Neural coding and memory formation depend on temporal spiking sequences that span high-dimensional neural ensembles. The unsupervised discovery and characterization of these spiking sequences requires a suitable dissimilarity measure to spiking patterns, which can then be used for clustering and decoding. Here, we present a new dissimilarity measure based on optimal transport theory called SpikeShip, which compares multi-neuron spiking patterns based on all the relative spike-timing relationships among neurons. SpikeShip computes the optimal transport cost to make all the relative spike-timing relationships (across neurons) identical between two spiking patterns. We show that this transport cost can be decomposed into a temporal rigid translation term, which captures global latency shifts, and a vector of neuron-specific transport flows, which reflect inter-neuronal spike timing differences. SpikeShip can be effectively computed for high-dimensional neuronal ensembles, has a low (linear) computational cost that has the same order as the spike count, and is sensitive to higher-order correlations. Furthermore, SpikeShip is binless, can handle any form of spike time distributions, is not affected by firing rate fluctuations, can detect patterns with a low signal-to-noise ratio, and can be effectively combined with a sliding window approach. We compare the advantages and differences between SpikeShip and other measures like SPIKE and Victor-Purpura distance. We applied SpikeShip to large-scale Neuropixel recordings during spontaneous activity and visual encoding. We show that high-dimensional spiking sequences detected via SpikeShip reliably distinguish between different natural images and different behavioral states. These spiking sequences carried complementary information to conventional firing rate codes. SpikeShip opens new avenues for studying neural coding and memory consolidation by rapid and unsupervised detection of temporal spiking patterns in high-dimensional neural ensembles. Author summaryNeuronal coding and memory formation depend on temporal activation patterns spanning high-dimensional ensembles of neurons. With new recording technologies like Neuropixels, it has now become possible to measure from > 1000 neurons simultaneously. This raises the problem, how we can detect temporal sequences of spikes in these high-dimensional ensembles in an unsupervised manner. Here, we present a new method to solve this problem based on optimal transport theory, called SpikeShip. SpikeShip is a fast method for the unsupervised discovery of spiking patterns in high-dimensional data, and provides a principled measure of dissimilarity of multi-neuron spiking sequences. SpikeShip can be effectively computed for high-dimensional neuronal ensembles, has a low (linear) computational cost that has the same order as the spike count, and is sensitive to higher-order correlations. We apply SpikeShip to high-dimensional neural data to study the encoding of behavioral states and visual information by temporal spiking sequences. SpikeShip opens new avenues for studying neural coding and memory consolidation by rapid and unsupervised detection of temporal spiking patterns in high-dimensional neural ensembles.
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