices ., One family of unsupervised clustering methods comprises so called density clustering algorithms , including DBSCAN , HDBSCAN or density peak clustering ., Here , we use the HDBSCAN unsupervised clustering method 58–61 ( see Methods ) ., To examine the separability of the clusters in a low dimensional 2-D embedding , we employ the t-SNE projection method 62 , 63 ( see Methods ) ., The SPOTDis measure is constructed as follows: To test the SPOTDisClust method for cases in which the ground truth is known , we generated P input patterns in epochs of length T = Tepoch = 300 samples , defined by the instantaneous rate of inhomogeneous Poisson processes , and then generated spiking outputs according to these ( Fig 1A and 1B ) ( see Methods ) ., Because the SPOTDis is a binless measure , in the sense that it does not require any binning beyond the sampling frequency , the epochs could for example represent spike series of 3s with a sampling rate of 100Hz , or spike series of 300ms with a sampling rate of 1000Hz ., Each input pattern was constructed such that it had a baseline firing rate and a pulse activation firing rate , defined as the expected number of spikes per sample ., The pulse activation period ( with duration Tpulse samples ) is the period in the epoch in which the neuron is more active than during the baseline , and the positions of the pulses across neurons define the pattern ., For each neuron and pattern , the position of the pulse activation period was randomly chosen ., We generated M/ ( 2 * P ) realizations for each of the P patterns , and a matching number of M/2 noise epochs ( i . e . 50 percent of epochs were noise epochs ) ., We performed simulations for two types of noise epochs ( S3 Fig ) ., First , noise was generated with random firing according to a homogeneous Poisson process with a constant rate ( see Fig 1 ) ., We refer to this noise , throughout the text , as “homogeneous noise” ., For the second type of noise , each noise epoch comprised a single instantiation of a unique pattern , with randomly chosen positions of the pulse activation periods ., We refer to this noise as “patterned noise” ., For both types of noise patterns , the expected number of spikes in the noise epoch was the same as during an epoch in which one of the P patterns was realized ., The second type of noise also had the same inter spike interval statistics for each neuron as the patterns ., Importantly , because SPOTDisClust uses only the relative timing of spiking among neurons , rather than the timing of spiking relative to the epoch onset , the exact onset of the epoch does not have to be known with SPOTDis; even though the exact onset of the pattern is known in the simulations presented here , this knowledge was not used in any way for the clustering ., Fig 1 illustrates the different steps of the algorithm for an example of P = 5 patterns ., For the purpose of illustration , we start with an example comprising five patterns that are relatively easy to spot by eye; later in the manuscript we show examples with a very low signal-to-noise ratio ( Fig 5 ) or sparse firing ( Fig 6 ) ., We find that in the 2-D t-SNE embedding , the P = 5 different patterns form separate clusters ( Fig 1E ) , and that the HDBSCAN algorithm is able to correctly identify the separate clusters ( S4 Fig ) ., We also show a simulation with many more noise epochs than cluster epochs , which shows that even in such a case t-SNE embedding is able to separate the different clusters ( S5 Fig ) ., In S3 Fig we compare clustering with homogeneous and patterned noise ., The homogeneous noise patterns have a consistently small SPOTDis dissimilarity to each other and are detected as a separate cluster , while the patterned noise epochs have large SPOTDis dissimilarities to each other and do not form a separate cluster , but spread out rather uniformly through the low-dimensional t-SNE embedding ( S3 Fig ) ., A key challenge for any pattern detection algorithm is to find a larger number of patterns than the number of measurement variables , assuming that each pattern is observed several times ., This is impossible to achieve with traditional linear methods like PCA ( Principal Component Analysis ) , which do not yield more components than the number of neurons ( or channels ) , although decomposition techniques using overcomplete base sets might in principle be able to do so ., Other approaches like frequent itemset mining and related methods 48–50 require that exact matches of the same pattern occur ., Because SPOTDisClust clusters patterns based on small SPOTDis dissimilarities , it does not require exact matches of the same pattern to occur , but only that the different instantiations of the same pattern are similar enough to one another ,, i . e ., have SPOTDis values that are small enough , and separate them from other clusters and the noise ., Fig 2 shows an example where the number of patterns exceeds the number of neurons by a factor 10 ( 500 to 50 ) ., In the 2-D t-SNE embedding , the 500 patterns form separate clusters , with the emergence of a noise cluster that has higher variance ., Consistent with the low dimensional t-SNE embedding , the HDBSCAN algorithm is able to correctly identify the separate clusters ( S4 Fig ) ., When many patterns are detectable , the