Open Access

Boris Sotomayor-Gomez, Francesco P. Battaglia, Martin Vinck

• 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-P urpura 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.