geometry of the low dimensional t-SNE embedding needs to be interpreted carefully: In this case , all 500 patterns are roughly equidistant to each other , however , there does not exist a 2-D projection in which all 500 clusters are equidistant to each other; this would only occur with a triangle for P = 3 patterns ., Thus , although the low dimensional t-SNE embedding demonstrates that the clusters are well separated from each other , in the 2-D embedding nearby clusters do not necessarily have smaller SPOTDis dissimilarities than distant clusters when P is large ., Temporal patterns in neuronal data may consist not only of ordered sequences of activation , but can also have a more complex character ., As explained above , a key advantage of the SPOTDis measure is that it computes averages over the EMD , which can distinguish complex patterns beyond patterns that differ only by a measure of central tendency ., Indeed , we will demonstrate that SPOTDisClust can detect a wide variety of patterns , for which traditional methods that are based on the relative activation order ( sequence ) of neurons may not be well equipped ., We first consider a case where the patterns consist of bimodal activations within the epoch ( Fig 3A ) ., These types of activation patterns might for example be expected when rodents navigate through a maze , such that enthorinal grid cells or CA1 cells with multiple place fields are activated at multiple locations and time points 64–66 ., A special case of a bimodal activation is one where neurons have a high baseline firing rate and are “deactivated” in a certain segment of the epoch ( Fig 3B ) ., These kinds of deactivations may be important , because e . g . spatial information about an animal’s position in the medial temporal lobe ( 67 ) or visual information in retinal ganglion cells is carried not only by neuronal activations , but also by neuronal deactivations ., We find that the different patterns form well separated clusters in the low dimensional t-SNE embedding based on SPOTDis ( Fig 3A and 3B ) , and that HDBSCAN correctly identifies them ( S4 Fig ) ., Next , we consider a case where there are two coarse patterns and two fine patterns embedded within each coarse pattern , resulting in a total number of four patterns ., This example might be relevant for sequences that result from cross-frequency theta-gamma coupling , or from the sequential activation of place fields that is accompanied by theta phase sequences on a faster time scale 68 , 69 ., These kinds of patterns would be challenging for methods that rely on binning , because distinguishing the coarse and fine patterns requires coarse and fine binning , respectively ., We find that the SPOTDis allows for a correct separation of the data in four clusters corresponding to the four patterns and one noise cluster ( Fig 4A ) , and that HDBSCAN identifies them ( S4 Fig ) ., As expected , we find that the two patterns that share the same coarse structure ( but contain a different fine structure ) have smaller dissimilarities to each other in the t-SNE embedding as compared to the patterns that share a different coarse structure ., Finally , we consider a set of patterns consisting of a synchronous ( i . e . without delays ) firing of a subset of cells , with a cross-correlation function that is symmetric around the delay τ = 0 ( i . e . , correlation without delays ) ., This type of activity may arise for example in a network in which all the coupling coefficients between neurons are symmetric ., Previous methods to identify the co-activation ( without consideration of time delays ) of different neuronal assemblies relied on PCA 24 , which has the key limitation that it can identify only a small number of patterns ( smaller than the number of neurons ) Furthermore , while yielding orthonormal , uncorrelated components that explain the most variance in the data , PCA components do not necessarily correspond to neuronal spike patterns that form distinct and separable clusters; e . g . a multivariate Gaussian distribution can yield multiple PCA components that correspond to orthogonal axes explaining most of the data variance ., Fig 4B shows four patterns , in which a subset of cells exhibits a correlated activation without delays ., Separate clusters emerge in the t-SNE embedding based on SPOTDis ( Fig 4B ) and are identified by HDBSCAN ( S4 Fig ) ., This demonstrates that SPOTDisClust is not only a sequence detection method in the sense that it can detect specific temporal orderings of firing , but can also be used to identify patterns in which specific groups of cells are synchronously co-active without time delays ., A major challenge for the clustering of temporal spiking patterns is the stochasticity of neuronal firing ., That is , in neural data , it is extremely unlikely to encounter , in a high dimensional space , a copy of the same pattern exactly twice , or even two instantiations that differ by only a few insertions or deletions of spikes ., Furthermore , patterns might be distinct when they span a high-dimensional neural space , even when bivariate correlations among neurons are weak and when the firing of neurons in the activation period is only slightly higher than the baseline firing around it ( see further below ) ., The robustness of a sequence detection algorithm to noise is therefore critical ., We can dissociate different aspects of “noise” in temporal spiking patterns ., A first source of noise is the stochastic fluctuation in the number of spikes during the pulse activation period and baseline firing period ., In the ground-truth simulations presented here , this fluctuation is driven by the generation of spikes according to inhomogeneous Poisson processes ., This type of noise causes differences in SPOTDis values between epochs , because of differences in the amount of mass in the pulse activation and baseline period , in combination with the normalization of the cross-correlation histogram ., In the extreme case , some neurons may not fire in an given epoch , such that all information about the temporal structure of the pattern is lost ., Such a neural “silence” might be prevalent when we search for spiking patterns on a short time scale ., We note that fluctuations in the spike count are primarily detrimental to clustering performance because there is baseline firing around the pulse activation period , in other words because “noisy” spikes are inserted at random points in time around the pulse activations ., To see this , suppose that the probability that a neuron fires at least one spike during the pulse activation period is close to one for all M epochs and all N neurons , and that the firing rate during the baseline is zero ., In this case , because SPOTDis is based on computing optimal transport between normalized cross-correlation histograms ( Eq ( 5 ) ) , the fluctuation in the spike count due to Poisson firing would not drive differences in the SPOTDis ., A second source of noise is the jitter in spike timing ., Jitter in spike timing also gives rise to fluctuations in the SPOTDis and in the ground-truth simulations presented here , spike timing jitter is a consequence of the generation of spikes according to Poisson processes ., As explained above , because the SPOTDisClust method does not require exact matches of the observed patterns , but is a “cross-bins” dissimilarity measure , it can handle jitter in spike timing well ., Again , we can distinguish jitter in spike timing during the baseline firing , and jitter in spike timing during the pulse activation period ., The amount of perturbation caused by spike timing jitter during the pulse activation period is a function of the pulse period duration ., We will explore the consequences of these different noise sources , namely the amount of baseline firing , the sparsity of firing , and spike timing jitter in Figs 5 and 6 ., We define the SNR ( Signal-to-Noise-Ratio ) as the ratio of the firing rate inside the activation pulse period over the firing rate outside the activation period ., This measure of SNR reflects both the amount of firing in the pulse activation period as compared to the baseline period ( first source of noise ) , and the pulse duration as compared to the epoch duration ( second source of noise ) ., We first consider an example of 100 neurons that have a relatively low SNR ( Fig 5A ) ., It can be appreciated that different realizations from the same pattern are difficult to identify by eye , and that exact matches for the same pattern , if one would bin the spike trains , would be highly improbable , even for a single pair of two neurons ( Fig 5A ) ., Yet , in the 2-D t-SNE embedding based on SPOTDis , the different clusters form well separated “islands” ( Fig 5A ) , and the HDBSCAN clustering algorithm captures them ( S4 Fig ) ., To systematically analyze the dependence of clustering performance on the SNR , we varied the SNR by changing the firing rate inside the activation pulse period , while leaving the firing rate outside the activation period as well as the duration of the activation ( pulse ) period constant ., Thus , we varied the first aspect of noise , which is driven by spike count fluctuations ., A measure of performance was then constructed by comparing the unsupervised cluster labels rendered by HDBSCAN with the ground-truth cluster labels , using the Adjusted Rand Index ( ARI ) measure ( see Methods ) ., As expected , we find that clustering performance increases with the firing rate SNR ( Fig 5B ) ., Importantly , as the number of neurons increases , we find that the same clustering performance can be achieved with a lower SNR ( Fig 5B ) ., Thus , SPOTDisClust does not suffer from the problem of combinatorial explosion as the number of neurons that constitute the patterns increases , and , moreover , its performance improves when the number of recorded neurons is higher ., The reason underlying this behavior is that each neuron contributes to the separability of the patterns , such that a larger sample of neurons allows each individual neuron to be noisier ., This means that , in the brain , very reliable temporal patterns may span high-dimensional neural spaces , even though the bivariate correlations might appear extremely noisy; absence of evidence for temporal coding in low dimensional multi-neuron ensembles should therefore not be taken as evidence for absence of temporal coding in high dimensional multi-neuron ensembles ., We also varied the SNR by changing the pulse duration while leaving the ratio of expected number of spikes in the activation period relative to the baseline constant ., The latter was achieved by adjusting the firing rate inside the activation period , such that the product of pulse duration with firing rate in the activation period remained constant ,, i . e ., Tpulseλpulse = c ., Thus , we varied the second aspect of noise , namely the amount of spike timing jitter in the pulse activation period ., We find a similar dependence of clustering performance on the firing rate SNR and the number of neurons ( Fig 5B ) ., Hence , patterns that comprise brief activation pulses of very high firing yield , given a constant product Tpulseλpulse , clusters that are better separated than patterns comprising longer activation pulses ., We performed further simulations to study in a more simplified , one-dimensional setting how the SPOTDis depends quantitatively on the insertion of noise spikes outside of the activation pulse periods , which further demonstrates the robustness of the SPOTDis measure to noise ( S6 Fig ) ., In addition , we performed simulations to determine the influence of spike sorting errors on the clustering performance ., In general , spike sorting errors lead to a reduction in HDBSCAN clustering performance , the extent of which depends on the type of spike sorting error ( contamination or collision ) 70 and the structure of the spike pattern ( S7 and S8 Figs ) ., This result is consistent with the dependence of the HBDSCAN clustering performance on signal-to-noise ratio and pulse duration shown in Fig 5 , as well with the notion that contamination mixes responses across neurons , such that the number of neurons that carries unique information decreases ., We further note that in general , SPOTDisClust provides flexibility when detecting patterns using multiple tetrodes or channels of a laminar silicon probe: A common technique employed when analyzing pairwise correlations ( e . g . noise correlations ) is to ignore pairs of neurons that were measured from the same tetrode or from nearby channels ., When the number of channels is large , this will only ignore a relatively small fraction of neuron pairs ., Because the SPOTDis measure is defined over pairs of neurons , rather than the sequential ordering of firing defined over an entire neuronal ensemble , this can be easily implemented by , in Eq 2 , letting the sum run over neuron pairs from separate electrodes ., As explained above , an extreme case of noise driven by spike count fluctuations is the absence of firing during an epoch ., If many neurons remain “silent” in a given epoch , then we can only compute the EMD for a small subset of neuron pairs ( Eq ( 2 ) ) ., Such a sparse firing scenario might be particularly challenging to latency-based methods , because the latency of cells that do not fire is not defined ., We consider a case of sparse firing in Fig 6 where the expected number of spikes per epoch is only 0 . 48 ., Despite the firing sparsity , the low-dimensional t-SNE embedding based on SPOTDis shows separable clusters , and HDBSCAN correctly identifies the different clusters ( Fig 6 ) ., We also performed a simulation in which patterns consist of precise spike sequences , and examined the influence of temporal jitter of the precise spike sequence , as well as the amount of noise spikes surrounding these precise spike sequences ., Up to some levels of temporal jitter , and signal-to-noise ratio , HDBSCAN shows a relatively good clustering performance ( S9 Fig ) ., In general , given sparse firing , a sufficient number of neurons is needed to correctly identify the P patterns , but , in addition , the patterns should be distinct on a sufficiently large fraction of neuron pairs ., Furthermore , the lower the signal-to-noise ratio , the more neurons are needed to separate the patterns from one another ., A key aim of the SPOTDisClust methodology is to identify temporal patterns that are based on consistent temporal relationships among neurons ., However , in addition to temporal patterns , neuronal populations can also exhibit fluctuations in the firing rate that can be driven by e . g . external input or behavioral state and are superimposed on temporal patterns ., A global scaling of the firing rate , or a scaling of the firing rate for a specific assembly , should not constitute a different temporal pattern if the temporal structure of the pattern remains unaltered ,, i . e ., when the normalized cross-correlation function has the same expected value , and should not interfere with the clustering of temporal patterns ., This is an important point for practical applications , because it might occur for instance that in specific behavioral states rates are globally scaled 71 , 72 ., In Fig 7A , we show an example where there are three different global rate scalings , as well as two temporal patterns ., The temporal patterns are , for each epoch , randomly accompanied by one of the different global rate scaling factors ., The t-SNE embedding shows that the temporal patterns form separate clusters , but that the global rate scalings do not ( Fig 7A ) ., Furthermore , HDBSCAN correctly clusters the temporal patterns , but does not find separate clusters for the different rate scalings ( Fig 7A and S4 Fig ) ., This behavior can be understood from examination of the sorted dissimilarity matrix , in which we can see that epochs with a low rate do not only have a higher SPOTDis to epochs with a high rate , but also to other epochs with a low rate , which prevents them from agglomerating into a separate cluster ( Fig 7A ) ; rather the epochs with a low rate tend to cluster at the edges of the cluster , whereas the epochs with a high rate tend to form the core of the cluster ( Fig 7A ) ., Another example of a rate scaling is one that consists of a scaling of the firing rate for one half of the neurons ( Fig 7B ) ., Again , the t-SNE embedding and HDBSCAN clustering show that rate scalings do not form separate clusters , and do not interfere with the clustering of the temporal patterns ( Fig 7B and S4 Fig ) ., We conclude that the unsupervised clustering of different temporal patterns with SPOTDisClust is not compromised by the inclusion of global rate scalings , or the scaling of the rate in a specific subset of neurons ., We apply the SPOTDisClust method to data collected from monkey V1 ., Simultaneous recordings were performed from 64 V1 channels using a chronically implanted Utah array ( Blackrock ) ( see Methods ) ., We presented moving bar stimuli in four cardinal directions while monkeys performed a passive fixation task ., Each stimulus bar was presented 20 times ., We then pooled all 80 trials together , and added 80 trials containing spontaneous activity ., Our aim was then to recover the separate stimulus conditions using unsupervised clustering of multi-unit data with SPOTDisClust ., The low dimensional t-SNE embedding shows four dense regions that are well separated from each other and correspond to the four stimuli , and HDBSCAN identifies these four clusters ( Fig 8 ) ., Furthermore , when we performed clustering on the firing rate vectors , and constructed a t-SNE embedding on distances between population rate vectors , we were not able to extract the different stimulus directions from the cluster labels ., This shows that the temporal clustering results are not trivially explained by rate differences across stimulus directions , but also indicates that the temporal pattern of population activity m
Temporally ordered multi-neuron patterns likely encode information in the brain ., We introduce an unsupervised method , SPOTDisClust ( Spike Pattern Optimal Transport Dissimilarity Clustering ) , for their detection from high-dimensional neural ensembles ., SPOTDisClust measures similarity between two ensemble spike patterns by determining the minimum transport cost of transforming their corresponding normalized cross-correlation matrices into each other ( SPOTDis ) ., Then , it performs density-based clustering based on the resulting inter-pattern dissimilarity matrix ., SPOTDisClust does not require binning and can detect complex patterns ( beyond sequential activation ) even when high levels of out-of-pattern “noise” spiking are present ., Our method handles efficiently the additional information from increasingly large neuronal ensembles and can detect a number of patterns that far exceeds the number of recorded neurons ., In an application to neural ensemble data from macaque monkey V1 cortex , SPOTDisClust can identify different moving stimulus directions on the sole basis of temporal spiking patterns .
The brain encodes information by ensembles of neurons , and recent technological developments allow researchers to simultaneously record from over thousands of neurons ., Neurons exhibit spontaneous activity patterns , which are constrained by experience and development , limiting the portion of state space that is effectively visited ., Patterns of spontaneous activity may contribute to shaping the synaptic connectivity matrix and contribute to memory consolidation , and synaptic plasticity formation depends crucially on the temporal spiking order among neurons ., Hence , the unsupervised detection of spike sequences is a sine qua non for understanding how spontaneous activity contributes to memory formation ., Yet , sequence detection presents major methodological challenges like the sparsity and stochasticity of neuronal output , and its high dimensionality ., We propose a dissimilarity measure between neuronal patterns based on optimal transport theory , determining their similarity from the pairwise cross-correlation matrix , which can be taken as a proxy of the “trace” that is left on the synaptic matrix ., We then perform unsupervised clustering and visualization of patterns using density clustering on the dissimilarity matrix and low-dimensional embedding techniques ., This method does not require binning of spike times , is robust to noise , jitter and rate fluctuations , and can detect more patterns than the number of neurons .
action potentials, medicine and health sciences, engineering and technology, signal processing, applied mathematics, membrane potential, vertebrates, electrophysiology, neuroscience, animals, jitter, mammals, simulation and modeling, algorithms, primates, probability distribution, mathematics, clustering algorithms, old world monkeys, research and analysis methods, monkeys, animal cells, probability theory, macaque, cellular neuroscience, eukaryota, cell biology, physiology, neurons, signal to noise ratio, biology and life sciences, cellular types, physical sciences, amniotes, neurophysiology, organisms, modulation